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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Computational Mechanics Boundary Values - Project 05\n",
"\n",
"![6-string guitar diagram](../images/guitar.png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this final project, we will consider all six strings of a guitar and the deflection of the neck of the guitar. Here are the inputs for each of the strings, all L=0.64 m:\n",
"\n",
"|string|density (g/m)|tension (kg)|\n",
"|---|---|---|\n",
"|E|0.401|7.28|\n",
"|B|0.708|7.22|\n",
"|G|1.140|7.32|\n",
"|D|2.333|8.41|\n",
"|A|4.466|9.03|\n",
"|E|6.790|7.71|"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. The neck of the guitar can be considered a cantilever beam with an applied moment, shown above. At the tip we have a moment equal to the sum of the (tensions in the strings) $\\times$ (bridge height). Here we will consider it as $h=4~mm$. \n",
"\n",
"a. Use a finite difference approximation to determine the deflection of the guitar's bridge if the Young's modulus is E=10 GPa and it is a rectangular cross-section $2\\times4~cm^2$ and $I=\\frac{4\\cdot2^3}{12}~cm^4.$\n",
"\n",
"b. Demonstrate that your finite difference solution has converged. _e.g. decrease the step size $h$ and show the solution converges to a final value._"
]
},
{
"cell_type": "code",
"execution_count": 259,
"metadata": {},
"outputs": [],
"source": [
"#Constants\n",
"dE = 0.000401 #kg/m\n",
"dB = 0.000708 #kg/m\n",
"dG = 0.001140 #kg/m\n",
"dD = 0.002333 #kg/m\n",
"dA = 0.004466 #kg/m\n",
"dE2 = 0.006790 #kg/m\n",
"tE = 7.28 #kg\n",
"tB = 7.22 #kg\n",
"tG = 7.32 #kg\n",
"tD = 8.41 #kg\n",
"tA = 9.03 #kg\n",
"tE2 = 7.71 #kg"
]
},
{
"cell_type": "code",
"execution_count": 260,
"metadata": {},
"outputs": [],
"source": [
"#Problem 1a\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"E=10e9 #Pascals\n",
"height=0.04 #meters\n",
"I = (0.04*0.02**3)/12\n",
"L = 0.64 #meters\n",
"g = 9.81 #m/s^2\n",
"h = 0.004 #meters\n",
"M = (tE+tB+tG+tD+tA+tE2)*g*h #kg*m\n",
"x = np.linspace(0,L,100)\n",
"#Deflection equation generated based on beam definition\n",
"w = (M*L**2/(2*E*I))*(x/L)**2"
]
},
{
"cell_type": "code",
"execution_count": 261,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[ 7. -4. 1. 0. 0. 0. 0. 0. 0.]\n",
" [-4. 6. -4. 1. 0. 0. 0. 0. 0.]\n",
" [ 1. -4. 6. -4. 1. 0. 0. 0. 0.]\n",
" [ 0. 1. -4. 6. -4. 1. 0. 0. 0.]\n",
" [ 0. 0. 1. -4. 6. -4. 1. 0. 0.]\n",
" [ 0. 0. 0. 1. -4. 6. -4. 1. 0.]\n",
" [ 0. 0. 0. 0. 1. -4. 6. -4. 1.]\n",
" [ 0. 0. 0. 0. 0. 1. -4. 5. -2.]\n",
" [ 0. 0. 0. 0. 0. 0. 2. -4. 2.]]\n",
"[-0.0000000e+00 -0.0000000e+00 -0.0000000e+00 -0.0000000e+00\n",
" -0.0000000e+00 -0.0000000e+00 -0.0000000e+00 -2.8310059e-05\n",
" 5.6620118e-05]\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"h_1=L/10\n",
"Na=9\n",
"A_1=np.diag(np.ones(Na)*6)\\\n",
"+np.diag(np.ones(Na-1)*-4,-1)\\\n",
"+np.diag(np.ones(Na-1)*-4,1)\\\n",
"+np.diag(np.ones(Na-2),-2)\\\n",
"+np.diag(np.ones(Na-2),2)\n",
"A_1[0,0]+=1\n",
"A_1[-1,-1]+=1\n",
"A_1[7]= [0,0,0,0,0,1,-4,5,-2]\n",
"A_1[8] = [0,0,0,0,0,0,2,-4,2]\n",
"b_1=-np.zeros(Na)\n",
"b_1[7]=-h_1**2*M/(E*I)\n",
"b_1[8]=2*h_1**2*M/(E*I)\n",
"w_1=np.linalg.solve(A_1,b_1)\n",
"xnum=np.arange(0,L+h_1/2,h_1)\n",
"plt.plot(x,w*1000,label='Analytical Data')\n",
"plt.plot(xnum[1:-1],w_1*1000,'s',label='Finite Difference 10 Segments')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left')\n",
"plt.xlabel('Neck Length (m)')\n",
"plt.ylabel('Deflection (mm)')\n",
"plt.title('Guitar Neck Deflection vs Neck Length')\n",
"print(A_1)\n",
"print(b_1)"
]
},
{
"cell_type": "code",
"execution_count": 262,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Guitar Neck Deflection vs Neck Length')"
]
},
"execution_count": 262,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"h_2=L/30\n",
"Nb=29\n",
"A_2=np.diag(np.ones(Nb)*6)\\\n",
"+np.diag(np.ones(Nb-1)*-4,-1)\\\n",
"+np.diag(np.ones(Nb-1)*-4,1)\\\n",
"+np.diag(np.ones(Nb-2),-2)\\\n",
"+np.diag(np.ones(Nb-2),2)\n",
"A_2[0,0]+=1\n",
"A_2[-1,-1]+=1\n",
"A_2[27]= [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-4,5,-2]\n",
"A_2[28] = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-4,2]\n",
"b_2=-np.zeros(Nb)\n",
"b_2[27]=-h_2**2*M/(E*I)\n",
"b_2[28]=2*h_2**2*M/(E*I)\n",
"w_2=np.linalg.solve(A_2,b_2)\n",
"xnum2=np.arange(0,L+h_2/2,h_2)\n",
"plt.plot(x,w*1000,label='Analytical Data')\n",
"plt.plot(xnum2[1:-1],w_2*1000,'s',label='Finite Difference 30 Segments')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left')\n",
"plt.xlabel('Neck Length (m)')\n",
"plt.ylabel('Deflection (mm)')\n",
"plt.title('Guitar Neck Deflection vs Neck Length')"
]
},
{
"cell_type": "code",
"execution_count": 263,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Guitar Neck Deflection vs Neck Length')"
]
},
"execution_count": 263,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"h_3=L/6\n",
"Nc=5\n",
"A_3=np.diag(np.ones(Nc)*6)\\\n",
"+np.diag(np.ones(Nc-1)*-4,-1)\\\n",
"+np.diag(np.ones(Nc-1)*-4,1)\\\n",
"+np.diag(np.ones(Nc-2),-2)\\\n",
"+np.diag(np.ones(Nc-2),2)\n",
"A_3[0,0]+=1\n",
"A_3[-1,-1]+=1\n",
"A_3[3]= [0,1,-4,5,-2]\n",
"A_3[4] = [0,0,2,-4,2]\n",
"b_3=-np.zeros(Nc)\n",
"b_3[3]=-h_3**2*M/(E*I)\n",
"b_3[4]=2*h_3**2*M/(E*I)\n",
"w_3=np.linalg.solve(A_3,b_3)\n",
"xnum3=np.arange(0,L+h_3/2,h_3)\n",
"plt.plot(x,w*1000,label='Analytical Data')\n",
"plt.plot(xnum3[1:-1],w_3*1000,'s',label='Finite Difference 6 Segments')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left')\n",
"plt.xlabel('Neck Length (m)')\n",
"plt.ylabel('Deflection (mm)')\n",
"plt.title('Guitar Neck Deflection vs Neck Length')"
]
},
{
"cell_type": "code",
"execution_count": 264,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Guitar Neck Deflection vs Neck Length')"
]
},
"execution_count": 264,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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4E7iBfz8l2oGjEhGUiEiFNFhaRBIgaDJ0NdDL3bclMhgRkRrTYGkRqaGgy3EsI/RgRBEREZEGJWjLUBmwyMz+ycFjhjS1XkRERFJa0GRoNnrAoogk0cJPtzMk2UGISIMUKBly98cTHYiIyEFiZo7FTYQ0WFpEDkHQJ1B/H7gV6BY+xwgtL9YygbGJSDqLN3NMg6VFpBYF7Sa7FxgFfBReYFVERESkQQg6m2wdsFSJkIiIiDQ0QVuGfgm8bGbzOHg22T0JiUpE0trKz3fSJ9lBiEjaCJoM3Q7sApoCjRMXjoikpZjB0kqERKQuBU2G2rj7aQmNRETSl5bZEJEkCpoMzTWz09z97wmNRkQklmaOiUiCBR1AfSnwqpntMbMSM9tpZiWJDExERESkLgR96GKLmlRuZsOB+4BM4CF3vyPmeCvgSSAnHMtd7v5oTa4lIqlp+aYS+iU7iDS1cOHC9llZWQ8BAwj+x7FIqikHlpaWll40ZMiQCvvk4yZDZtbd3dfGOW5AF3dfX8GxTOBPwDBgPfC+mc1x98KoYpcChe5+lpm1A1aY2VPuvq+qOxORFBUzWFqJUPJkZWU91LFjx37t2rXbnpGRoUenSINUXl5uW7duzdu8efNDwNkVlanqL4E7zew5M7vAzPqbWXszyzGz75rZrcCbVP5/WQGwyt3XhJObmcDImDIOtAgnVc2BL4HSgPcnIqlIg6XrkwHt2rUrUSIkDVlGRoa3a9eumFALaIXitgy5+7lmlgeMBX4GdAJ2A8uBl4Hb3f3rSk7vQuhhjRHrgeNjyvwRmANsBFoA57l7eWxFZjYeGA+Qk5MTL2QRSWUaLF3XMpQISToIf59X2gBUZR+xuxe6+w3uPtTd+7r7se4+xt2fjJMIQWj9sm9UF7N9OrAI6AwcA/zRzL6x3pm7T3f3fHfPb9euXVUhi4hICnniiSdam9mQDz/8sOmh1HPOOed0f/TRRw+PV2by5Mkdo7ePPfbY3Jpc6+qrr+580003dahof/v27Qfm5ubmdevWbcBpp53Wc+HChVXe15QpU45Yu3Zto5rEIocukQPm1gNHRm13JdQCFG0cMMtDVgGfADX6xhSR+m/+yq3JDkHqoZkzZ7YZPHjwrhkzZrRJ9LWmTJnSKXr7ww8/LKrta0yYMOHzoqKiwk8//XTpueee++Xpp5/ed+PGjXF7Yp588sm2n332mZKhJElkMvQ+0NvMephZY+B8Ql1i0T4DvgdgZh2AvsCaBMYkInXpzt5wS6sDr+/8uVeyI5J6pri4OGPBggXNH3300bXPP//8gVadF198sUVBQUHf4cOHH9WjR4/+Z599do/y8tAoimuvvbbTgAED+vXu3bv/j3/8426R/RF/+9vfWgwbNqxnZPv5559vedppp/WcOHFil71792bk5ubmnX322T0AmjVrdmyk3I033tihT58+eX379s2bOHFiF4C777677YABA/r17ds37/TTT++5c+fOav3evPjii7efdNJJxQ8//HCbymJ/9NFHD1+6dGmzCy644Kjc3Ny8Xbt2WVX3KLUr6EMXq83dS81sEvAaoan1j7j7MjObED4+DbgVeMzMPiLUrXa9u29LVEwiUsc0WDplXPfs4iNXbt7ZrDbr7NOxxe47Rw9aF6/MU0891Xro0KHFAwcO3Nu6deuyN954o9mJJ564G2D58uXZixYtWtO9e/f9Q4YMyf3HP/7R/PTTT9913XXXbbnrrrs2AfzgBz/oMXPmzFZjxow5MODsrLPO2nnllVfmbNy4Matz586ljzzyyBEXXnjhtjFjxhQ/9thj7YuKigpj43jmmWdavvTSS4cvXLiwqEWLFuWff/55JsDYsWO3X3PNNdsALr/88s5Tpkxpe8MNN1TjGxuOPfbY3UVFRU0BKop93Lhx26dOndr+rrvuWved73xnd2Xlou9RalfgZMjMugDdos9x9/nxznH3lwkNtI7eNy3q642AlvkQSUcaLC3AM8880+aKK67YAnDOOed8OWPGjDaRZOjoo4/+qmfPnvsB+vfvv3v16tWNAV555ZUW99xzT8evv/46Y8eOHVl5eXl7gAPfUBkZGfzoRz/64sEHH2xz6aWXfvHBBx80nzVr1ifx4vjHP/7R8ic/+cm2Fi1alAN06NChDGDhwoXZN910U5edO3dmfvXVV5knn3xytb9x3f89XLaq2KtbTmpHoGTIzH4HnAcUAmXh3Q7ETYZERCQ1VNWCkwibN2/OfOedd1quXLkye9KkSZSVlZmZ+dSpU9cDNGnS5EAWkZmZSWlpqe3evduuueaabu+++25hr1699l999dWdv/766290XV1yySVfnHnmmb2aNm3qZ5111vZGjeIPx3F3Qk95Odj48eN7PPvss6u+9a1v7ZkyZcoR8+bNq/ZDiBctWtRsyJAhu4PGHrSc1J6gb+4PgL7ufoa7nxV+VfjgIhFJUzHjg7ilVbIjknpuxowZh48aNeqLjRs3frRhw4aPNm/evKRr1677/v73vzev7Jzdu3dnAHTs2LG0uLg444UXXqhw9lj37t33d+jQYf/dd9/d6eKLLz4w/CIrK8v37t37jaxn+PDhJTNmzGgbGRMU6SbbvXt3Rk5Ozv69e/fazJkzqz3A+7HHHmv9r3/9q9XPfvazL+PF3rx587Li4uID1wxyj1J7giZDawCNcheRylVnfJAI8Ne//vWIUaNGbY/eN3LkyO3xZpW1bdu2bOzYsVvz8vL6jxgxotegQYO+qqzs+eef/0WnTp32DRky5MBjYMaOHbu1X79+BwZQR4wePbpkxIgRO4455ph+ubm5ebfeemtHgMmTJ28sKCjod9JJJ/Xp3bt3vMfJHDBt2rQOkan1Tz311BGvvfbais6dO5fGi/2CCy7Ydtlll3XLzc3Na9q0aXnQe5TaYdF9mZUWMnsOGAT8P2BvZL+7X5640CqWn5/vCxYsqOvLikhVqtMSdFh7uO7jxMUi32BmC909P3rf4sWL1w4aNKjBTlq54IILco499tjdV111VYO9Rwlu8eLFbQcNGtS9omNBB1DP4ZvT4kVEgtFgaalj/fv375ednV3+wAMP1PlYKEk9QVetfzz8rKA+4V0r3H1/4sISkVSye18ptTonW+QQLVu2bHmyY5DUEXQ22VDgcWAtoecBHWlmP61qar2INEAxq84DSoREJKUF7Sa7GzjN3VcAmFkf4GlgSKICE5F6qroDpfUwRRGp54ImQ40iiRCAu680M80uE5GDaWyQiKSgoMnQAjN7GJgR3h4LLExMSCIiIiJ1J+hzhi4BlgGXA1cQehL1hEQFJSIi6SEzM3NIbm5uXuS1YsWKxvPnz2924YUXHlnVuccee2wuwIoVKxpPmzat2g9EjFy7V69e/fv27Zt3yy23dCgrCy2yEB3Dnj177IQTTuiTm5ub9+CDDx7+6quvNu/Vq1f/yKKq1b1uXbn99tvbd+/efUCvXr36T5gwoWtk/69+9auOOTk5A7p37z7gueeea1nRuU8//XSrfv365fXt2zevZ8+e/e+88862dRd5MJMnT+5YW3UFnU22F7gn/BKRdFHBYGlJU7/rMYg9X37zd0Z2m1Ku/2RxTatt0qRJeezCqX379t0XWbA0ng8//LAI4OOPP27yl7/8pc2ECRO+rOm1N2zYkHXuueceVVxcnPmHP/xh43e+853dkRjeeuutZvv377dI2TFjxuRcdtllm6+44oovglynvLwcdyczM7M64R2SF154ocVLL73Uevny5cuys7N9w4YNWQALFy5sOmvWrDYrVqxY9umnnzYaNmxYn5EjRy7Nyvr3R7t371674oorur399tvLe/bsuX/Pnj22cuXKxnUWfEBTpkzpdMcdd2yujbritgyZ2TPhfz8ysyWxr9oIQETqMa06LxEVJULx9h+CF198scUpp5zSC+Dqq6/ufO6553YvKCjo27Vr16Nvu+22A99ozZo1Oxbghhtu6LJgwYLmubm5ef/1X//VvrS0lF/84hddBwwY0K9Pnz55QVo1unTpUvrQQw+tffTRR9uXl5cfiGHDhg1Z48aN61FUVJSdm5ubd+edd7Z96aWX2vz+97/vHHmK9W9+85sOkWtdddVVnSHUWnXUUUf1/8lPfpLTv3//vNWrVzeeNWtWy2OOOSY3Ly+v34gRI44qLi7OCF/76KuuuqpzXl5evz59+uR9+OGHTQGKi4szRo8e3b1Pnz55ffr0yXvsscdaA1RWT7SpU6e2++Uvf7kpOzvbI/cH8Oyzz7YeNWrUl9nZ2Z6bm7uvW7due19//fXDos/dsWNHRmlpqXXo0KEUIDs72wcNGrQXYOPGjVmnn356zwEDBvQbMGBAv7///e+HRfafcMIJvfPy8vqNGTOmW+fOnY/etGlT1ooVKxr36NGj/3nnndetd+/e/c8+++wes2fPbjF48ODcbt26DfjnP//ZDKCkpCTj3HPP7T5gwIB+/fr1y3vyySdbA0yZMuWI0047redJJ53Uu1u3bgMiLVwTJ07ssnfv3ozc3Ny8s88+u0dJSUnG0KFDe/Xt2zevd+/e/R988MFqLWFSVTfZFeF/vw+cVcFLRNLVLcUHv/REaamByC+03NzcvGHDhvWsqMyqVauazps3b+X777+//K677uocu7bY7bffviE/P39XUVFR4c0337zl3nvvbduqVauypUuXLl+8ePHyxx9/vF1RUVGVLRt5eXn7ysvLibSiQCiJuP/++z+N1H/ddddtO/XUU3fcdttt6+fMmfPJrFmzWq5atarpkiVLli9fvrxw0aJFzV555ZXmAGvXrm06bty4L5YvX17YokWL8v/5n//pNH/+/JWFhYXLBw8evPvWW2/tELlO27ZtSwsLC5f/7Gc/23rHHXd0AJg8eXKnli1blq1cubJw5cqVhWeeeebOTZs2ZcWrJ2LNmjVN582b12LgwIG5xx13XN958+Y1A9iwYUPjI488cl+kXOfOnfetW7fuoPemQ4cOZcOGDduRk5Mz8KyzzuoxderUNpHuw1/84hdHXn311Z8vXbp0+fPPP796woQJ3cOxdj755JN3FhYWLh81atT2TZs2Hahz3bp1Ta+55potRUVFy1avXt30qaeeOmLBggVFt99++/rbb7+9E8Cvf/3rTqecckrJ0qVLl//rX/9aceONN3YtKSnJACgsLGw2e/bsNcuXL182Z86cw1etWtXo/vvv3xBp2Yt8Dh07dty/YsWKwo8//njZqFGjSqr6vKPFzejdfVP4y4nufn30sfBK9td/8ywREZFgKuomi3XaaaftyM7O9uzs7NI2bdrsX79+fVbPnj0rffDv3LlzWxYVFTWbM2fO4QA7d+7MLCwsbJqbm7uvsnMigixRFe3VV19tOX/+/JZ5eXl5EFpktaioqOlRRx21r1OnTvu+973vfQXw+uuvH7Z69eqmBQUFuQD79++3IUOG7IrUM2bMmO0ABQUFuyNxz58/v+XMmTPXRMq0a9eu7Omnn24Vr56IsrIy2759e+aiRYuK5s2b12zMmDE9161b91FF92dm39j5l7/85dP33ntvyyuvvNJiypQpHefOndvyueeeW/vmm2+2/Pjjj7Mj5Xbt2pW5ffv2jPfee6/57NmzV0FonbeWLVuWRcp06dJlb0FBwR6APn367Pnud79bkpGRweDBg3ffdtttncPvT8vXXnut9ZQpUzpCqKtu1apVjQFOPPHEkiOOOKIMoFevXl+vXr26Sa9evQ76/AcPHrznhhtuOPKSSy7pMnLkyOLhw4d/4z2JJ2jz5jC+mfiMqGCfiKQqjQ+SeqpJkyYHfllnZmZSWload9Cyu9vdd9/92TnnnFOt1oHCwsLGmZmZdOnSpXTx4mDDoNydK6+8ctN111130PpnK1asaNysWbPy6HInnnhiyQsvvPBJRfU0bdrUAbKysjxyf+6O2cG3WlU9ER07dtw3evToHRkZGZxyyim7MzIyfPPmzVldu3Y9qCVo48aNjbt27VphYllQULCnoKBgz/jx47/s1avX0cBad2fBggXLmzdvflACFS+JbNy48YGDGRkZB+41MzOTsrKyA/f67LPProp0x0W88cYbh0Wfn5mZ6fv37//G5z9w4MC9H3zwQeFzz8ATlu0AABUISURBVD3X6oYbbugyd+7ckrvuumtTbLnKVDVm6BIz+wjIjRkv9AnwUdCLiEgKUCIkKapVq1Zlu3btOjA6ediwYcVTp05tF+lOW7JkSZNIl0tlNm7cmHXxxRd3Gzdu3JaMjKATrWHEiBElM2bMaBsZt/PJJ580iu5mixg6dOhXCxYsaL506dImADt37sxYsmRJk3h1Dx06tOSee+45MEZq69atmUHrOeuss3bMnTu3BYTuf//+/RkdO3YsPeecc3bMmjWrzZ49e6yoqKjx2rVrmw4dOvSr6HOLi4szXnzxxRaR7XfffTe7c+fO+yDUSvO73/3uQExvvfVWNkBBQcGuGTNmtIHQmKaSkpJqjRY/5ZRTSu6+++4O5eWh/PHNN9/MruIUsrKyPPIZr127tlGLFi3KJ06c+OWVV175+aJFi6r1YPyqWob+DLwC/BaYHLV/p7tXa9S+iDQgGiydfrLblFY6myzJCgoK9mRlZXnfvn3zxowZs+3GG2/csnbt2iZHH310P3e3Nm3a7H/55ZdXx54XGa9UWlpqmZmZft55531x8803f16da48aNapk2bJlTY877rhcgGbNmpU/9dRTn2RlZR3UVNK5c+fSBx54YO35559/1L59+wzg5ptv3jBw4MC9FdUL8Nvf/nbTuHHjcnr37t0/IyPDf/3rX2/86U9/uiNIPZdffvm28847r3vv3r37N2rUqHz69OmfZGRkkJ+f//UPfvCDL/v06dM/MzOTe+6559PomWQQmv125513dpg0aVK3pk2bljdr1qz84Ycf/gRg+vTp6y666KKcPn365JWVldnxxx+/84QTTvjsjjvu2Dh69Oij8vLyDv/Wt761q127dvtbt25dVlUSGnHHHXdsHD9+fE5ubm6eu1vXrl33/vOf/1wV75yxY8du7devX96AAQN2//SnP/3iV7/6VdeMjAyysrL8/vvv/zTIdSMsSP+omf0HsMzdd4a3WwB57v5udS5WG/Lz833BggV1fVmRhu+WVnGO6cnSqc7MFrp7fvS+xYsXrx00aNC2ys4RCWrPnj2WlZXljRo1Yu7cuYdNmjSpW1Vjwera4sWL2w4aNKh7RceCjhmaCgyO2v6qgn3fYGbDgfuATOAhd7+jgjJDgXuBRsA2dz85YEwiUlMaHyQitWjVqlWNf/SjH/UsLy+nUaNG/sADD6xNdkzVETQZMo9qQnL3cjOLe66ZZQJ/IjT4ej3wvpnNcffCqDKtgfuB4e7+mZmp7V2kLigREpFadPTRR+9dvnx5vWoJqo6go8TWmNnlZtYo/LoCWFPFOQXAKndf4+77gJnAyJgyY4BZ7v4ZgLvrf2iR+kbjg0SkgQvaMjQBmALcCDjw/4DxVZzTBVgXtb0eOD6mTB+gkZm9DrQA7nP3J2IrMrPxkevl5OQEDFlEakTjg9JJeXl5uWVkZFTv4ToiKaa8vNyA8sqOB12bbAtwfjWvXdFzIGJ/4LKAIcD3gGzgbTN7x91Xxlx/OjAdQgOoqxmHiIhUbOnWrVvz2rVrV6yESBqq8vJy27p1aytgaWVlAiVDZtaH0IDpDu4+wMwGAme7+21xTlsPRK863BXYWEGZbe7+FfCVmc0HBgErEZHaocHSUonS0tKLNm/e/NDmzZsHEHzYhEiqKQeWlpaWXlRZgaDdZA8C1wEPALj7EjP7MxAvGXof6G1mPYANhFqWxsSU+Rvwx/Bg7MaEutH+EDAmEQlCi61KJYYMGbIFODvZcYgkW9BkqJm7vxfzWPC4D9py91IzmwS8Rmhq/SPuvszMJoSPT3P35Wb2KrCEUOb2kLtX2owlIrVM44NERAInQ9vMrCfhMT9mNhqocs0Pd38ZeDlm37SY7TuBOwPGISIiIlKrgiZDlxIawJxrZhuAT4CfJCwqEakZjQ8SEam2oLPJ1gCnmtlhQEZkWQ4RqWeUCImIVFtVT5G+upL9ALj7PQmISUTqggZLi4gAVbcMtaiTKEQk8TRYWkSkQlUlQ83c/XozO9fd/1onEYlIMBofJCJSK6p6yNYZZtYI+FVdBCMi1aBESESkVlTVMvQqsA04zMxKCC2x4ZF/3b1lguMTkdqg8UEiIpWKmwy5+3XAdWb2N3ePXXFeROorjQ8SEQks6NT6kWbWDejt7nPNLBvI0hR7kTqi8UEiIgkTaGE+M7sYeJbw2mSEFl2dnaigRCSGEiERkYQJukrxpcC3gRIAd/8Y0CAEkfpI44NERKol6HIce919X+Rhi+FV5j1hUYmks+p2iWl8kIjIIQnaMjTPzH4NZJvZMOCvwAuJC0skjalLTESkTgVNhiYDW4GPgF8QWon+xkQFJSIiIlJXgs4mKzez2cBsd9+a4JhEJCiNDxIROWRVLdRqwM3AJEIPWjQzKwP+193/uw7iE2nYND5IRCTpquomu5LQLLLj3P0Id28DHA9828yuSnh0Ig2dxgeJiCRdVcnQBcCP3f2TyA53XwP8JHxMROqKusRERBKiqjFDjdx9W+xOd98aXsBVRBJFXWIiInWiqmRoXw2PAWBmw4H7gEzgIXe/o5JyxwHvAOe5+7NV1SuSkrSkhohIvVRVMjQovFp9LAOaxjvRzDKBPwHDgPXA+2Y2x90LKyj3O+C1wFGLpCIlQiIi9VJVq9ZnHkLdBcCq8BgjzGwmMBIojCl3GfAccNwhXEukYdH4IBGROhN0OY6a6AKsi9peT2gm2gFm1gX4IfBd4iRDZjYeGA+Qk5NT64GK1DpNmRcRSRlBn0BdE1bBvtj1zO4Frnf3sngVuft0d8939/x27drVWoAiCaMuMRGRlJHIlqH1wJFR212BjTFl8oGZ4QVg2wJnmFmpu89OYFwiIiIiByQyGXof6G1mPYANwPnAmOgC7t4j8rWZPQa8qERIUs6hzhLT+CARkaRKWDLk7qVmNonQLLFM4BF3X2ZmE8LHpyXq2iJ1qrqJkMYHiYjUK4lsGcLdXya0wn30vgqTIHe/MJGxiIiIiFQkkQOoRSSWusREROqdhLYMiTQ4mjIvItLgqGVIpDo0ZV5EpMFRMiSSKOoSExFJCeomE6lITabLq0tMRCQlqWVIpCLqDhMRSRtKhkRERCStqZtM5FCfIA0aHyQiksKUDIlobJCISFpTN5mIiIikNbUMSXrRoqoiIhJDyZCkF3WJiYhIDHWTiYiISFpTy5A0XOoSExGRAJQMScOlLjEREQlAyZA0DLXxrCAREUlLGjMkDYMemigiIjWkliFJT+oSExGRMCVDknrUJSYiIrUood1kZjbczFaY2Sozm1zB8bFmtiT8esvMBiUyHmkg1CUmIiK1KGEtQ2aWCfwJGAasB943sznuXhhV7BPgZHffbmYjgOnA8YmKSVJQbbQCqUtMRETiSGTLUAGwyt3XuPs+YCYwMrqAu7/l7tvDm+8AXRMYj6QitQKJiEiCJXLMUBdgXdT2euK3+vwceKWiA2Y2HhgPkJOTU1vxSUOkViAREammRCZDVsE+r7Cg2SmEkqETKzru7tMJdaGRn59fYR3SAGhgtIiIJEEik6H1wJFR212BjbGFzGwg8BAwwt2/SGA8Ut+pS0xERJIgkcnQ+0BvM+sBbADOB8ZEFzCzHGAW8J/uvjKBsUh9o4HRIiJSTyQsGXL3UjObBLwGZAKPuPsyM5sQPj4NuAk4ArjfzABK3T0/UTFJPaJWIBERqSfMPbWG4OTn5/uCBQuSHYZUh1qBRJLOzBbqj02RimltMkk8DYoWEZF6TMtxSO1KxIwwdYmJiEgCKRmS2lUbiZC6xEREpA4pGZKaUyuQiIg0AEqGpObUCiQiIg2AkiEJRq1AIiLSQCkZkmDUCiQiIg2UkiH5JrUCiYhIGlEylM4SuTCqWoFERCRF6KGL6SxRiZBagUREJIWoZShdqBVIRESkQkqGGqJEJj6x1AokIiIpTslQqqvLxAfUCiQiIg2OkqFUUteJTyy1AomISAOkZKi+Smbic1h7uO7j5FxbRESkjikZqg+S3eKjri8REUljSobqWrITn1jq+hIRkTSnZCiR6mPio+4vERGRgygZqkp9S2iCUuIjIiISSEKTITMbDtwHZAIPufsdMcctfPwMYDdwobt/kMiYgDgJjgGe8MvXOiU+IiIiNZawZMjMMoE/AcOA9cD7ZjbH3Qujio0AeodfxwNTw/8mVqUtPSmQCCnxERERqVWJbBkqAFa5+xoAM5sJjASik6GRwBPu7sA7ZtbazDq5+6baDmbeyq3c+mIh5e78X21XnihKfERERBIukclQF2Bd1PZ6vtnqU1GZLsBByZCZjQfGA+Tk5NQomOZNsujboQVmwM4aVZFYSnxERESSIpHJkFWwL7YfKkgZ3H06MB0gPz+/Rn1ZQ7odzpBuh4c2bqlJDbVIiY+IiEi9kchkaD1wZNR2V2BjDcqkNiU+IiIi9Voik6H3gd5m1gPYAJwPjIkpMweYFB5PdDxQnIjxQt9wWPvqzSZTQiMiItJgJSwZcvdSM5sEvEZoav0j7r7MzCaEj08DXiY0rX4Voan14xIVz0GU2IiIiEhYQp8z5O4vE0p4ovdNi/ragUsTGYOIiIhIPBnJDkBEREQkmZQMiYiISFpTMiQiIiJpTcmQiIiIpDULjWFOHWa2Ffi0hqe3BbbVYjh1TfEnTyrHDqkdfyrHDvUn/m7u3i7ZQYjURymXDB0KM1vg7vnJjqOmFH/ypHLskNrxp3LskPrxi6QDdZOJiIhIWlMyJCIiImkt3ZKh6ckO4BAp/uRJ5dghteNP5dgh9eMXafDSasyQiIiISKx0axkSEREROYiSIREREUlrDTIZMrPhZrbCzFaZ2eQKjpuZTQkfX2Jmg5MRZ2UCxJ9rZm+b2V4zuzYZMVYmQOxjw+/5EjN7y8wGJSPOygSIf2Q49kVmtsDMTkxGnBWpKvaocseZWZmZja7L+KoS4L0fambF4fd+kZndlIw4KxLkvQ/Hv8jMlpnZvLqOUUTicPcG9QIygdXAUUBjYDGQF1PmDOAVwID/AN5NdtzVjL89cBxwO3BtsmOuZuwnAIeHvx6Rgu99c/491m4gUJTsuIPGHlXu/4CXgdHJjrua7/1Q4MVkx1rD2FsDhUBOeLt9suPWSy+9/v1qiC1DBcAqd1/j7vuAmcDImDIjgSc85B2gtZl1qutAK1Fl/O6+xd3fB/YnI8A4gsT+lrtvD2++A3St4xjjCRL/LnePzDo4DKgvMxCCfN8DXAY8B2ypy+ACCBp/fRQk9jHALHf/DEI/w3Uco4jE0RCToS7Auqjt9eF91S2TLPU5tqpUN/afE2qhqy8CxW9mPzSzIuAl4Gd1FFtVqozdzLoAPwSm1WFcQQX93vmWmS02s1fMrH/dhFalILH3AQ43s9fNbKGZXVBn0YlIlbKSHUACWAX7Yv96D1ImWepzbFUJHLuZnUIoGao3Y24IGL+7Pw88b2bfAW4FTk10YAEEif1e4Hp3LzOrqHhSBYn/A0Lra+0yszOA2UDvhEdWtSCxZwFDgO8B2cDbZvaOu69MdHAiUrWGmAytB46M2u4KbKxBmWSpz7FVJVDsZjYQeAgY4e5f1FFsQVTrvXf3+WbW08zaunuyF+IMEns+MDOcCLUFzjCzUnefXTchxlVl/O5eEvX1y2Z2fwq99+uBbe7+FfCVmc0HBgFKhkTqgYbYTfY+0NvMephZY+B8YE5MmTnABeFZZf8BFLv7proOtBJB4q+vqozdzHKAWcB/1sO/ioPE38vC2UR4FmJjoD4kdFXG7u493L27u3cHngUm1pNECIK99x2j3vsCQv9/pcR7D/wNOMnMssysGXA8sLyO4xSRSjS4liF3LzWzScBrhGZ5POLuy8xsQvj4NEIzac4AVgG7gXHJijdWkPjNrCOwAGgJlJvZlYRmr5RUWnEdCPje3wQcAdwf/r1W6vVkRe+A8Z9DKJHeD+wBzosaUJ00AWOvtwLGPxq4xMxKCb3356fKe+/uy83sVWAJUA485O5Lkxe1iETTchwiIiKS1hpiN5mIiIhIYEqGREREJK0pGRIREZG0pmRIRERE0pqSIREREUlrSoYkZZiZm9ndUdvXmtktNaxrV22UORRmdqGZdY7aXmtmbQOcd6yZPVTNa800s/rwtGYRkXpHyZCkkr3AqCAJQ4q4EOhcVaEK/Br432qeMxX4ZQ2uJSLS4CkZklRSCkwHroo9YGbtzOw5M3s//Pp2eH9zM3vUzD4ysyVmdk7MeW3N7G0zOzNIAHGuc4uZPRJeiHONmV0edc5vzKzIzP5hZk+HW7RGE1oe4ykzW2Rm2eHil5nZB+F4cyu4fgtgoLsvjrru42b293DL0igz+334/FfNrFH41H8Bp5pZg3vQqojIoVIyJKnmT8BYM2sVs/8+4A/ufhyhp0RHupF+Q2i5laPdfSDwf5ETzKwDoZXnb3L3lwJev7LrAOQCpwMFwM1m1sjM8sPljgVGEUqAcPdnCT1FfKy7H+Pue8J1bHP3wYRacq6t4Pr5QOyTi3sCZwIjgSeBf7r70YSe0nxm+HrlhJ64PijgfYqIpA39lSgpxd1LzOwJ4HJCv+wjTgXy7N+rsbcMt6KcSmitqMj528NfNgL+H3Cpu8+rRgiVXQfgJXffC+w1sy1AB+BE4G+RZMfMXqii/lnhfxcSSp5idQK2xux7xd33m9lHhJaDeDW8/yOge1S5LYS65RZWEYOISFpRMiSp6F7gA+DRqH0ZwLeiWlgACC/sWdGaM6WEkoLTgeokQ5VdB0JjmiLKCP18GdUTqSNyfqw9QNOKznH3cjPbH7VeV3lMHU05OIEUERHUTSYpyN2/BJ4Bfh61++/ApMiGmR1Tyf7DI9UAPwNyzWxyNS5f2XUq8wZwlpk1NbPmhLutwnYCLSo+rVLLgV7VPCeiD7CshueKiDRYSoYkVd0NRM8quxzIDw+SLgQmhPffBhxuZkvNbDFwSuQEdy8j1IV2iplNrOAazcxsfdTr6jjXqZC7vw/MARYT6gJbABSHDz8GTIsZQB2XuxcBraK65gIJj4/a4+6bqnOeiEg60Kr1IglmZs3dfZeZNQPmA+Pd/YNDqO8qYKe7B37WUPicEnd/uKbXFRFpqNQyJJJ4081sEaFxTs8dSiIUNpWDxycFsQN4/BCvKyLSIKllSERERNKaWoZEREQkrSkZEhERkbSmZEhERETSmpIhERERSWtKhkRERCSt/X+c5aQiIIPW/QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"h_4=L/60\n",
"Nd=59\n",
"A_4=np.diag(np.ones(Nd)*6)\\\n",
"+np.diag(np.ones(Nd-1)*-4,-1)\\\n",
"+np.diag(np.ones(Nd-1)*-4,1)\\\n",
"+np.diag(np.ones(Nd-2),-2)\\\n",
"+np.diag(np.ones(Nd-2),2)\n",
"A_4[0,0]+=1\n",
"A_4[-1,-1]+=1\n",
"A_4[57]= [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-4,5,-2]\n",
"A_4[58] = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-4,2]\n",
"b_4=-np.zeros(Nd)\n",
"b_4[57]=-h_4**2*M/(E*I)\n",
"b_4[58]=2*h_4**2*M/(E*I)\n",
"w_4=np.linalg.solve(A_4,b_4)\n",
"xnum4=np.arange(0,L+h_4/2,h_4)\n",
"plt.plot(x,w*1000,label='Analytical Data')\n",
"plt.plot(xnum4[1:-1],w_4*1000,'s',label='Finite Difference 60 Segments')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left')\n",
"plt.xlabel('Neck Length (m)')\n",
"plt.ylabel('Deflection (mm)')\n",
"plt.title('Guitar Neck Deflection vs Neck Length')"
]
},
{
"cell_type": "code",
"execution_count": 266,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fe7977c2908>"
]
},
"execution_count": 266,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"h = np.array([L/4,L/8,L/12,L/20])\n",
"werr = []\n",
"xnumerr = []\n",
"for i in range(len(h)):\n",
" shape = int(L/h[i])\n",
" A2=np.diag(np.ones(shape)*6)+np.diag(np.ones(shape-1)*-4,-1)\\\n",
" +np.diag(np.ones(shape-1)*-4,1)+np.diag(np.ones(shape-2),-2)+np.diag(np.ones(shape-2),2)\n",
" A2[0,0]+=1\n",
" A2[-1,-1]+=1\n",
" A2[-2]= np.zeros(shape)\n",
" A2[-2,-4:]=[1,-4,5,-2]\n",
" A2[-1] = np.zeros(shape)\n",
" A2[-1,-3:] = [2,-4,2]\n",
" b2=-np.zeros(shape)\n",
" b2[-2]=-h[i]**2*M/(E*I)\n",
" b2[-1]=2*h[i]**2*M/(E*I)\n",
" werr.append(np.linalg.solve(A2,b2))\n",
" xnumerr.append(np.arange(0,L+h[i]/2,h[i]))\n",
" \n",
"plt.plot(xnumerr[0],1000*np.block([0,werr[0]]),'*',label='4 Finite Difference Segments')\n",
"plt.plot(xnumerr[1],1000*np.block([0,werr[1]]),'*',label='8 Finite Difference Segments')\n",
"plt.plot(xnumerr[2],1000*np.block([0,werr[2]]),'*',label='12 Finite Difference Segments')\n",
"plt.plot(xnumerr[3],1000*np.block([0,werr[3]]),'*',label='20 Finite Difference Segments');\n",
"plt.plot(x,w*1000,label='Analytical Data')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 267,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Absolute Error vs Number of Finite Difference Segments')"
]
},
"execution_count": 267,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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7VQryMijMy6BfbjqpydE/Geras4r47WsfMGP2eu770pioL88YExxL9E1QVaoO15yUxDeHPN+5/wjh923pnd2Nwh4ZDO2Xw4VD+jQk9UL/yMtMjYkDoFndUrhh3EDueeND1u06QFl+dtAhGWOipMsm+praOnbsP9LQH74lrEtla2U1B47UnDBNWnISBXnpFPbIYOLg/JADnMdb4+mpyQF9ota78bwSps9ZzwNz1/M/V48IOhxjTJQkbKI/UH/KYRNJvLFTDntkplKQl0FJryzOK+vtEnhIi7xXVhpJzRzkjDe9s7vxuTEDeHrhZu742Kn0yUkPOiRjTBTEfaKvq1Pun7s+pG+8mi17D1FVfWJrvLFTDo8ncTc8My3uV0er3TahlCfe3cTMN8v5zqVDgw7HGBMFcZ/ZkpKEe974EKDhwOZYf8ph/XnjkZxy2FWV9M7iE8P789jbG7l9chk57TyjxxgTe+I+0QO8/f2LyOqWEB8lEFMmlvK35dt48t0KbptYGnQ4xpgOlhBFzSzJt8/IojzGlfbiwXkbOFpT1/IExpi4khCJ3rTftMllbK+q5q9LtgQdijGmg1miNwBMHNybof1ymDFnPXVhZyMZY+KbJXoDgIgwbVIZH+w8wBtrdgYdjjGmA1miNw0+OaI/hXkZTJ+9PuhQjDEdyBK9aZCanMSXJwzi3fI9LNq4N+hwjDEdxBK9OcE1ZxWRl5nK9Nnrgg7FGNNBLNGbE2SmpXDDuQN5ddUOPtx5IOhwjDEdwBK9OcmN55WQlpzE/XOsr96YRGCJ3pykV3Y3Pj+2iOcWb2FHVXXQ4Rhj2skSvWnUlycMoqaujoffLA86FGNMO1miN40a2CuLT5zRn8ff3sj+6mMtT2CMiVlRT/Qikiwii0XkxWgvy3SsaRPL2H+khj++synoUIwx7dAZLfqvAas6YTmmg50xIJfxp/TioTc3cKSmNuhwjDFtFNVELyIDgE8CD0RzOSZ6pk4sY0fVEf66ZGvQoRhj2ijaLfpfA98Bmqx9KyJTRGShiCzctWtXlMMxrTVhcG9O79+d6bPXWbEzY+JU1BK9iFwO7FTVRc29T1VnqOpYVR2bn58frXBMG4kIUyeVsm7XQV5bbcXOjIlH0WzRjweuEJFy4EngQhH5QxSXZ6Lkk2fUFzuzsgjGxKOoJXpV/b6qDlDVEuBa4HVVvT5ayzPRk5KcxG0TBrFw414Wlu8JOhxjTCvZefQmIp8/q4gemancZyWMjYk7nZLoVXWWql7eGcsy0ZGZlsIN40r456odfLhzf9DhGGNawVr0JmI3jBtIemoSM6zYmTFxxRK9iVhosbPt+6zYmTHxwhK9aZXbJpRSW6c8/OaGoEMxxkTIEr1plaKemXxyRAGPv7OJKit2ZkxcsERvWm3qxFIOWLEzY+KGJXrTasMLc5kwuDcPzbNiZ8bEA0v0pk2mTixj5/4j/GXxlqBDMca0wBK9aZPxp/RiWEF3ps9Zb8XOjIlxluhNm7hiZ2Ws33WQV1ftCDocY0wzLNGbNrtseD+KemZw3+x1qFqr3phYZYnetJkrdlbK4k2VLNy4N+hwjDFNsERv2uVzY4romZVmJYyNiWGW6E27ZKQlc+O4Ev65aidrd1ixM2NikSV60243jBtIRmqyFTszJkZZojft1iMrjWvOKuKvS7awbd/hoMMxxoSxRG86xK3nD6JO4aF5VuzMmFhjid50iKKemVw+oj9/fGcT+w5bsTNjYokletNhpkws5eDRWh5/Z2PQoRhjQliiNx1mWIErdvbwm+VUH7NiZ8bEihYTvYiki8hnReQ3IvK0iDwqIt8RkWGdEaCJL9MmlbFr/xGes2JnxsSMZhO9iNwJvAmMA94BpgNPATXAz0TkVREZEe0gTfw4r6wXZxTmcv+c9dRasTNjYkJKC+MXqOqdTYz7pYj0AYo7NiQTz1yxs1K++sfFvPr+Di4d3i/okIzp8ppt0avq31oYv1NVF3ZsSCbeXTqsH8U9M63YmTExIqKDsSIyVkSeE5H3RGSZiCwXkWXRDs7Ep5TkJG6bWMqSikre3bAn6HCM6fIiPevmceBh4DPAp4DL/V9jGvW5MQPolZXGdCuLYEzgIk30u1T1eVXdoKob6x9RjczEtfTUZG48r4TXV+9kzXYrdmZMkCJN9D8UkQdE5AsicnX9I6qRmbj3pXNdsbPpc6yEsTFBijTR3wyMAi7FddnUd98Y06QeWWlce3YRzy/ZytZKK3ZmTFAiTfQjVXWsqt6oqjf7xy1RjcwkhFvPH4Rixc6MCVKkif5tETk9qpGYhDSgRyafGtGfJ97dxL5DVuzMmCBEmujPB5aIyBo7vdK01tRJZRw8WssfrNiZMYFo6crYepdGNQqT0E7r351Jp+bz8JsbuPX8QaSnJgcdkjFdSkQten8qZRWQC/QKeRgTkamTStl94CjPvmfFzozpbBG16EXkx8BNwDqg/pp2BS6MTlgm0Ywr7cWIAbnMmLOOa84qIjlJgg7JmC4j0j76zwNlqjpZVS/wD0vyJmIiwrRJZZR/dIhXVm4POhxjupRIE/0KIK81M/Z17N8VkaUislJEftT68Ewi+fiwfgzsZcXOjOlskSb6/wEWi8jLIvJ8/aOFaY4AF6rqSPzFViJybnuCNfEtOUm4bUIpSzfv4+31VuzMmM4S6Vk3jwB3AcuBukgmUNdkO+BfpvqHNeO6uM+OGcCv/7mW6XPWMa7Mjucb0xkiTfS7VfW3rZ25iCQDi4BTgN+p6juNvGcKMAWguNjuYZLo0lOTuem8En7xylpWbavitP7dgw7JmIQXadfNIhH5HxEZJyJn1j9amkhVa1V1FDAAOFtEhjfynhm+vMLY/Pz8VoZv4tH15w4kMy2Z+62EsTGdItIW/Wj/N7SPPeLTK1W1UkRm4S68WhFxdCYh5WWmce1ZxTw6v5xvfnwIhXkZQYdkTEKL9IKpCxp5NJvkRSRfRPL88wzgYmB1+0M2ieDWCYMAeHCuFTszJtqaTfQicr2INPkeESkTkfObGN0feMPXxFkAvKqqL7Y9VJNICvMyuGJkAU8u2ETloaNBh2NMQmup66YX7rTKRbiDqruAdNzB1UnAbuB7jU2oqss43uVjzEmmTCrl2cVbeGz+Rv71osFBh2NMwmq2Ra+qvwHOBJ4A8oGL/OstwJdU9TOq+kHUozQJaWi/7kweks/Mt8qpPlYbdDjGJKwWD8aqai3wqn8Y06GmTSrj2hlv88yizVx/7sCgwzEmIUV6eqUxUXHOoJ6MLMrj/rnrqa2z6+mMiQZL9CZQIsK0iaVs/OgQL62wYmfGREOLiV5EkkTk850RjOmaLhnWj0G9s6zYmTFR0mKiV9U64KudEIvpouqLnS3fso/56z8KOhxjEk6kXTevisi3RKRIRHrWP6IamelSrj6zkN7Zadw328oiGNPRIk30twD/AszBnU+/CFgYraBM15OemszN4wcxZ+0u3t9aFXQ4xiSUSEsgDGrkURrt4EzXcv05A8lKS2bGnHVBh2JMQoko0YtIqoj8m4g84x9fFZHUaAdnupbczFS+cHYxLyzbxua9h4IOx5iEEWnXzb3AGOD3/jHGDzOmQ91y/iAEeMCKnRnTYSItU3yWvyVgvddFZGk0AjJdW0FeBleOKuRPCyr42kWD6ZGVFnRIxsS9SFv0tSJSVv9CREoBK05iomLKxFIOH6vlsbc3Bh2KMQkh0kT/bVzJ4VkiMht4Hfhm9MIyXdmQfjlcOLQPM98q5/BRa08Y014RXRkLHAYGA//mH0NU9Y0ox2a6sKkTS9lz8CjPLKoIOhRj4l6kV8berapHVHWZqi5V1SOdEJvpws4e1JPRxXncP3cDNbV1QYdjTFyLtOvmFRH5jIhIVKMxxhMRpk4sY9OeQ7y00oqdGdMekSb6bwBPA0dEpEpE9ouIXb5ooupjp/el1IqdGdNukfTRCzBMVZNUNU1Vu6tqjqp274T4TBeWnCTcNrGUFVuqeGudFTszpq0i6aNX4LlOiMWYk3x6dCH5Od24b7aVRTCmrSLtunlbRM6KaiTGNMIVOyth7ge7Wbl1X9DhGBOXIk30FwDzRWSdiCwTkeUisiyagRlT77pzBpLdLYXpVsLYmDaJtATCJ6IahTHNyM1I5YvnFPPgvA18++NDKOqZGXRIxsSVZlv0InIhgKpuBJJUdWP9A1fYzJhOcfP4EpIEHpxnxc6Maa2Wum5+EfL8z2Hj/qODYzGmSf1zXbGzJxdsYs/Bo0GHY0xcaSnRSxPPG3ttTFRNnVhK9bE6Hp1fHnQoxsSVlhK9NvG8sdfGRNXgvjlcfFofHrFiZ8a0SkuJvlREnheRF0Ke178e1AnxGXOCqZPK2HvoGE9bsTNjItbSWTdXhjz/Rdi48NfGRN3YgT04sziPGXPW88Wzi0lJjvQMYWO6rmYTvarO7qxAjImEiDBtUhlTHlvE31ds54qRBUGHZEzMs+aQiTsXn9aX0vwspluxM2MiYonexJ2kJGHqxFJWbq1i3oe7gw7HmJjXqkQvIlnRCsSY1rhqdCF9crpZWQRjIhBRoheR80TkfWCVfz1SRH4f1ciMaUa3lGRuOX8Q8z7czYotVuzMmOZE2qL/FfBx4CMAVV0KTGxuAhEpEpE3RGSViKwUka+1L1RjTvTFc4pdsbM51qo3pjkRd92oaviJyy1dsVIDfFNVTwPOBf5FRE5vZXzGNKl7eirXnVPM35ZtZdNHh4IOx5iYFWmirxCR8wAVkTQR+Ra+G6cpqrpNVd/zz/f79xe2K1pjwtxy/iCSk4QH5lmr3pimRJropwH/gkvUm4FRwFciXYiIlACjgXcaGTdFRBaKyMJdu3ZFOktjAOjbPZ1Pjy7kqYUVfHTgSNDhGBOTIk30Q1T1OlXtq6p9VPV64LRIJhSRbFzly6+r6kk3FFfVGao6VlXH5ufnRx65Md4UX+zskfkbgw7FmJgUaaL/vwiHnUBEUnFJ/nFVfbY1gRkTqVP65HDxaX15dH45h47WBB2OMTGn2RIIIjIOOA/IF5FvhIzqDiS3MK0ADwKrVPWX7Q3UmObcPrmUz9y7g6cWVHDTeKu3Z0yollr0aUA27h9CTsijCvhsC9OOB74EXCgiS/zjsnbGa0yjxgzsydiBPbh/7gZqauuCDseYmBJJUbPZIjLT3z4wYqo6D7s5ielEUyeVcdujC/nb8m1cOcpO8DKmXqQ3B58pIidVj1LVCzs4HmPa7KKhfTilTzb3zV7PFSMLcL2HxphIE/23Qp6nA5/BXRBlTMxIShKmTCzlO88sY+4Hu5l4qp3FZQxEeNaNqi4Kebypqt8AzolybMa02pWjCujbvRv3zV4XdCjGxIxIi5r1DHn0FpGPA/2iHJsxrdYtJZlbxg/irXUfsWxzZdDhGBMTIj2PfhGw0P+dD3wTuDVaQRnTHl88p5gcK3ZmTIOI+uhV1U5MNnEjJz2V684dyIw569j40UEG9rLbKJiuraULpq5ubrxd7Wpi1c3jS3ho3gbun7uen1x1RtDhGBOollr0n2pmnAKW6E1Mqi929vTCzXz94lPpnd0t6JCMCUxLF0zd3FmBGNPRpkwq5alFFTz6VjnfuGRI0OEYE5hIz7rJFZFf1pcTFpG7RSQ32sEZ0x5l+dl87LS+PDJ/IweP2GUfpuuK9Kybh4D9wOf9owp4OFpBGdNRpk4qY9/hY/xpQfgN0ozpOiJN9GWq+kNVXe8fPwJKoxmYMR1hzMAenF3SkwfnbeCYFTszXVSkif6wiJxf/0JExgOHoxOSMR1r6qRStlQe5m/LtgUdijGBiLTWze3AI75fXoA9wE3RCsqYjnTBkD4M7pPNfbPXceUoK3Zmup5Ia90sUdWRwAjgDFUdrapLoxuaMR2jvtjZ6u37mb3W7ktsup5Iz7r5moh0xx2Q/aWIvCcil0Q3NGM6zpWjCunXPZ3ps60sgul6Iu2jv8Xf2PsSoA9wM/CzqEVlTAdLS0ni1vMHMX/9RyytsGJnpmuJNNHXd2peBjzsu22so9PElWvPLiInPYXpc6yEselaIq5eKSKv4BL9yyKSA9i5aiau5KSncv25A/nHiu2U7z4YdDjGdJpIE/2twPeAs1T1EO6m4VYewcSdm8eXkLmyGdUAABM6SURBVJqUxP1zra/edB2RnnVTB5QAPxCRu4GJqrosmoEZEw19ctL5zJhCnl60mV37jwQdjjGdItKzbn4PTAOWAyuAqSLyu2gGZky03DahlGO1dTzyVnnQoRjTKSK9YGoSMFxVFUBEHsElfWPiTml+Nh8/vR+Pzi/n9sllZHWLdDcwJj5F2ke/BigOeV0EWNeNiVtTJ5VSVV3DE+9uCjoUY6Ku2UQvIi+IyPNAL2CViMwSkTeAVUB+ZwRoTDSMLu7B2YOs2JnpGlr6zfqLZsZpRwZiTGebNqmUW2Yu5IWlW7n6zAFBh2NM1LR0h6nZjQ331Su/CMyJRlDGdIYLhvRhSN8cps9ez6dHF1qxM5OwIu2jR0RGicjPRaQc+Amu+8aYuCXiip2t2bGfWWus2JlJXC310Z8qIj8QkVXAPUAFIKp6gare0ykRGhNFnxpZQP/cdO6bbWURTOJqqUW/GrgI+JSqnq+q/wfURj8sYzpHfbGzdzbsYfGmvUGHY0xUtJToPwNsB94QkftF5CKsmJlJMNeeXUz39BQrYWwSVrOJXlWfU9VrgKHALOAOoK+I3Gv16E2iyO6WwpfGDeTl97ezfteBoMMxpsNFWuvmoKo+rqqXAwOAJbgiZ8YkhJvOG0RqchL3z90QdCjGdLiIz7qpp6p7VHW6ql4YjYCMCUJ+Tjc+O2YAf35vMzv3VwcdjjEdqtWJPlIi8pCI7BSRFdFahjEdqb7Y2cw3y4MOxZgOFbVED8wELo3i/I3pUIN6Z3HpsH489vZGDhypCTocYzpM1BK9qs4B9kRr/sZEw7RJZeyvruFJK3ZmEkg0W/QREZEpIrJQRBbu2mVXJ5pgjSzK49zSnjwwdwNHa6zYmUkMgSd6VZ2hqmNVdWx+vhXENMGbOqmM7VXVPL90a9ChGNMhAk/0xsSayafmM7RfDjPmrKOuzoq0mvhnid6YMCLC1EmlrN1xgFlrdwYdjjHtFs3TK58A5gNDRGSziNwarWUZ09EuH1FAQW46982ysggm/kXzrJsvqGp/VU1V1QGq+mC0lmVMR0tNTuLWCaW8W76HRRut2JmJb9Z1Y0wTrj2riNyMVGbMsRLGJr5ZojemCVndUrhh3EBeeX8H66zYmYljluiNacaN55WQmpzEV/7wHr94eQ3/fH8Huw8cCTosY1qlpZuDG9Ol9c7uxk+vGs7Mt8q5d/Y6av3plkU9Mxhd1INRRXmMLs7j9ILudEtJDjhaYxonqrFznvDYsWN14cKFQYdhTKMOH61l+ZZ9LKnYy+JNlSypqGTbPlfpMi05idMLujck/jOLezCgR4bdcNxEnYgsUtWxzb7HEr0xbbd9X3VD4l9cUcmyzZVUH3OlE3plpTUk/lFFPRhRlEv39NSAIzaJJpJEb103xrRDv9x0Ls3tz6XD+wNQU1vHmh37G1r8izft5bXV7qIrETglP7sh8Y8uzuPUvjkkJ1mr30SXteiNibJ9h4+xtOJ44l9SUcneQ8cAyExLZsSA3IbEP7oojz7d0wOO2MQTa9EbEwNyM1KZeGo+E091RftUlY0fHToh8T8wdz01/kBvYV5GQ5fP6OI8hhXkkp5qB3pN21miN6aTiQglvbMo6Z3FVaMLAag+VsvKrVUNiX/xpkr+tnwbAClJcsKB3lFFPSjplWkHek3ErOvGmBi1c381Sxr6+t2B3oNHawHIy0x1ib+oB6OK8xg1II/cTDvQ2xVZ140xcaxPTjqXDOvHJcP6AVBbp3ywcz9LNlU2HOydvXYt9W210vws3+rvweiiPIb0yyE12a6JNNaiNyau7a8+xvLN+1hcUZ/897L7wFEA0lOTGFGYxyh/kHdUcR79czMCjth0NDuP3pguRlXZvPcwiysqXcu/Yi8rt1RxtNad29+ve3pIX38eZwzIJTPNftjHM+u6MaaLERGKemZS1DOTK0YWAHCkppZV2/azZNNe9w+gopKXVm4HIDlJGNI3pyHxjy7uQWnvLJLs3P6EYi16Y7qgjw4cYenm4339SzZVsv9IDQA56Sn+QK9L/COL8uiZlRZwxKYp1nVjjIlIXZ2yfvcB3gs5y2fN9irqb5lb0iuzocU/qiiP0/p3Jy3FDvTGAkv0xpg2O3ikxhdxcxd2Ld5Uyc79rkRzWkoSwwu6NyT+0cV5FOZZEbcgWKI3xnQYVWXbvuqGs3uWVFSybPM+jtS4A729s7uF9PXnMWJAHtnd7DBgtNnBWGNMhxERCvIyKMjL4JMjXBG3Y7V1rNm+37X4fV//q+/vACBJ4NS+OSdc0XtKn2wr4hYAa9EbYzpU5aGj7gBvxfGDvfsOuyJu2d1SGDEgtyHxjyrKIz+nW8ARxzdr0RtjOl1eZhqTh/Rh8pA+gOvy2bD74AmJf/rs40XcBvTIOKGvf5jdravDWaI3xkSViFCan01pfjZXnzkAcEXcVmzZ15D4F5Xv4YWlWwFITRZOL8j1p3e6Pv/inlbErT2s68YYExN2VFX7O3XtZckmd6D38DFXxK1n/d26fCmHkUV5drcuz7pujDFxo2/3dC4d3o9Lh7sibjW1dazdcaAh8S+pqOT1kLt1leVnNyT+0UU9OLVvNilWxK1R1qI3xsSNqupjLKvYd7xuf0Ulew66Im4Zqf5uXT7xjy7Oo28XuFuXteiNMQmle3oq5w/uzfmDewPuQG/FnsMsDrlB+0PzNnCsdj0ABbnpDYl/VHEeZxR2zbt1WaI3xsQtEaG4VybFvTK5ctTxu3W9v63KV+90V/X+fbkr4paSJAztn+MSvz/YO6h3VsIf6LWuG2NMwtu1/4g/t3+vv1vXPg74Im65Ge5uXaHlm/My46eIm5VAMMaYRtTWKR/uPNCQ+JdUVLJmx/7jd+vqnXXCFb1D+8fu3bos0RtjTIQOHKlh2ebjV/Qu3lTJ7gOuiFu3lCTOKDx+Re/o4jz656bHRJePJXpjjGkjVWVL5eETruhdvmUfR30Rtz453U5I/CMCuluXnXVjjDFtJCIM6JHJgB6ZXD7C3a3raE0dq7dX+Ra/O8Xz5ZXHi7gN6df9eAXPojzK8rNj4m5d1qI3xph22HPwKEvra/b7Ym77q4/frWvkgOMHeUcV5dEru2OLuFmL3hhjoqxnVhoXDO3DBUNdETd3t66Dxy/q2lTJ72eto9YXcSvumXnCPXpP74S7dUW1RS8ilwK/AZKBB1T1Z82931r0xphEdOhoDcs37zuhv397VTUAaclJjCrK48kp57apmyfQFr2IJAO/Az4GbAYWiMjzqvp+tJZpjDGxKDMthXNKe3FOaa+GYdv2HW6o4bPv8LGo9uVHs+vmbOBDVV0PICJPAlcCluiNMV1e/9wM+p+RwSfO6B/1ZUWzY6gQqAh5vdkPO4GITBGRhSKycNeuXVEMxxhjuqZoJvrGfoecdEBAVWeo6lhVHZufnx/FcIwxpmuKZqLfDBSFvB4AbI3i8owxxjQimol+ATBYRAaJSBpwLfB8FJdnjDGmEVE7GKuqNSLyVeBl3OmVD6nqymgtzxhjTOOiesGUqv4d+Hs0l2GMMaZ5sVl30xhjTIexRG+MMQkupoqaicguYGMbJ+8N7O7AcDqKxdU6FlfrWFytk4hxDVTVZs9Nj6lE3x4isrCleg9BsLhax+JqHYurdbpqXNZ1Y4wxCc4SvTHGJLhESvQzgg6gCRZX61hcrWNxtU6XjCth+uiNMcY0LpFa9MYYYxphid4YYxJcQiR6EUkWkcUi8mLQsdQTkTwReUZEVovIKhEZF3RMACJyh4isFJEVIvKEiKQHGMtDIrJTRFaEDOspIq+KyAf+b48Yiet//Xe5TESeE5G8WIgrZNy3RERFpHesxCUi/yoia/z29vNYiEtERonI2yKyxN8H4+wA4ioSkTd8XlgpIl/zw6O27SdEoge+BqwKOogwvwFeUtWhwEhiID4RKQT+DRirqsNxxeauDTCkmcClYcO+B7ymqoOB1/zrzjaTk+N6FRiuqiOAtcD3OzsoGo8LESnC3bJzU2cH5M0kLC4RuQB3R7kRqjoM+EUsxAX8HPiRqo4CfuBfd7Ya4JuqehpwLvAvInI6Udz24z7Ri8gA4JPAA0HHUk9EugMTgQcBVPWoqlYGG1WDFCBDRFKATAK8R4CqzgH2hA2+EnjEP38EuKpTg6LxuFT1FVWt8S/fxt1fIfC4vF8B36GRG/t0hibiuh34maoe8e/ZGSNxKdDdP88lgO1fVbep6nv++X5cI7CQKG77cZ/ogV/jNvK6oAMJUQrsAh72XUoPiEhW0EGp6hZcy2oTsA3Yp6qvBBvVSfqq6jZwOwTQJ+B4GnML8I+ggwAQkSuALaq6NOhYwpwKTBCRd0RktoicFXRA3teB/xWRCty+EMQvswYiUgKMBt4hitt+XCd6Ebkc2Kmqi4KOJUwKcCZwr6qOBg4STBfECXyf35XAIKAAyBKR64ONKr6IyP/D/fR+PAZiyQT+H64LItakAD1wXRPfBp4SkcZuL9rZbgfuUNUi4A78r+4giEg28Gfg66paFc1lxXWiB8YDV4hIOfAkcKGI/CHYkAB3G8XNqvqOf/0MLvEH7WJgg6ruUtVjwLPAeQHHFG6HiPQH8H87/Sd/U0TkRuBy4DqNjQtQynD/tJf6fWAA8J6I9As0Kmcz8Kw67+J+cXf6geJG3Ijb7gGeBjr9YCyAiKTikvzjqlofT9S2/bhO9Kr6fVUdoKoluIOKr6tq4C1UVd0OVIjIED/oIuD9AEOqtwk4V0QyfevqImLgIHGY53E7I/7vXwOMpYGIXAp8F7hCVQ8FHQ+Aqi5X1T6qWuL3gc3AmX77C9pfgAsBRORUII3YqBq5FZjkn18IfNDZAfh970Fglar+MmRU9LZ9VU2IBzAZeDHoOELiGQUsBJbhNvoeQcfk4/oRsBpYATwGdAswlidwxwqO4ZLUrUAv3BkHH/i/PWMkrg+BCmCJf9wXC3GFjS8HesdCXLjE/ge/nb0HXBgjcZ0PLAKW4vrFxwQQ1/m4g8LLQrany6K57VsJBGOMSXBx3XVjjDGmZZbojTEmwVmiN8aYBGeJ3hhjEpwlemOMSXCW6E1U+EqKd4e8/paI3NlB854pIp/tiHm1sJzP+QqDb4QNTxKR3/oKoMtFZIGIDIp2PK3hqzReFnQcJjZYojfRcgS4Ooiyuc0RkeRWvP1W4CuqekHY8GtwJSRGqOoZwKeBWClaV28U7txsYyzRm6ipwd0H847wEeEtchE54P9O9gWwnhKRtSLyMxG5TkTe9S3nspDZXCwic/37LvfTJ/u68Qt83fipIfN9Q0T+CCxvJJ4v+PmvEJG7/LAf4C5suU9E/jdskv7ANlWtA1DVzaq61093iYjMF5H3RORpX88EEblMXD37ef7XwIt++J0i8oiIvCIi5SJytYj83Mfzkr9UHhEZ49fNIhF5OeRS+VkicpdfR2tFZIKIpAH/BVwjru76NSIyyT9f4gvt5bTu6zRxrbOvCrNH13gAB3DlYMtx5WC/Bdzpx80EPhv6Xv93Mq5l3B/oBmzB1Q4Hd8+BX4dM/xKuoTIYd9VjOjAF+A//nm64K5MH+fkeBAY1EmcBrjREPq4Q1+vAVX7cLFzt/vBpBvjPtQS4Gxjth/cG5gBZ/vV3cQXH0nFX1Q7yw5/AX8UN3AnMA1Jx9y04BHzCj3sOV6o2FXgLyPfDrwEeConxbv/8MuCf/vlNwD0hMb8AjPfPs4GUoLcRe3TeI6Xx9G9M+6lqlYg8irvZyeEIJ1ugvlSriKwD6ssoLwdCu1CeUtei/kBE1gNDgUuAESG/FnJx/wiOAu+q6oZGlncWMEtVd/llPo67l8Bfmvlcm30dowv94zUR+RyQAZwOvOkLNaYB831s60OW/wTun1K9f6jqMRFZjrsZzEshn7kEGAIMB171803GXdpfr74o1iL//sa8CfzSf75nVXVzU5/PJB5L9Cbafo2rdfJwyLAafLehL/CUFjLuSMjzupDXdZy4vYbX7lBAgH9V1ZdDR4jIZFyLvjFtKp2r7oYa/wD+ISI7cC3vV4BXVfULYcsf3cLs6m/OUScix1S1/rPVf2YBVqpqU7ejrF9HtTSxT6vqz0Tkb7hW/9sicrGqrm4hLpMgrI/eRJWq7gGewh3YrFcOjPHPr8R1TbTW5/zZL2W4G72sAV4Gbg/p1z5VWr7hyzvAJBHp7Q/UfgGY3dwEInKmiBT450nACGAj7s5T40XkFD8u01duXA2UirvJBLiul9ZYA+SLv++wiKSKyLAWptkPNPTDi0iZumqXd+G6tIa2MgYTxyzRm85wNyfWIr8fl1zfBc6h6dZ2c9bgEvI/gGmqWo27neT7uJrsK4DptPCr1XcTfR94A1fR8D1Vbak8bB/gBb+MZbhfKPf47p+bgCdEZBku8Q9V1cPAV4CXRGQesAPYF+kHVdWjwGeBu0RkKe7YQEv3EXgDOL3+YCzwdX+weSmuGy0m7pBlOodVrzSmE4hItqoe8F1VvwM+UNVfBR2X6RqsRW9M57hNRJYAK3EHiacHHI/pQqxFb4wxCc5a9MYYk+As0RtjTIKzRG+MMQnOEr0xxiQ4S/TGGJPg/j9Jf93f/qsYuAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"analytical = np.max(w)\n",
"error = []\n",
"for j in range(len(h)):\n",
" numerical = np.max(werr[j])\n",
" error.append(np.abs(analytical-numerical))\n",
"stepsize = np.array([20,12,8,4])\n",
"plt.plot(stepsize,error)\n",
"plt.ylabel('Absolute Error (mm)')\n",
"plt.xlabel('Number of Segments')\n",
"plt.title('Absolute Error vs Number of Finite Difference Segments')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2. Here we will record the first three frequencies of the 6-string guitar. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"a. Consider the G-string on the guitar, L=0.64 m, $\\mu=1.14~g/m,$ and T=71.81 N [1]. \n",
"\n",
"__Guitar string equation:__ $\\mu\\frac{\\partial^2 y}{\\partial t^2}=T\\frac{\\partial ^2 y}{\\partial x^2}$\n",
"\n",
"a. Calculate the first, second, and third natural frequencies using 6, 30, 45, and 60 nodes. Plot the mode shapes and determine the number of nodes needed to converge for the first three modes. "
]
},
{
"cell_type": "code",
"execution_count": 268,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"K=T/mu/h^2*\n",
"First 3 Natural frequencies of 6-element string (Hz)\n",
"[194.43708661 379.1242858 544.80061022]\n",
"\n",
"Longest time period =5.143 ms\n",
"shortest time period =1.174 ms\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fe797707c50>"
]
},
"execution_count": 268,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from scipy import linalg\n",
"#Constants\n",
"TG = 71.81 #Newtons\n",
"mu = 0.00114 #kg/m\n",
"#6 Nodes\n",
"N6=6 # 6-node guitar string\n",
"dx6=L/(N6+1)\n",
"\n",
"k6 = TG/dx6**2/mu\n",
"\n",
"A6 = k6*(np.diag(np.ones(N6)*2)\\\n",
" -np.diag(np.ones(N6-1),-1)\\\n",
" -np.diag(np.ones(N6-1),1))\n",
"print('K=T/mu/h^2*')\n",
"e6,v6=linalg.eig(A6)\n",
"isort = np.argsort(e6.real)\n",
"e6=e6[isort]\n",
"v6=v6[:,isort]\n",
"\n",
"print('First 3 Natural frequencies of {}-element string (Hz)'.format(N6))\n",
"print(e6.real[:3]**0.5/2/np.pi)\n",
"f16=np.sqrt(e6.real[0])/2/np.pi\n",
"fn6=np.sqrt(e6.real[-1])/2/np.pi\n",
"print('\\nLongest time period ={:1.3f} ms\\nshortest time period ={:1.3f} ms'.format(1/f16*1000,1/fn6*1000))\n",
"plt.plot(v6[:,0],label='Mode 1')\n",
"plt.plot(v6[:,1],label='Mode 2')\n",
"plt.plot(v6[:,2],label='Mode 3')\n",
"plt.title('First Two Vibration Modes for 6-Node Guitar String')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 269,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"K=T/mu/h^2*\n",
"First 3 Natural frequencies of 30-element string (Hz)\n",
"[195.99464595 391.48617646 585.97276757]\n",
"\n",
"Longest time period =5.102 ms\n",
"shortest time period =0.259 ms\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fe7976f22b0>"
]
},
"execution_count": 269,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"TG = 71.81 #Newtons\n",
"mu = 0.00114 #kg/m\n",
"#30 Nodes\n",
"N30=30 # 30-node guitar string\n",
"dx30=L/(N30+1)\n",
"\n",
"k30 = TG/dx30**2/mu\n",
"\n",
"A30 = k30*(np.diag(np.ones(N30)*2)\\\n",
" -np.diag(np.ones(N30-1),-1)\\\n",
" -np.diag(np.ones(N30-1),1))\n",
"print('K=T/mu/h^2*')\n",
"e30,v30=linalg.eig(A30)\n",
"isort = np.argsort(e30.real)\n",
"e30=e30[isort]\n",
"v30=v30[:,isort]\n",
"\n",
"print('First 3 Natural frequencies of {}-element string (Hz)'.format(N30))\n",
"print(e30.real[:3]**0.5/2/np.pi)\n",
"f130=np.sqrt(e30.real[0])/2/np.pi\n",
"fn30=np.sqrt(e30.real[-1])/2/np.pi\n",
"print('\\nLongest time period ={:1.3f} ms\\nshortest time period ={:1.3f} ms'.format(1/f130*1000,1/fn30*1000))\n",
"plt.plot(v30[:,0],label='Mode 1')\n",
"plt.plot(v30[:,1],label='Mode 2')\n",
"plt.plot(v30[:,2],label='Mode 3')\n",
"plt.title('First Two Vibration Modes for 30-Node Guitar String')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 270,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"K=T/mu/h^2*\n",
"First 3 Natural frequencies of 45-element string (Hz)\n",
"[196.04043699 391.85229959 587.20727994]\n",
"\n",
"Longest time period =5.101 ms\n",
"shortest time period =0.174 ms\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fe797665dd8>"
]
},
"execution_count": 270,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#45 Nodes\n",
"N45=45 # 45-node guitar string\n",
"dx45=L/(N45+1)\n",
"\n",
"k45 = TG/dx45**2/mu\n",
"\n",
"A45 = k45*(np.diag(np.ones(N45)*2)\\\n",
" -np.diag(np.ones(N45-1),-1)\\\n",
" -np.diag(np.ones(N45-1),1))\n",
"print('K=T/mu/h^2*')\n",
"e45,v45=linalg.eig(A45)\n",
"isort = np.argsort(e45.real)\n",
"e45=e45[isort]\n",
"v45=v45[:,isort]\n",
"\n",
"print('First 3 Natural frequencies of {}-element string (Hz)'.format(N45))\n",
"print(e45.real[:3]**0.5/2/np.pi)\n",
"f145=np.sqrt(e45.real[0])/2/np.pi\n",
"fn45=np.sqrt(e45.real[-1])/2/np.pi\n",
"print('\\nLongest time period ={:1.3f} ms\\nshortest time period ={:1.3f} ms'.format(1/f145*1000,1/fn45*1000))\n",
"plt.plot(v45[:,0],label='Mode 1')\n",
"plt.plot(v45[:,1],label='Mode 2')\n",
"plt.plot(v45[:,2],label='Mode 3')\n",
"plt.title('First Two Vibration Modes for 45-Node Guitar String')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 271,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"K=T/mu/h^2*\n",
"First 3 Natural frequencies of 60-element string (Hz)\n",
"[196.05687232 391.9837462 587.65070938]\n",
"\n",
"Longest time period =5.101 ms\n",
"shortest time period =0.131 ms\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fe7975f0eb8>"
]
},
"execution_count": 271,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#60 Nodes\n",
"N60=60 # 60-node guitar string\n",
"dx60=L/(N60+1)\n",
"\n",
"k60 = TG/dx60**2/mu\n",
"\n",
"A60 = k60*(np.diag(np.ones(N60)*2)\\\n",
" -np.diag(np.ones(N60-1),-1)\\\n",
" -np.diag(np.ones(N60-1),1))\n",
"print('K=T/mu/h^2*')\n",
"e60,v60=linalg.eig(A60)\n",
"isort = np.argsort(e60.real)\n",
"e60=e60[isort]\n",
"v60=v60[:,isort]\n",
"\n",
"print('First 3 Natural frequencies of {}-element string (Hz)'.format(N60))\n",
"print(e60.real[:3]**0.5/2/np.pi)\n",
"f160=np.sqrt(e60.real[0])/2/np.pi\n",
"fn60=np.sqrt(e60.real[-1])/2/np.pi\n",
"print('\\nLongest time period ={:1.3f} ms\\nshortest time period ={:1.3f} ms'.format(1/f160*1000,1/fn60*1000))\n",
"plt.plot(v60[:,0],label='Mode 1')\n",
"plt.plot(v60[:,1],label='Mode 2')\n",
"plt.plot(v60[:,2],label='Mode 3')\n",
"plt.title('First Two Vibration Modes for 60-Node Guitar String')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 272,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Mode Shape of First Eigen Vector')"
]
},
"execution_count": 272,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#Prove convergence\n",
"#set x boundaries\n",
"x1 = np.linspace(0,L,8)\n",
"x2 = np.linspace(0,L,32)\n",
"x3 = np.linspace(0,L,47)\n",
"x4 = np.linspace(0,L,62)\n",
"#plot first mode shape convergence\n",
"plt.title('First Mode Shape Convergence')\n",
"plt.plot(x1[1:-1],-v6[:,0]/np.max(-v6[:,0]),'o',label='6 nodes')\n",
"plt.plot(x2[1:-1],-v30[:,0]/np.max(-v30[:,0]),'s',label='30 nodes')\n",
"plt.plot(x3[1:-1],v45[:,0]/np.max(v45[:,0]),'*',label='45 nodes')\n",
"plt.plot(x4[1:-1],-v60[:,0]/np.max(-v60[:,0]),'--',label='60 nodes')\n",
"plt.legend()\n",
"plt.ylabel('Mode Shape of First Eigen Vector')"
]
},
{
"cell_type": "code",
"execution_count": 273,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Mode Shape of First Eigen Vector')"
]
},
"execution_count": 273,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#plot second mode shape convergence\n",
"plt.title('Second Mode Shape Convergence')\n",
"plt.plot(x1[1:-1],v6[:,1]/np.max(-v6[:,1]),'o',label='6 nodes')\n",
"plt.plot(x2[1:-1],-v30[:,1]/np.max(-v30[:,1]),'s',label='30 nodes')\n",
"plt.plot(x3[1:-1],v45[:,1]/np.max(v45[:,1]),'*',label='45 nodes')\n",
"plt.plot(x4[1:-1],-v60[:,1]/np.max(-v60[:,1]),'--',label='60 nodes')\n",
"plt.legend()\n",
"plt.ylabel('Mode Shape of First Eigen Vector')"
]
},
{
"cell_type": "code",
"execution_count": 274,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Mode Shape of First Eigen Vector')"
]
},
"execution_count": 274,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#plot Third mode shape convergence\n",
"plt.title('Third Mode Shape Convergence')\n",
"plt.plot(x1[1:-1],-v6[:,2]/np.max(-v6[:,2]),'o',label='6 nodes')\n",
"plt.plot(x2[1:-1],-v30[:,2]/np.max(-v30[:,2]),'s',label='30 nodes')\n",
"plt.plot(x3[1:-1],v45[:,2]/np.max(v45[:,2]),'*',label='45 nodes')\n",
"plt.plot(x4[1:-1],-v60[:,2]/np.max(-v60[:,2]),'--',label='60 nodes')\n",
"plt.legend()\n",
"plt.ylabel('Mode Shape of First Eigen Vector')"
]
},
{
"cell_type": "code",
"execution_count": 275,
"metadata": {},
"outputs": [],
"source": [
"#Based on the above graphs 45 nodes are nnecessary for convergence."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"b. Use the number of nodes necessary for convergence to calculate the first 3 modes of vibration for the other 5 strings on the guitar. Display the first three natural frequencies for all six strings. "
]
},
{
"cell_type": "code",
"execution_count": 276,
"metadata": {},
"outputs": [],
"source": [
"#Tension values\n",
"g = 9.81 #gravity m/s^2\n",
"TE = tE*g #Newtons\n",
"TB = tB*g #Newtons\n",
"TG = tG*g #Newtons\n",
"TD = tD*g #Newtons\n",
"TA = tA*g #Newtons\n",
"TE2 = tE2*g #Newtons"
]
},
{
"cell_type": "code",
"execution_count": 277,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"K=T/mu/h^2*\n",
"First 3 Natural frequencies of 45-element string (Hz)\n",
"[329.63523775 658.88613556 987.36880161]\n",
"\n",
"Longest time period =3.034 ms\n",
"shortest time period =0.104 ms\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fe797c10048>"
]
},
"execution_count": 277,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#First E string\n",
"k45E = TE/dx45**2/dE\n",
"\n",
"A45E = k45E*(np.diag(np.ones(N45)*2)\\\n",
" -np.diag(np.ones(N45-1),-1)\\\n",
" -np.diag(np.ones(N45-1),1))\n",
"print('K=T/mu/h^2*')\n",
"e45E,v45E=linalg.eig(A45E)\n",
"isort = np.argsort(e45E.real)\n",
"e45E=e45E[isort]\n",
"v45E=v45E[:,isort]\n",
"\n",
"print('First 3 Natural frequencies of {}-element string (Hz)'.format(N45))\n",
"print(e45E.real[:3]**0.5/2/np.pi)\n",
"f145E=np.sqrt(e45E.real[0])/2/np.pi\n",
"fn45E=np.sqrt(e45E.real[-1])/2/np.pi\n",
"print('\\nLongest time period ={:1.3f} ms\\nshortest time period ={:1.3f} ms'.format(1/f145E*1000,1/fn45E*1000))\n",
"plt.plot(v45E[:,0],label='Mode 1')\n",
"plt.plot(v45E[:,1],label='Mode 2')\n",
"plt.plot(v45E[:,2],label='Mode 3')\n",
"plt.title('First Two Vibration Modes for 45-Node Guitar First E String')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 278,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"K=T/mu/h^2*\n",
"First 3 Natural frequencies of 45-element string (Hz)\n",
"[247.05411832 493.82018258 740.01047461]\n",
"\n",
"Longest time period =4.048 ms\n",
"shortest time period =0.138 ms\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fe7974754a8>"
]
},
"execution_count": 278,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#B string\n",
"k45B = TB/dx45**2/dB\n",
"\n",
"A45B = k45B*(np.diag(np.ones(N45)*2)\\\n",
" -np.diag(np.ones(N45-1),-1)\\\n",
" -np.diag(np.ones(N45-1),1))\n",
"print('K=T/mu/h^2*')\n",
"e45B,v45B=linalg.eig(A45B)\n",
"isort = np.argsort(e45B.real)\n",
"e45B=e45B[isort]\n",
"v45B=v45B[:,isort]\n",
"\n",
"print('First 3 Natural frequencies of {}-element string (Hz)'.format(N45))\n",
"print(e45B.real[:3]**0.5/2/np.pi)\n",
"f145B=np.sqrt(e45B.real[0])/2/np.pi\n",
"fn45B=np.sqrt(e45B.real[-1])/2/np.pi\n",
"print('\\nLongest time period ={:1.3f} ms\\nshortest time period ={:1.3f} ms'.format(1/f145B*1000,1/fn45B*1000))\n",
"plt.plot(v45B[:,0],label='Mode 1')\n",
"plt.plot(v45B[:,1],label='Mode 2')\n",
"plt.plot(v45B[:,2],label='Mode 3')\n",
"plt.title('First Two Vibration Modes for 45-Node Guitar B String')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 279,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"K=T/mu/h^2*\n",
"First 3 Natural frequencies of 45-element string (Hz)\n",
"[146.88611909 293.60097554 439.97350639]\n",
"\n",
"Longest time period =6.808 ms\n",
"shortest time period =0.233 ms\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fe7973de6d8>"
]
},
"execution_count": 279,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#D string\n",
"k45D = TD/dx45**2/dD\n",
"\n",
"A45D = k45D*(np.diag(np.ones(N45)*2)\\\n",
" -np.diag(np.ones(N45-1),-1)\\\n",
" -np.diag(np.ones(N45-1),1))\n",
"print('K=T/mu/h^2*')\n",
"e45D,v45D=linalg.eig(A45D)\n",
"isort = np.argsort(e45D.real)\n",
"e45D=e45D[isort]\n",
"v45D=v45D[:,isort]\n",
"\n",
"print('First 3 Natural frequencies of {}-element string (Hz)'.format(N45))\n",
"print(e45D.real[:3]**0.5/2/np.pi)\n",
"f145D=np.sqrt(e45D.real[0])/2/np.pi\n",
"fn45D=np.sqrt(e45D.real[-1])/2/np.pi\n",
"print('\\nLongest time period ={:1.3f} ms\\nshortest time period ={:1.3f} ms'.format(1/f145D*1000,1/fn45D*1000))\n",
"plt.plot(v45D[:,0],label='Mode 1')\n",
"plt.plot(v45D[:,1],label='Mode 2')\n",
"plt.plot(v45D[:,2],label='Mode 3')\n",
"plt.title('First Two Vibration Modes for 45-Node Guitar D String')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 280,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"K=T/mu/h^2*\n",
"First 3 Natural frequencies of 45-element string (Hz)\n",
"[110.00809489 219.88792527 329.51137616]\n",
"\n",
"Longest time period =9.090 ms\n",
"shortest time period =0.311 ms\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fe797358dd8>"
]
},
"execution_count": 280,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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VkJal/E/Jyv+7bAdbG0Iauio/AD71aN/EnU5NPanvZK/G4aodF4/A0SWKwaedVKY5e0JwP8XEfdrcvAYvJaSfhdhIiN0Oufqxh7xbKeu1uwsCuv57PY0KEUIclFJ2uem82hq+fjzMs8AQlNFf9gMTpZQnyyzTEzglpbwqhBgOvC6l7H6rbWuGr1FVpJQkZuRyIP4qBxKuciA+g3Np1wHFZwI8XWjpW4/mPm609K1HCx83mvm44uLw74fcTQmbeH7H89jb2tOrcS/6B/Snt39vPJ08b1p2el46Oy/sZPuF7ey5qAzU9VG/j+jTpM+/ls0pKCYm7frfP0Dn0q5zNjWbC1fz/tbayteNLkGedGnqReemnjTxdEaYanPH5bOw9S04tQrsnCCwxz81db/2YFONJxidDtJO/PNkEL8bivOg5XAY9Ar4tjXGHlgcxjb8HigGPkz//QUAKeV7FSzvCRyXUt5slPsb0AxfozIy84rYcfYykafT2BmTzuVsZcQ3Nyc7OgV60jXIk85Nvbg9wP2mxn4zFp5ayAf7PqB9w/bMHTi3QpOviMu5l5mzZQ5nr57l1R6vMr7F+Cqtd72gmL+SrrE/PoODCVc5nHiN6wXFAPjVd6JPC28GhvrQu4U3bqbwBHAtCba9D38tAnsX6PEo9JgDTvUNV0ZhDkR/Dbs/h4IspbY/4AXwMuRwsZaHsQ3/TiBcSvmI/vv9QHcp5aMVLP8MEFq6/E3mTwemAwQGBnZOSKiks0fDqpBScv7ydbaeTmPLqTQOJFylRCfxcLGnb4uGdAv2okuQJy193LCxqV6NWCd1fHLwE3468RODAgfxfp/3cbKr8ljYN5BTlMPT255m98XdzLp9FrNun1XtGnqJTnI6JYuDCVfZG5vBznOXycovxt5W0C3Yi4GhvgwK9SHI27VGGmvM9cuw8yM48D0goOsj0OcpcPU2Xpm5GbD7M9j7DeiKoNMD0Pe/UL+R8co0Y4xt+HcBw8oZfjcp5WM3WXYA8BXQW0p55Vbb1mr4GgBnU7NZcTiZtccukXAlF4BQPzcGhvowqLUPHQI8sa2mwZelsKSQl3e9zLr4dUwMnchzXZ/D1qZ20TVFuiLe2PMGK8+vZHyL8bwc9jL2NjWvmReV6DiYcJXI02lsOZ1GjL65KqShK6PaN2Zch8aENKxXK82VIiXs+xY2v6E0s3SYDP2fB/cmxiuzPNkpsP1DOLQAbOyV2n7Px7XonnKYRJOOEKI9sBwYLqU8W5Vta4ZvvaRm5bPqyEWWH07m5KUsbG0EvZp7M6SNLwNDffD3cDZIOVmFWTwR+QT7U/bzZOcnebDtgwZrL5dS8uWRL/nm6Df09u/NR/0+wsXexSDbTrySy9bTqWw8mUpU7BWkhNubuDOuoz+j2jemoZujQcoBoOA6rH4cji+F5kMg/D3wbmG47VeXjDjY+DKcXgOho2DcV+Dkrp4eE8PYhm+H0mk7CEhG6bSdJKU8UWaZQGAr8ICUck9Vt60ZvnWRV1jC2mOXWHE4md3n041rYkBKTgqzNs8iPiuet3u9zciQkQbdfil/nP2Dt6PfJtQrlC8HfYm3s2GbP1Iy81n9140/jn1aeHNHR3+GtfXDyb4WTyvp52DJfUokzcCXodeT1euINRZSKu37m14Bj6Zwzy9ap64eoxq+voARwKcoYZk/SCnfEULMBJBSzhNCfAdMAEob5IsrElQWzfCtg/j0HH6JTuCPA0lk5RcT6OXCuI7+Rm2mKCopYnLEZJKyk/h0wKd0b3TLoLFasT1pO8/ueJbWXq35YdgPtW4yqojS5q+VRy6SfC0PL1cH7u4SwOTugQR4VfPp4uRKWDEH7BxgwvfQbIBRNNeKhCj4YwoUZMPoz6D93WorUh2jG76x0AzfcinRSbadSePnqAS2n72MnY0g/DY/7g9rSrdgL6OHIX5+6HPmH5vPpwM+ZVDgIKOWVcrq86t5cdeLPNHpCR5u97BRy9LpJFGxV/g5Kp5NJ1MBGBjqywM9mtK7uXflndolxbDlddgzF/w7w90/121bfXXJToE/HoTEPdBtOgx9R/mRslI0w9cwGbLyi1i8L5FfohNIysjDx82RSd0DmdQtEJ/6NYuKqS6H0w4zdf1UxjYby5u93qyTMkFp0396+9NEJkWyaMQiWjdoXSflJl/LY9HeBBbvS+JKTiHB3q7cH9aUe7oG4OpYLlw1Jx3+mArxO6HLw0p7vZ1hm9KMQkkRbH4dor6AJt2UHykrjeLRDF9DdTJyCvlhVxwLouLJzi+mW7AXU3oEMbStL/Z1mF4gpyiHO1fdiUSydMxSXO3rNqzxWv41xq8aT32H+iwZvQRH27oz04LiEtYdS2FBVDyHE6/h6WLPg72CmdIjCHcXe8i5AgtGQUas0jxy+711ps1gnFiuNEO5+cGDEcp/K0MzfA3VSMnM59sdsfy2L5H84hLC2/oxu39z2jVRJ6ritT2vsSJmBT+F/0RHn46qaNidvJuZm2dyX+v7eK7bc7dewQgcTLjKV5ExbDmdRj1HOx7p7MGjSU9gdzUWJv2u5LMxVxL3wq/jwa0RTF0Lbr5qK6pTKjN8LXmahlFIuJLDvO2xLD14gRIpGduhMbP7N6O5j5tqmrYkbmHZuWVMazdNNbMH6OXfi4mhE/n11K/0C+hHWKOwOtfQuakn30/tysmLWSzYepghB6ZRIi6ysPmHDPbqxi1fgzdlArvD5D/h1wmwYLRi+vUaqq3KJNBq+BoGJTUrn083n+P3A0nY2gju7tKEGX2bVT9CxMCk56UzfuV4/Fz9WDhiIfa26qYnyCvO454195BTlMOyMctwd1QpjjzvKvw8Dpl6kh8C3uX9GMXqJ3dvyqMDm+Ndzwza7ysifhf8eid4BsHUNcZ9G9iE0Jp0NIxOZl4R87af58fdcZToJJO7N2V2/2Z11hFbGVJKHt36KHsv7WXJqCU082imtiQATlw5wX1r72NI0yF82O/DuheQnwk/j4OUY3DvImg5lIvX8pi7NYbfDyThZGfDtL4hPNInhHrlO3fNhdjtsOhu8GoGU1aDawO1FRmdygzfBN6g0DBn8otK+Gb7efp+GMm87ecJb+vHlqf68/qYtiZh9gB/nvuTHRd28GTnJ03G7AHaNmjLrA6zWBe/jojYiLotPD9LafJIOaa8tNRyKACNPZx5b3w7Nj7Zl36tGvLp5nP0+zCSn3bHUVisq1uNhiCkH0xcDBnn4ZexSl4eK0ar4WvUiBKdZOmhC3yy6SyXMvPp17Ih/w1vRdvGpvWKe2JWIneuvpMODTswb8g8bIRp1XGKdcVMXT+V2GuxLBu7DD/XOogqKbiudGomH4S7FkDrURUueiTpGh+sO01U7BUCvJx5Zmgrxtze2HTTNVdEzGb4bRL4hMIDq8DZQ21FRkOr4WsYlEOJVxn35W7+++dRfOo78du0MBY81M3kzB7gw/0fYifseKvXWyZn9gB2Nna81/s9imUxHx/82PgF6nSwbDpcOAB3/lCp2QN0CPBg0bTuLHioG26O9vxn8RHumhfF8eRM42s1JM0Hw70LIfWk8p5BSbHailTB9O4ADZMlLTufp3//i/Ff7SEtO5/P7u3Aitk96dHMNNtFj6QdYfuF7TzU7iF8XU03NC+gfgCTW09mfdx6zl6tUl7BmrP9fTizFoa9A23GVmkVIQT9WjZkzWO9+XBCe+LScxj9xS5eWn6MqzmFxtVrSFoMgVEfK6NrbX5NbTWqoBm+xi0pKtHx3c5YBv1vO6v+SmZmv2Zsebo/Yzv4m/Sj/dzDc/Fy8mJS6CS1pdySqW2nUs++Hl8c/sJ4hZxcBds/UFIbd59Z7dVtbAR3dw1g6zP9mdIjiMX7kxjw0TZ+iU6gRGe6TcM30OkBJf1C1Bfw1xK11dQ5muFrVMqemHSGf7aTt9eeonOQJxue6Mvzw0NNPmoj+lI0+1L2Ma3dNIOlJDYm7o7uTGk7hcikSI5dPmb4AlJPwPKZ4N8FRn5cqxzy7s72vD6mLRGP9yHUz41XVhxn9NxdHIg3kw7RYe9CUB9Y9RgkH1JbTZ2iGb7GTbmaU8jTv//FpO/2Ulis47sHuvDj1K7GHWTDQEgpmXtoLr4uvtzV6i615VSZ+9rch6ejJ3MPzzXshnMz4LeJ4OgG9/wK9oaJnmrl58Zv08L4YlJHruYWcue8KF5afoys/CKDbN9o2NorndX1fGHxZMhOVVtRnaEZvsYNSClZ/ddFhnyynZVHkpkzoBkbn+zL4Da+Jt18U5btF7ZzNP0os26fVae5amqLq70rD7d7mKhLUexP2W+YjZYUK+mDsy8pnZYGTigmhGBU+8ZsebofD/cO5rd9iQz9eMffGTpNFtcGMHER5F+D3++H4gK1FdUJmuFr/M2lzDym/XyAx347TGMPZ1Y92ptnh4XWbgCNOkYndcw9PJdAt0DGNB+jtpxqc0+re/Bx9uHzQ59jkJDpTa9A3A4lGVqTWw5BUWNcHOx4ZVQbls3uhYeLPdN+PsCcRYf+HljeJPFrp4yWlbQXIp5RBlWxcDTD10Cnk/wSFc+Qj3ewKyadl0e2ZtmsnrRpXF9tadVmY/xGzl49y+wOs2s1hqxaONk5MeP2GRy5fISdyTtrt7HDCyH6K+g+CzrUTcd1hwAPVj3am2eGtmTTiVQGf7yd3w8kGebHyxi0vQP6PAOHfob936mtxuhoL15ZOYlXcnnmj7/YF59B7+bevHtHOwIbmH4n580o1hVzx8o7sLOxY+mYpSYZd18VikqKGL1iNPUd6rN41OKa7cfFw/D9UAgMg/uWg23dd7LHpF3nhWVH2R9/lT4tvPnwzvY0cjfMWMQGRaeDxZMgZpOSaC2w7pPZGRLtxSuNfyGlZPG+RIZ/toNTl7L48M72/PJwN7M1e1BGlIrPiufRjo+ardkD2NvaM7vDbE5lnGJzwubqb6AwF5ZOAxdvpXNSBbMHaO5TjyXTe/DW2LYciL/K0E92sOJwsunV9m1sYPy3yqhey6YpaScsFPO9KzRqTFp2Po8sOMDzy47RvokH65/sy91dAsymU/ZmFJYUMu+vedzW4DYGBgxUW06tGRk8khD3EL488iUlupLqrbzpVbhyDu74Gly8jCOwitjYCO7vEcS6//ShhU89nlhyhEcXHTa9F7ac6sP4+ZB5AdY/r7Yao6EZvpWx/vglhn2yg50x6bwyqg0LH+mOv4cJPmZXkz/P/snFnIs81vExs/7hKsXWxpY5HeYQmxnL2ri1VV/x3CbYPx/C5kBIf2PJqzZB3q78PqMHzw5rxcaTKQz9dAeRZ9LUlnUjAd2U9vwjC5UB3C0QzfCthKz8Ip5acoSZvx6iiacLax/rzcO9gysfzNpMyCvOY/6x+XT27UyPxj3UlmMwBjcdTGuv1nx15CuKSqoQ255zBVbOAZ82MOhV4wusJna2NswZ0JwVc3opwyv+uJ8Xlx8jp8CE8tr0+y807gSr/wNZl9RWY3A0w7cCDiVeZfinO1n510UeH9icZbN70sJXvZGnDM2fZ/8kPS+dxzs+bhG1+1JshA2PdXyM5OvJrDq/qvKFpYTVjysDmoz/1mAvVxmDto3dWfVob6b3DeG3fYmMmrvLdJKx2dorx68oH1bOVjp0LQjN8C0YnU7y9bbz3DUvCiHgj5k9eGpoqzodNNzYlOhKWHRqEZ18OtHJt5PacgxOb//etPJsxcLTCyvv7DyyEE6vgYGvKPHlJo6TvS0vjmjNokfCyC0sZvxXe/hpd5xpdOh6t1CSy53fqjSPWRCWc+dr3MDl7AKm/LiPD9afJrytH2sf70OnQE+1ZRmcnck7uXD9ApNbT1ZbilEQQjC59WTOXT3HgdQKQpQz4mDdc0p+mB6P1q3AWtKjWQPW/acvvVt48/rqk0z/5SDXck2gQ7fLQ9BimNIBnnZabTUGQzN8C2TXOSXh2b64DN654za+mNQRd2fzewmpKiw8tRBfF18GBpp/ZE5FDA8ejoejBwtPLfz3zJJiWD4DhC2M+1oJMTQzvFwd+H5KF14e2ZptZ9IY8dlO9qudiE0IGDMXHFxh2SNQbAI/QgbA/K4OjQopLtHxfxtOc/8Pe/FwsWflo72Y3L2pRbVrl+X8tfNEX4rm3tB7sWRmtBsAACAASURBVLMx7eydtcHJzokJLSYQmRRJ8vXkG2fu+kRJDTDyI/AIUEegARBC8EifEJbO6om9nQ33fhvNF1vPqZt22c1XMf2UY7DtXfV0GBDN8C2EtKx8Js3fy5eR57m7cwCrHu1FqJ/5pUaoDotOLcLBxoEJLSaoLcXo3NPqHgSCJafL5HC/dFQZ0OS2CdDefLKCVkb7Jh6seaw3I9o14n8bzzL1x31kqBmzHzpSyaG/61NI3KueDgOhGb4FsC8ug5Fzd3EsOZNP7+nAB3e2x8XBcmu8AJkFmayOXc3IkJF4Olle30R5GtVrxMDAgSw9t5S84jzQlSihg86eMOJ/asszKG5O9nx+bwfeG9+OvXEZjJ67i7+SrqknaNh7UN8f1jwBVQmPNWE0wzdjpJR8tzOWifOjqedox4o5vRjX0V9tWXXCipgV5BXnMam16Y9mZSgmt55MVmEWa2PXKom+Lh6C8PdVf5vWGAghmNgtkKUzewJw17woFu5NUCeKx7EejPwfpJ2EPZ/XffkGRDN8M+V6QTGPLjrM22tPMbi1Dysf7UUrP8uJra+MEl0Jv53+jc6+nQn1ClVbTp3RyacToV6hLDyxALnlLWg2UGnOsWDaNXFnzWO96dGsAS8tP84zfxwlv6iaqSYMQavh0Ho0bP8QMmLrvnwDoRm+GRKTls3YL3ax7vglnh8eyrz7OlPfyTKjcG7Gjgs7SL6ebLGhmBUhhGBS6CRisuLZb0+thyo0FzxdHfhhalf+M6gFyw5fYPxXe0i8klv3QoZ/CDb2sPZps82drxm+mbHu2CXGfrGba7lF/Ppwd2b2a2axUTgVsfD0Qvxc/RgQMEBtKXXOiCKBZ0kJC4NuB69gteXUGbY2gieHtOSHKV1JvpbHqLk7iTxdx7l46jdWUlac3wrH/qzbsg2EZvhmgk4n+XjjGWYtPERLPzfWPN6bns291ZZV58RcjWHvpb3c0+oeiw7FvCkF2Tiuf5EJJU5sy7vw7xBNK2BAqA9rHutNE08XHlqwn6+3na/bdv2uD4N/Z9jwgjJWsJmhGb4ZcL2gmJm/HuTzrTHc1bkJi6eHmeZAEnXAotOLcLR1tIpQzH+x9R3Iusg9/d/9d4imFRHg5cLSWT0Z2a4RH6w/zRNLjtRdu76NrTJcZG4GbH6tbso0IJrhmziJV3KZ8NUetpxO49VRbfjwzvY42pnPGLOGJLMgk9XnrScU8waSD8G+b6DLQ/i1CGdQ4CD+PPcnuUUqtGWbAM4Otsyd2JFnh7Vi1V8XufubKC5l5tVN4X7toMccZVjEhD11U6aB0AzfhNkTk86YL3eRkpXPgge78VDvYKtrry/L8nPLyS/JZ1Ko9YRiAkr6hNX/AdeGf6c9ntx6MtmF2dXLlW9hCCGYM6A58+/vwvm064yeu5uDCVfrpvD+z4N7IKx+AopNeKD2cmiGb4JIKVmwJ577f9hHw3qOrJzTi94trK+9viyloZhdfLvQyquV2nLqln3fQMpRGP4BOHsA0NGnI629WrPo1CLTyDCpIoPb+LJ8Ti9cHW2Z+G00vx9IMn6hDq4w6mNIPwO7zSc2XzN8E6OoRMeLy4/z2qoTDGjVkGWzexLk7aq2LNXZcWEHF3MuWl0oJpnJStt9i6HQZtzfk4UQTGo9iZhrMexP2a+iQNOgpa8bK+f0oluwF//98yhvrzlp/Dw8LYZA2ztgx/+ZTWy+ZvgmRGZeEQ/+uJ/f9iUyq38zvr2/C25WFF9fGctiluHt7E3/gP5qS6lbNr8OumIlBrxcc154UDhu9m4sj1mujjYTw8PFgZ8e7MqUHk35blccM345aPzRtIa9BzZ2sPEV45ZjIAxi+EKIcCHEGSFEjBDiXyMACyFChRBRQogCIcQzhijT0ki8ksuEr/ewN+4KH97ZnufCQy1i+EFDkJ6Xzs4LOxkdMtq6QjGT9sGx36HnozeNuXeycyI8OJzNCZvJLsxWQaDpYWdrwxtjb+ONMW3ZejqVu+YZuTO3fiPo+7Qy+EzsNuOVYyBqbfhCCFvgS2A40AaYKIRoU26xDOBxwLKyPBmIgwkZ3PHVbi5nF/DzQ925u4v5prk1Bmtj11IiSxjXfNytF7YUdDplUJN6ftD7qQoXG9d8HPkl+WyI31CH4kyfKT2D+H5KVxKu5DDuy93GHUIxbA54NIX1Lygd7CaMIWr43YAYKWWslLIQWAyMLbuAlDJNSrkfMO9Uc0Zg5ZFkJs7fi5uTHctn96RHswZqSzIppJSsiFlBe+/2hHiEqC2n7ji6WEmONvh1JXlXBbTzbkeIewgrY1bWmTRzYUCoD3/O6omtENw1L4pNJ1ONU5C9Ewx9W0mudvBH45RhIAxh+P5A2W7xC/ppNUIIMV0IcUAIceDy5cu1FmeqSCn5bPM5/rP4CB2aeLBsdi9CGlZ8Y1srJ6+cJOZaDGObj731wpZCQTZsfkN5o7P9PZUuKoRgXPNxHLl8hLjMuDoSaD60blSfFXN60dK3HtN/OcB3O2ONE9XUerQyxGTkOyb9Bq4hDP9mDc01PqJSym+llF2klF0aNmxYC1mmS2Gxjmf+OMonm88yvpM/vzzSDS9XB7VlmSTLY5bjaOvI8ODhakupO3Z+DNdTIPyDKg1ZOLrZaGyFrVbLrwCf+k4snt6D8LZ+vL32FK+uPGH4CB4hlFTV+Zmw/QPDbtuAGMLwLwBlG52bABcNsF2LJDu/iIcX7GfpoQs8ObglH911u9W+OXsrCkoKiIiLYFDgINwcrCP1MxlxEPWFUrMP6FqlVbydvent35vV51dTolMhdbAZ4Oxgy5eTOjGjbwi/RCcw89eD5BUa+Fj53Qadp8K++SY78LkhDH8/0EIIESyEcADuBVYZYLsWR0pmPnd/E03U+Sv8353t+c/gFlb95uytiEyMJLsw27qacza9ooT5DX69WquNbT6WtLw09lw0r1f96xIbG8ELI1rzxpi2bD6VysT50Vy5buC3ZAe8pPS5bHjBJFMo19rwpZTFwKPABuAU8LuU8oQQYqYQYiaAEMJPCHEBeAp4WQhxQQhh2QOuluNsajbjv9pN4pUcvp/albu0SJxbsiJmBX6ufnT36662lLohbgecWg19nlJS8VaD/k364+HowYqYFUYSZzlM6RnE15M7c+pSFhO+3kN8eo7hNu7qDf1fUFIonzW9yCmDxOFLKSOklC2llM2klO/op82TUs7Tf06RUjaRUtaXUnroP2cZomxzIOr8FSZ8vYdinWTJjB70a2mZfROGJCUnhT0X9zCm2RhsbaygyaukWAnrcw+EHo9We3V7W3tGhowkMimSzAIjhiBaCOG3+bFoWhiZeUWM/3oPhxMNmIOn6yPg3VKp5RerOAD7TdDetDUyq/66yJQf9uFb34lls3tym7+72pLMgtXnVyORjGtmJbH3hxZA6nEY+hbY1yz19bjm4yjSFSlj3mrcks5NPVk6qyf1HO2YOD/acGGbtvbKG7gZsbB3nmG2aSA0wzci3+2M5fHfDtMh0IOlM3vSxNNFbUlmQWnsfWffzgTUt4Kmr/xM2Po2NO0NbWreXxHqFUqoV6jWrFMNQhrWY9nsnrTydWPGLwdYtDfRMBtuMRhaDFPGwM1JN8w2DYBm+EZASsl7Ead4e+0pRrTz4+eHuuHuouXEqSpHLh8hMTvRet6s3fUp5GXAsHdqPUbtuObjOJVxijMZZwwkzvLxrufIb9PD6NeyIS8uP8bnW84ZJlZ/6NtQlKuYvomgGb6BKSpRYuy/2RHL/WFNmTuxE072VtAGbUBWxKzA2c6ZoU2Hqi3F+GQmQ/RX0O4uaNyh1psbETwCOxs7Vp7XYvKrg4uDHd8+0IXxnfz5eNNZXltlgFj9hi2h0/1w4Hu4ct4wQmuJZvgGJK+whBm/HPw7xv7NsW2x1RKgVYvcolzWx61naNOhuNhbQRPYtndB6mDgywbZnKeTJ/2b9Gdt7FqKdFomk+pgb2vDR3fdzoy+IfwclcDjiw9TUFzLWP3+L4CtA2x9yzAia4lm+AbiWm4hk7+LZtuZNN654zYtxr6GbE7cTG5xrnU056SdgiOLoOs08Awy2GbHNR9HRn4GOy7sMNg2rQUhlFj9F0eEsvboJR78cT/Z+bX44XTzU6KuTiyH5IOGE1pDNMM3AJcy87hrXhTHk7P4anInJndvqrYks2VFzAoC3ALo7NtZbSnGZ/Pr4OAGfQ2bMbyXfy+8nb21zttaML1vMz6++3b2xWUwcX40l7Nr8YJWr8fBxRs2vab6y1ia4deSmLTrTPhqDymZ+Sx4qBvhtzVSW5LZciH7AvtT9jO22VjLfzqK3w1n10PvJ8DFy6CbtrOxY3TIaHZe2El6nulEiJgb4zs1Yf6ULpxPy+GueXtIyqjhgPGObtDvOYjfCec2GVZkNdEMvxYcu5DJ3d9EUVgiWTwjTEttXEtK48dHNxutshIjIyVsehXcGkPYLKMUMabZGEpkiZYnv5YMaOXDwmnduZZXxISv93A2tYYDzXSeCp7BsPk1UDHfkWb4NSTq/BUmzo/GxcGWP2f2oG1j7YWq2iClZG3cWjr5dKJxveqlFTA7Tq6E5AMw4MUav2R1K5p7NqeVZysiYiOMsn1rolOgJ0um9wDg7m+iavZWrp0DDHpVyZn/12IDK6w6muHXgM0nU5ny4z783J34c6Y2yLghOHP1DHGZcYwMGam2FONSUgRb3oCGraHDJKMWNSJkBEfTj5KUlXTrhTUqpZWfG3/O7El9J3smf7eX3TE1aCprewc07qTkzC8y4rCLlaAZfjVZfvgCM349SGs/N36f0QM/dye1JVkEEbER2Ak7hjQdorYU43LwJ+WV+yFvgJFzBA0PUsYQiIjTavmGILCBC3/O7EGApwsP/rif9cdTqrcBIWDIm5CVrFrKBc3wq8GCPfE8ueQvugV5sXBamDZoiYHQSR0RcRH09O+Jp5On2nKMR0E2bHtfSaHQwvgvlTWq14hOPp1YG7fWOKM8WSE+9Z1YMiOMtv71mb3wIH8cqObTU3AfJeXCzk9UGRlLM/wqIKVk7pZzvLbqBEPa+PLjg12p52intiyL4VDqIVJzUxkRPEJtKcZlz1zITVdqeXUUhTQyZCRxmXGcuaqlWjAUHi4O/Ppwd3o19+bZP4/y/a5qDi05+HUozIadHxlDXqVohn8LpJS8G3GKjzYpwxF+PVlLlWBoIuIicLZzZkDAALWlGI/rabDnC2gzDprU3TsGQ5oOwU7YaZ23BsbV0Y7vpnRh+G1+vLXmJJ9uPlv1pyjfNnD7JNj3LVyr2/4VzfAroUQneXH5cebvjGNKj6b8787bsbPVDpkhKSopYmPCRvoH9LfsVAo7P4bifBj4Sp0W6+nkSU//nkTERaCTujot29JxtLNl7sSO3Nm5CZ9uPse7Eaeqbvr9n1f+1/H4t5p7VUBRiY6nfj/Cb/sSmd2/Ga+PaYuNlhfH4Oy5uIfMgkxGhYxSW4rxuJakJNDqMAm8m9d58SODR5Kam8qh1EN1XralY2drw4cT2jOlR1Pm74zjxeXHq5Z0zSMAujyspNZIP2d8oXo0w78JBcUlzF54iJVHLvLssFb8NzzU8t/8VIm1cWvxcPSgR+MeaksxHqW1uH7PqVJ8/4D+ONs5a9E6RsLGRvD6mLbM7t+M3/Yl8tTvRygqqcLTVJ+nwM4JIt81vkg9muGXI7ewmEcWHGDTyVReH92GOQPqvkZmLeQW5bItaRtDmw7F3sZCxwtIP6fU4ro8rNTqVMDF3oUBAQPYmLCRohItg6YxEELw3/BQnh3WipVHLjJ74aFbZ9qs56O8aX1iGVw6Wic6NcMvQ1Z+EVN+2MfumHQ+vLM9U3sFqy3JoolMiiSvOI8RIRYcnRP5rlKL6/OUqjJGhowksyCTPRf3qKrD0pkzoDmvj27DppOpPLLgALmFxZWv0PMxcHJXXsaqAzTD13M1p5DJ8/dyOPEacyd24u4uVjC0nspExEXg5+pHR5+OaksxDpeOKrW3sFlKbU5FejTugYejB2vjtPFujc3UXsF8eGd7dsekM+WHfWRVll7Z2QN6PaEk0kvca3RtmuEDl7MLuPfbaM6kZvPtA50Z2V7LeGlsruZfZU/yHoYHD8dGWOhluPVtpfbW8zG1lWBvY8/QpkPZlrSN3KIaZn3UqDJ3dwlg7sROHE68xv3f7eVabmHFC3efAa4+sOVNo6dPttA7repcyszjnm+iSMzI5cepXRkY6qu2JKtgU8ImimUxI4MtNHdOYjSc26DU3pw91FYDKLl18orziEyKVFuKVTCyfSPm3deZU5eyuffbaNKvV5BT38EV+j4LCbsg1rjnxqoNPykjl7u/iSItu4CfH+5Gr+beakuyGtbGrqWZezNaerZUW4rhkRK2vKXU2rrPUFvN33T06Yifq58WrVOHDG7jy/dTuxB/JYd7v40mNSv/5gt2ngLugUav5Vut4cel53D3N1Fk5RWz8JHudA0y7CAUGhVz6folDqUdYkTICMsMd42NVGprfZ9Vam8mgo2wYXjwcPYk7+Fqfg1S/GrUiD4tGvLTg924dC2Pu7+J4sLVmzSp2TlC/+fg4mE4vcZoWqzS8M+mZnP3N1EUFOv4bVoYtweYxiO3tVBawxwePFxlJUZASqWW5h6o1NpMjJHBIymWxWyM36i2FKsiLKQBvzzSnYycQu75JpqEKzn/Xqj9vdCghdL3Y6RBUqzO8I8nZ3Lvt9EIYMn0MNo0rq+2JKsjIi6C9g3bE+BmgZFQp9cotbT+zyu1NhOjpWdLmrk305p1VKBToCe/TQsjt7CYu+ZFEZNWbvQsWzsY+BJcPg3H/jCKBqsy/CNJ15g0Pxpne1t+n9GDFr5uakuyOmKuxnD26lnLzIypK1FqZ94tof09aqu5KUIIRoSM4FDaIS5dv6S2HKvjNn93Fk/vgU7CPd9Ec+pS1o0LtB4Lfu1h23tQXElkTw2xGsM/EJ/Bfd/txcPFgcXTw7RRqlRiffx6bIQNw4KGqS3F8BxfqtTO+r+g1NZMlNKBUbTxbtWhlZ8bv88Iw97WhonzozmenPnPTBsbGPYO9HkajBCubBWGH3X+Cg/8sA8fN0eWzAgjwMuCszKaMFJK1sevp6tvV7ydLSwiqqRYGdzE9zYlBbIJE1A/gLYN2rIufp3aUqyWkIb1WDIjDFcHOybNj75xnNzgvtDpAaNUGize8Heeu8yDP+3D38OZxdPDaORunEGjNW7N6YzTJGQlEB4crrYUw3N0MWScVwYmtzH922p48HBOXjlJYlai2lKslqYNXFkyIwwPFwfu/34f++ONPwKW6V+ZtSDydBoPLzhAUANXFk8Pw6e+Nv6smqyLX4edsGNw4GC1pRiW4kLY9gE07gitzKNvorRJbX38epWVWDdNPF34fUYPfNwcmfLDPvacr8Hg6NXAYg1/w4kUpv9ygFa+bvw2LYwG9UwvYsKakFKyIW4DYY3D8HCysDDYw79AZiIMeLnOhi6sLaU5jNbFac06auPn7sTiGWH4ezjz4I/72X72stHKskjDX3NUSU96m787vz7SHU9tsHHVOZp+lIs5Fy0v9r4oH3b8DwK6Q/NBaqupFuFB4cRciyHmaozaUqweHzcnFk8PI6RhPaYtOMCWU6lGKcfiDP9qTiHPLz1G50BPfnm4O+7OFppn3cxYH7ceext7yxu39uCPkH0RBppP7b6UoUFDsRE2WrOOidCgniO/TetOKz83nv3zKNcLbpFauQaYbuxYDfF0deDXR7rT0rceLg4Wt3tmSYmuhA3xG+jj3wc3Bwt696EwB3Z+BEF9lMgKM8Pb2Zuuvl3ZEL+BOR3mWGaaCzPDw8WBhdO6k3gll3qOWpROlegQ4KGZvQlxKO0Ql/MuW150zr75kHNZqd2bKcOChxGfFc/pjNNqS9HQU9/Jntv83Y2ybYs0fA3TYkP8BpztnOnXpJ/aUgxHfhbs/gyaD4bAMLXV1JjBgYOxE3Zas46VYBDDF0KECyHOCCFihBDP32S+EEJ8rp9/VAjRyRDlapg+xbpiNiVsol+TfrjYW9ALb3vnQV4GDHhJbSW1wtPJk7DGYWyI34A08uAbGupTa8MXQtgCXwLDgTbARCFEm3KLDQda6P+mA1/XtlwN82Bfyj4y8jMID7Kg5py8q7DnC2g1EvzNv+4SHhRO8vVkjqUfU1uKhpExRA2/GxAjpYyVUhYCi4Gx5ZYZC/wsFaIBDyGENo6gFbA+bj2u9q70btJbbSmGY88XUJCpvFVrAQwMHIi9jb0Wk28FGMLw/YGkMt8v6KdVdxkAhBDThRAHhBAHLl823gsIGsanqKSIzYmbGRgwEEdbC3nxLeeK0pzT9g7wu01tNQbBzcGN3v692Ri/EZ3UqS1Hw4gYwvBvFstVvjGwKssoE6X8VkrZRUrZpWHDhrUWp6Eeey7uIbsw27Kic3Z/CkW5SkZMC2J48HDS8tI4lHpIbSkaRsQQhn8BKDuSRRPgYg2W0bAw1sWvo75DfXo06qG2FMOQnaqEYra7Gxq2UluNQenXpB9Otk5atI6FYwjD3w+0EEIECyEcgHuBVeWWWQU8oI/WCQMypZTa6AsWTH5xPpGJkQxpOgR7Wwt523nXx1BSCP3+q7YSg+Ni70K/gH5sSthEsc7wb3hqmAa1NnwpZTHwKLABOAX8LqU8IYSYKYSYqV8sAogFYoD5wOzalqth2uxM3kluca7lNOdkXoADP0DHydCgmdpqjMLwoOFk5GewL2Wf2lI0jIRBXkeVUkagmHrZafPKfJbAHEOUpWEerI9bj5eTF118u6gtxTDs+J8yQHnfZ9VWYjR6N+mNq70rG+I30LNxT7XlaBgB7U1bDYOTW5TLjgs7GNp0KHY2FpDiIiNOSYHceSp4BKqtxmg42joyMGAgmxI2UVRSpLYcDSOgGb6GwdmatJX8knzLac7Z8X9gY6eMM2rhhAeHk12Yze6Lu9WWomEENMPXMDjr49bj6+JLR5+OakupPenn4K/foMvDUN/y3xXs0agH7o7u2ktYFopm+BoGJbMgk90XdzM8eDg2wgIur23vg50T9H5SbSV1gr2tPUOaDiEyKZK84jy15WgYGAu4IzVMidKwPosY2Sr1JBxfCt1nQD3reQlwRPAI8orz2J60XW0pGgZGM3wNg7Iubh1B9YNo7dVabSm1Z9u74OgGPR9XW0md0smnEz7OPkTERdx6YQ2zwjINPyddyWioUaek5aaxP2U/4cHh5j960sUjcGo1hM0GFy+11dQptja2DA0ayq7kXWQVZqktR8OAWJ7h512DzzspcdMadcrG+I1IpGU050S+C04e0MM63xEcETyCIl0RWxK2qC1Fw4BYnuE7e0DrUUrOk8xktdVYFevi1hHqFUqIe4jaUmpHYjSc2wC9Hgcn4ww1Z+rc5n0bAW4BWrSOhWF5hg/Q7zmQOiV+WqNOSMpO4mj6UfOv3UsJW94EVx/oPvPWy1soQgjCg8LZm7KX9Lx0teVoGAjLNHzPptDlQeXtyCvn1VZjFayPU7Ismv3IVue3QsJuJYWCg6vaalRlePBwdFLHxviNakvRMBCWafgAfZ4BG3sljlrD6KyLX0eHhh1oXK+x2lJqTmnt3j0QOk9RW43qtPBsQXOP5lrKZAvCcg3fzRfCZsKxPyD1hNpqLJqYqzGcu3rO/JtzTq2GS0eg//NgZyEjdNWSEcEjOJx2mEvXtWzmloDFGX5RSRGrzq/ir8t/KfHTjm6w9R21ZVk0EXER2AgbhgYNVVtKzdGVwNa3wbsltL9HbTUmQ2k+pHXxWudtXbE/ZT8RsRFGGZfA4gwf4P/2/x8LTy5U4qd7Pg5n1sKFA2rLskiklKyLW0c3v254O3urLafmHP0d0s/AgJfA1gIyfBqIALcA2nm306J16pAfj//Ixwc/NkpqEoszfHtbe4YFDSMyKZKcohylWcfFW2mb1TA4x9OPc+H6BUYEj1BbSs0pLlTeqm10O7Qeo7Yak2N48HBOZ5wmNjNWbSkWT0Z+Bnsu7mFkyEjN8KvKqJBR5JfksyVxi9Kk0+dpiNsOsdvUlmZxrItfh72NPYOaDlJbSs05tACuJcLAV8HGIm+JWjEsaBgC8XcklobxWB+3nhJZwsiQkUbZvkVe3bc3vB3/ev6sOb9GmdDlIajvD1veUiIxNAxCia6EDXEb6O3fm/oO9dWWUzMKc5W3sgN7QnMz/tEyIj4uPnT168q6uHVI7f4xKmtj19LSsyUtPVsaZfsWafhCCEaFjGJvyl7SctPA3kl5GSv5AJzR2iINxaG0Q6TlpZl3dM7++XA9BQa9Auae/8eIhAeHE58Vz6mMU2pLsVgSshI4mn6UUSGjjFaGRRo+wMiQkeik7p/Opg6TwKuZEomh06krzkKIiIvA2c6Zfk36qS2lZuRnwq5PoPkQaKqN4VoZQwKHYCfstM5bIxIRG4FAGLUCZbGGH+weTNsGbVkbu1aZYGsPA16EtBNw/E91xVkARSVFbErYRP+A/rjYu6gtp2bs+ULJqjrwZbWVmDweTh709O/Jurh16KRWYTI0UkrWxK6hm183/Fz9jFaOxRo+KJ23pzJOcf6aPr1C2/Hg2w62vgXFBeqKM3N2Je8isyCTkcHG6VwyOtkpEPUFtBkHjTuorcYsGBk8ktTcVA6mHlRbisVxLP0YidmJRuusLcWiDT88OBxbYftPLd/GBoa8oURk7P9eXXFmzurY1Xg5edHT30ybQra9DyWFMOhVtZWYDQMCB+Bq78qq86vUlmJxrIldg4ONA4ObDjZqORZt+N7O3oQ1DmNt7Np/HkObD4KQ/komzfxMNeWZLZkFmWxL2saI4BHY29irLaf6pJ+DQz8r0VsNmqmtxmxwtnNmaNOhbIzfqI13a0CKdEVsiN9A/4D+uDm4GbUsizZ8UB5DL+Zc5HDa4X8mDn4D8jJg16fqCTNj1setp0hXxJhmqBiDJgAAIABJREFUZvqS0ubXwd4Z+v5XbSVmx+hmo8ktzlXecdEwCFEXo8jIzzBqdE4pFm/4gwIH4Wzn/E+zDihttu3uguivtEFSasCq2FU092hOqFeo2lKqT+JeOL0Gev3HqgYmNxSdfTvT2LUxq8+vVluKxbAmdg3uju709u9t9LIs3vBd7F0YGDiQDfEbKCwp/GfGwJeVQVK2vaueODMkPjOeo5ePMqbZGPMbt1ZK2PQq1POFHnPUVmOW2AgbRjUbRfSlaFJzUtWWY/bkFOUQmRhJeFA49rbGbx61eMMHJVonqzCLnck7/5noGQRdp8GRRZCmvUxSVVbHrsZG2Bg9msAonImApGgl/bGVD25SG0aHjEYndUTERagtxezZmriV/JL8OrufrMLwwxqF4eXkdWOzDkDfZ8DBTWnT1bglOqljzfk1hDUKw8fFR2051aOkWDnPDVpAxwfUVmPWBLkH0b5he1adX6WlWqgla2LX4F/Pnw4N6yY02CoM387GjuHBw9mWtI2swqx/Zrh4Qe8n4Ox6iN+tnkAz4WDqQS7mXGR0s9FqS6k+R36F9LMw+DUt/bEBGBMyhphrMZzOOK22FLPlcu5loi9FMzJkZJ01j1qF4YPSrFOkK2JzwuYbZ4TNArfGStuuVluplNXnV+Ni58KgQDNLMlaYA5HvQUB3CDV+JIQ1EB4cjr2NvRaTXwtK31quy+ZRqzH8tg3aElQ/iDWxa26cYe+spFxIPgAnV6ojzgzIK85jY8JGhgYNxdnOWW051SPqKyVB2pA3tQRpBsLd0Z3+Af2JiIugSFekthyzZG3cWto2aEuIe0idlWk1hi+EYETICPan7P/3+JwdJkHD1rDlDSjRLt6bEZmoDChjdrH3Oemw+zOlZh8YprYai2J0yGgy8jOIuhilthSzI/ZaLCevnKzz4AerMXyAUcHK4/zauHKdtza2SsqFjFg48IMKykyfVbGraOTaiM6+ndWWUj22vQ9FuTDoNbWVWBy9/Xvj6eipNevUgNJot7pOLW5Vhh9QP4DOvp1Zdm7ZvzP+tRgKwf0g8l3IzVBHoIlyOfcyURejGBUyyijDrhmN1JPKD3iXB6GhcQaUsGbsbe0ZHjycyMTIG4MhNCqlWFfMypiV9PHvU+fjQJvR3WsYJrSYQFJ2EgdSyg1qLgSEvw8FWYrpa/xNRFwEOqkzr+gcKWH988oQlwNeUluNxTKm2RgKdYVsjN+othSzYeeFnVzOu8yEFhPqvGyrM/whTYfgZu/G0nNL/z3Ttw10eRgOfK/UDjUAWHV+Fe292xPsHqy2lKpzJkIZx3jAi0r4rYZRaNOgDSHuIVqqhWqw7NwyGjo3pE+TPnVettUZvpOdEyNDRrI5YTOZBTfJljngRXCsr9QOtTBNzmSc4ezVs+ZVuy8ugA0vQcNQJSOmhtEQQjC62WgOpR0iKStJbTkmT2pOKjuSdzC2+VjsbOr+fZBaGb4QwksIsUkIcU7/37OC5X4QQqQJIY7XpjxDcWfLOynUFf47RBOU2uCAF5Xa4Rnt1fFV51dhZ2NHeFC42lKqTvTXcDUOhr2rjHSmYVRGhYxCIG5+P2ncwMrzK9FJHeObj1el/NrW8J8HtkgpWwBb9N9vxk+AyThGK69WtG3Qlj/P/nnzV8O7PKTUDje8ZNUjYxXpilgbu5a+/n3xcPJQW07VyE5VxjpoOVwZ+0DD6Pi5/n97Zx5e07XG4XdlkFFIQgQRMQeRiCGoqRSlptasaNCWjlRvB1RruFqdtW6rFcOlRMTUKlpjxVTVxpSEJIbEEEMSSSRIItO6f+xwkZDxZO/k7Pd5znNy9ll77d9ZD99ZZ+1v/T5nfGr63AtmOvmTI3PYeGYj7ZzbUceujioaShrwBwIrcv9eATybXyMp5T5AU6kvgxsP5uyNs4ReD837pqk59J6nzBL/+qHsxWmEPy7+QUJ6AoMbl/3NpWLzxxzlS/rpj9VWYlQMajiIy7cu6zn5j+Hw1cNcvnVZ1f9PJQ34NaSUVwFyn8uNo1Yftz5YmVmx8czG/Bs06K7MEvd9ocwajZB1keuoZVOLjrU6qi2lcFw+Csf8of0reiWrMqZH3R44WDqwNnKt2lI0y8YzG6liUYXurt1V01BgwBdC7BJChOXzGGgIQUKICUKIYCFEcHx8vCEuAYBtJVt6u/Xmt+jfuJ15O/9GT3+szBZ3zzGYDq0SnRzN4WuHGdpkKKYmpmrLKRgpYds0sKkGXd5VW43RUcm0Es81fI6gmCCu3b6mthzNkZSexO6Lu+lfvz8Wphaq6Sgw4Espe0gpPfJ5bAJihRA1AXKf40oqSErpJ6VsI6VsU726YSsSDWo0iLSsNLZFb8u/gWMDxVztuL8yezQi1kauxczEjGcb5rtKpz3CNihe9099BJZV1FZjlAxpPAQpZf4pz0bO5nObyczJZFAjdW7W3qWkSzq/Ar65f/sC5cp9zKu6Fw2qNHj0sg4os0WbakaVppmelc6mc5vo4dqjzHcCFouMVMXt1NkTWo5SW43R4lLZhY61O7Lh9AbdUO0+pJRsPLMRz+qeNLJvpKqWkgb8T4GeQogzQM/c1wghagkh7uU0CiECgENAEyFEjBDixRJet1QQQjC48WBCrodwOul0/o0s7ZRZ46XDEBJYtgJVYtv5bdzMuMmwJsPUllI49n8FKZehz2eKL5KOagxrPIz4tHj2XtqrthTNcCL+BOeSzzGk0RC1pZQs4EspE6SUT0kpG+U+J+YevyKlfOa+diOllDWllOZSShcp5dKSCi8t+tXvh7mJ+eNn+S1Hg0tb2D7dKHx21kaupX6V+rSp0UZtKQUTF6G4YXqOgLpPqK3G6Oni0gVnG2cCI41jclQYNpzZgLWZNU+7Pa22FOPbafsw9pb29HDtweZzm7mT/YicexMT6P8tpCfDzg/LVmAZcyrhFKHXQxnWZJj2i5Tn5MCWt8DCVk/D1AimJqYMaTSEv67+xYWUC2rLUZ1bGbfYfn47z9R/Bmtza7Xl6AEfYFDjQaRkpOSthnU/NZpDhzfg2Co4f6DsxJUxayPXYmlqWT6sFI79BBcPQa+5yn0WHU0wqNEgzIQZ6yLXqS1FdX6L/o20rDRVjNLyQw/4gI+zD7Vtaz9+WQeg6/tQtS5sfqtC7sC9mXGT36J/o0+9PthVslNbzuO5GavcqK3bSb9RqzGqW1enm2s3fjn3C+lZ6WrLUZWNZzbS2L4xzR2bqy0FAL2aM2AiTBjcaDALji3gYspFXO1c829YyRr6fg3+g+HAfHjyUU4S5ZMtUVtIy0rT5M3azMxMYmJiSE/PDSCpCdB1CVR2hgjjLqRtaWmJi4sL5uba8Q0a1mQYOy/sZOeFneXj16IBiEiM4GTCSab5TNPM8qge8HMZ2HAgC48vJCAigPd93n90w0Y9wGOwkhniMRiqqZtmVVpIKVkbuZZmjs3wqOahtpw8xMTEULlyZdzc3BB3bkJiOlRuAJVrqi1NVaSUJCQkEBMTQ7162rGvbufcDjc7NwIjA4024AdEBGBpalnmZQwfh76kk4uTtRN96vVhw5kN+dsm38/T85Ti51umVJjc/GNxxzh74yzDmwxXW0q+pKen4+joiJA5kHwJTC3AtobaslRHCIGjo+P/f/loBCEEQxsP5UT8CSITI9WWU+ZcT7vO5nObebbhs1Sx0M5GQD3g34dvc1/SstJYf3r94xtWrgE9ZsP5/XB8ddmIMzCBkYFUNq+saRtkIQTcugbZGVC1DpSncosGRCvLBQ8zsOFALEwtjNJfZ3X4arJysnih2QtqS3kA/X/MfTRxaEKHmh3wD/cnIzvj8Y1b+UKd9rDjA7h9vWwEGojE9MR7a61aSB17JJlpcCsOrByU0oU6mqaKRRWednuaLVFbHu1XVQFJzUwlMDKQHnV7qGaD/Cj0gP8QY5uPJT4tnt+iCyh+YmIC/b+BO7dgx4yyEWcgfjn7C5k5mZq8WXsPKeHGRTAxA7vaqkgQQjBmzJh7r7OysqhevTr9+vUrUj9ubm5cv174ScJ3331Hw4YNEUIU6TwtMLzJcFKzUtkatVVtKWXGz2d/JiUjBd/mvgU3LmP0gP8QHWp1oJF9I1acXJF/cZT7cWoKHSfDiQA485gcfg2TmZPJ2si1tK7RmgZVNWwpnHELMlOVYG+qTq6BjY0NYWFhpKWlAbBz505q1zb8l0/Hjh3ZtWsXdevWNfi1SpsW1Vrg7uBOQESAURRHycrJYuWplXg7eeNV3UttOXnQs3QeQgjB2OZj+eDABxy8cpBOtTs9/oQu70LEVtj0Grx6CGwcy0ZoKfF79O9cvnWZqT4aTjGNC4e0G2DRAKzsmb35JKeupJTqJZrVsmNm/4Jzpfv06cPWrVsZMmQIAQEBjBw5kv379wOQmJjI+PHjiYqKwtraGj8/Pzw9PUlISGDkyJHEx8fj4+PzwERi1apVLFiwgIyMDNq1a8fChQsxNX3QD8jb27tUP2tZIoTAt7kv0/ZPY8+lPTzlWrGrkO2+uJvLty7zblttWnTrM/x86OPWBycrJ5afXF5wY3NLGLwY0pJg86RylbWTnZPNktAlNLZvTFeXrmrLyZ+sO7DhZeUGbVVXUPkG5YgRI1izZg3p6emEhITQrl27e+/NnDkTb29vQkJC+OSTT3jhBeWG3ezZs+nUqRPHjh1jwIABXLx4EYDw8HACAwM5ePAgx48fx9TUFH9/f1U+lyHp7dYbF1sXFocsLvhXczlGSsnysOXUtavLky5Pqi0nX/QZfj6Ym5ozqtko5h+ZT3hCOE0dmz7+BOcW0H2GsvPzuD94jy4boSVk18VdRCdH80XXLzSb6cGejyE2VCkun1uQvDAzcUPh6enJ+fPnCQgI4JlnnnngvQMHDrBhg+IF3717dxISEkhOTmbfvn1s3Kjs4u7bty/29vYA7N69myNHjtC2bVsA0tLScHIqN0XjCo2ZiRkvtXiJWYdm8eeVP+lYu5xUUCsiR2KPEJYQxoftP9Rs0SB9hv8IhjQegrWZNStOrSi4MSg+O26d4ff3ITHasOJKASklfiF+uNm50dO1p9py8uf8ATi4AFqPVfY9aIQBAwbwzjvvMHLkyAeO5zd7vftFmt8XqpQSX19fjh8/zvHjx4mMjGTWrFkG0aw2AxoMoIZ1DRaFLKqws/wVJ1dgb2Gv6Y1mesB/BHaV7BjceDDborcVrmSbiSk8+wMIU/h5ImRnGV5kCdgbs5fTSad52fNlbc5G0pPh51fAoR700pYT5vjx4/noo49o0aLFA8e7dOlyb0kmKCiIatWqYWdn98Dx33//naSkJACeeuop1q9fT1ycUiguMTGRCxcqpsOkuak54z3GcyzuGMGxwWrLKXWikqMIiglihPsIrMy0Mzl5GD3gP4bRTZWlmVWnVhXuhKp1oO9XSrGUA/MNqKxkSClZHLKY2ra16VOvj9py8ue3dyHlCgxarNgfawgXFxcmT56c5/isWbMIDg7G09OTqVOnsmKF8utw5syZ7Nu3j1atWrFjxw5cXRWvpmbNmjF37lx69eqFp6cnPXv25OrVq3n6XbBgAS4uLsTExODp6clLL71k2A9oIAY1GoSjpSOLQxarLaXU+enkT1iYWjDCfYTaUh6PlFKzj9atW0u1eW/ve7KdfzuZciel8CetGyflbAcpY44YTlgJ+PPyn9JjuYcMjAhUW0r+hK6XcqadlHvm3Tt06tQpFQVpn/IyPstCl0mP5R7yRNwJtaWUGvGp8bLVT63knD/nqC1FSiklECwfEVP1GX4B+Db35XbmbTacLkJh5r5fKT4vG1+GDO3tMPQL8cPJykmbBcqTLyseRbXbQOd31FajU8oMazKMKhZVKtQsf03EGjJzMhnTbEzBjVVGD/gF0MyxGe2c27EyfCWZ2YUszGxlr6znJ5yFHdqqkHU09ijBscGM8xhHJdNKast5kJwc+OVVyM6EQX6qbbDSMRw25jaMbjqaoJigCmGqlpqZyprINXSr0w23Km5qyykQPeAXAt/mvsSlxvHz2Z8Lf1L9rkrmTvBSCCvCrwMD4xfqh4OlA4Mba6MCzwPs/xKi98LTn4Cjhnf96pSI55s+j625LYtDy/8sPzAykOQ7yZq0UcgPPeAXgk61O9HKqRXfH/+eWxm3Cn/iUzMVg7VfXoerIYYTWEhOXj/JwcsHGdNsjPYyCSK2Kjn3niOUNEydCotdJTtGuI9gx/kdRCVHqS2n2CSmJ+IX4qfEhxqt1JZTKPSAXwiEELzb9l0S0xOLNisxqwTDVyqbhtY8r7qrpl+IH5UrVWZEE41lEsSFw8YJUMtbMaTT6iYwnVJjTLMxWJhasDR0qdpSis3C4wtJy0rj3TbatFHIDz3gFxKPah70r9+fladWEnMzpvAn2jrB8FVwOx7WvqCsT6vA6aTT/HHpD0Y3HY1tJQ2lOaYmQsBIMLeG4f6a2mClYzgcLB0Y2mQoW6O2cunmJbXlFJmzSWdZd3odQxsPpX7V+mrLKTR6wC8Ck1pNwlSYMv9IEXPsa7eCAf+BCwdh2zTDiCuARScWYW1mzaimGir4nZ0F68dDcozypVhFHdvjwqKWPfKoUaNo0qQJHh4ejB8/nsxMdSYNpc3Y5mMxESYsCV2itpQi82Xwl9iY2fBay9fUllIk9IBfBJxtnBnnMY4dF3ZwLO5Y0U72HAZPTIJ/FsOR5QbR9ygOXTnEjgs7eKH5C5oqt8aumRC1B/p9Da7tCm6vMmrZI48aNYqIiAhCQ0NJS0tjyZLyFyDzw8naiRHuI/j5zM+ciD+htpxCc+DyAQ5eOchEr4nYW9qrLadI6HlvRWRs87FsOL2Bz//+HP++/pgUpcxej1kQexK2vgPV3cG1vaFk3uNO9h3m/jUX18quvNRCQzs0T6yBQ99B25ehVRHLwP0+Fa6Flq4e5xbQ59MCm6lhj3y/SZuPjw8xMUVYUtQ4r7d8ne3ntzPn0BzW9FuDuYm52pIeS1ZOFl/+8yWulV153v15teUUGX2GX0Ssza2Z3HoyYQlhRa/iY2IKQ5YqFgyBY5RNRgZmcchiLt68yIz2M7AwtTD49QrF5aPw6ySo2wl6z1NbTZFQ0x45MzOTlStX0ru3dusOFxUbcxum+0zndNJp/E9p3xp6/en1nEs+x9tt3sbcVNtfTvmhz/CLQb/6/fAP9+fbo9/So26PoqU4WtnDiABY0kPJ3Bm7xWD1WaOSo1gatpS+9fvSoVYHg1yjyCTHwJpRyk7kYSvuWR4XiULMxA2FmvbIr732Gl26dKFz586G+Giq0d21O0/WeZKFJxbSy60XtWxrqS0pX1IyUvj++Pe0qdGG7nW6qy2nWOgz/GJgIkx4r+17xKbGFq5IysM4ucPgJcqyhP9QpS5uKSOl5N+H/o21mbV20sZSrsDyfkq5wpGrwaaa2oqKhRr2yLNnzyY+Pp6vv/665B9AYwghmO4zHYCPD3+sWftkvxN+JN9J5r2272m3fkQB6AG/mLSu0ZqedXvy37D/EpcaV/QOmvRWlncu/Q2rh5W6586mc5sIjg1mSuspOFppoOzizWtKsL99HUZvVNbMyyllbY+8ZMkStm/fTkBAACYmFfO/bE3bmrze8nX2xexj10Xt1Ye+lHIJ/wh/BjYcWHBBJA1TMf/1lBFTWk8hKyeLBUcXFK+D5s8pnjEXD8Hq4ZCRWiq6ktKT+Cr4K7ydvBnUaFCp9FkibsYqwf5WLIzeAHXaqq2oRJS1PfIrr7xCbGwsHTp0oGXLlsyZM8ewH1AlRjUdhbuDO58e/rRoO9rLgK+PfI25iTmTvCepLaVkPMpGUwsPLdgjF8RX/3wlWyxvIf+++nfxOzkRKOXMKlKuGCBlRmqJNX2w/wPZckVLeSbxTIn7KjE346T8T1sp59aU8vzBYndTXux/1aKijE9IXIhssbyF/OSvT9SWco+gi0HSY7mH/PH4j2pLKRTo9siGY6LXRNyquPHO3ncKVxkrPzyHKe6aUXuVG7mZ6cXW88+1f9h0bhNjPcbS0L5hsfspFW5fh58GwI2LMGot1H1CXT06mqdF9RaMcB9BQEQAYdfD1JbDhZQLTNs/jaYOTcuNQdrj0AN+CbExt+Gbbt9wJ/sOb+15izvZd4rXUcuRMPA7OPcHBI6GrKL3k5GdwZxDc6htW5sJnhOKp6O0SE2EnwZCYhQ8HwhundTVo1NueNP7TapZVWPOoTlk5ahXKvR25m0m/zEZUxNT5nebj6WZpWpaSgs94JcC9avU55NOn3Ay4SRz/5pb/CwD79HQfwGc3amkLqanFOn0H0/8yPmU88xoP0NdN8yUK8rM/voZGBmgWEXr6BSSypUqM9VnKuGJ4cXLgisFpJR8ePBDolOi+bzL59S21bbtR2HRA34p0d21OxM9J/LL2V9YG7m2+B219oX+3yoz/cXdFCfJQrDu9DoWhy7m2YbP0qm2irPp6H3wY2dIiFJSLxuUz3xlHXXpWbcnPev2ZMHRBUXf4FgKLAtbxs4LO5nSaop29rCUAnrAL0Vea/kanWt35tO/P+Vo7NHid9R6LPj+qszwF3eH0PWPbb4tehv/PvRvurh04aMOHxX/uiVBSjjwjbKMY+0AE/ZAwx7qaNEp9wghmNd5Hm2c2/DBgQ/Ye2lvmV374OWDfHv0W3q79a4Q6/b3owf8UsREmPBpl0+pZVuLt4PeJvZ2bPE7c+sEE/eBsydseBF+fx+yMvI0O3D5ANMOTMPbyZsvu36pjhdJerJy32HXTGg6AF7+A6o3KXsdOhUKC1MLFnRbgLuDO//a+y/+ufaPwa956eYl3tv3Hg3tGzL7idnldoPVo9ADfiljV8mOb7p9Q2pWKm/vfZuM7LxBuvCd1VSsF9q9Cod/hBX9IOX/edpHY48yZc8UGlVtxHdPfafOun3sKfDrBpG/Q6+PYehyg1lFqI1a9sgvvvgiXl5eeHp6MmTIEG7d0laOuiGxrWTLDz1+oJZtLd78401OJZwy2LVSM1N5a89bSCTfPvkt1ubWBruWWpQo4AshHIQQO4UQZ3Kf83iFCiHqCCH2CCHChRAnhRB5d6xUMBrZN2Jux7mExIfwyeFPSrZV3NRc8Y4ZvBSuhcGizhAVRERiBG/sfgNnG2d+6PEDlSuVcZCVEk4EwpKnFKsE383wxBsVulqVWvbI8+fP58SJE4SEhODq6sp3331n8GtqCXtLe/x6+lGlUhVe2fmKQcoi5sgcZh2axZmkM3ze5XPq2NUp9WtogZKap00FdkspPxVCTM19/f5DbbKAf0kpjwohKgNHhBA7pZSG+6rWAL3cevFiwossDVtKfFo8s5+YTTWrEnjHtBgCNZpD4BjOrx7MxDp1sLGsil9Pv7K3TojeD7vnQMzf4NpBmdVXdi6zy3/292dEJEaUap/uDu687/PwP928qGGPbGdnByiZI2lpaRVumaEwONs449fLjxd+f4GJOyfyU++fqGlbs1T6vnb7GjMOzODwtcNM8p6kbtKDgSnpks5AYEXu3yuAZx9uIKW8KqU8mvv3TSAcqBg5TgUwqdUkpvpM5fDVwzy36Tl2XSihR4hTU66MXsMEt0aQnYnf2TBqbv9IyXUvC64cg5XPKUtLyTFKNpHvljIN9mqjlj3yuHHjcHZ2JiIigjfffNPwH1SD1LWri19PP25n3GbCzgnEp8aXqD8pJZvPbWbQpkGEXA9hZoeZ2qoZYQgetQW3MA/gxkOvkwpo7wZcBOwe02YCEAwEu7q6lvq2YzU4l3RODts8THos95DT90+XKXdSitxHfGq8/Ozvz2SblW1ke//28mTMISl3fCTlv2tIOdtBys1vSZl8xQDqpZRxkVIGjpFypp2Un7pJeXBBqVhAFAUtWAfY2NhIKaVs3bq1XLZsmZw2bZrcs2eP7Nu3r5RSypYtW8pz587da+/i4iJv3Lghvby8Hjhub28v4+Pj5X/+8x9Zs2ZN6eXlJb28vGTjxo3lzJkzH3n9rKws+eqrr8ply5bleU8L41NWHI09KtusbCN9VvnI+cHzZWJaYpH7SEpLkm/veVt6LPeQo7eOlheTLxpAqTrwGGuFApd0hBC7gPymcB8U5YtFCGELbADeklI+ckeRlNIP8ANo06aNNn1Si0j9qvVZ9cwqFp1YxOLQxfxz7R8+7vQxbZ0LNhGLT41nWdgy1p1eR1ZOFn3r92Wi50Rc7Vyhdnto/yrs/RyOroDjAeA1QkmHdOsEVlWLL/pmLETvhdPb4eRGpch41/ehwxtgaVf8fisAd+2Rg4KCSEhIuHdcFtMeed68whWBMTU1Zfjw4XzxxReMGzeumOrLP95O3gT2C+THEz+yLGwZqyNWM9J9JL7NfXGwdCjw/AOXD/DRwY9IupPE5FaTGdd8HKYmpgWeVxEoMOBLKR+ZTC2EiBVC1JRSXhVC1ATy9QkWQpijBHt/KeXGYqstx5ibmPOG9xt0dunM9P3TeXH7iwxqNIimDk2pbl2d6lbVqW5dHUcrR8xNzIlLjWNZ2DLWn15PVk4W/er3Y4LnBCXQ309lZ6Um7BNvwt7PIGQtHPkvCBOo1QrqP6k86viA2WMqXt25BRf+hKggpc5sXO4tFit7aPcKdP5XufWvL23Gjx9PlSpVaNGiBUFBQfeO37VB/vDDD/O1R54xY0Yee+SBAwcyZcoUnJycSExM5ObNm9StW/den1JKzp07R8OGDZUliM2bcXd3L+uPrDnqV63P510/Z6LXRBaFLOK/Yf8lICKAEU1G4NvcF0crRzKzM7medp34tHjiU+OJT4sn9Hoov577lYZVG7Kwx0LcHYxrLEV+s5JCnyzEF0CC/P9NWwcp5XsPtREo6/uJUsq3itJ/mzZtZHBwcLH1aZXUzFS+PvI160+vJ1tmP/CeQGBvac+tjFtky2z6N+jPhBYTCp81kJUBl4NzA3cQxASDzAYzK6jqmn8WjcxR7gPkZIGZpXIjtv6TysPSvG54AAAE+UlEQVTZEzTgwR4eHk7Tpur6kNva2uZJiQwKCuLLL79ky5YtJCYmMm7cOKKjo/O9aXv9+nW6du3Kxo0bOXLkCNWqVSMwMJB58+aRk5ODubk533//Pe3b/7/WcU5ODp07dyYlJQUpJV5eXvzwww/3buTeRQvjoyZRN6JYFLKIbee3UcmkElZmViTdScrTzszEjOfdn2dSq0naKflZygghjkgp2+T7XgkDviOwFnBFWZsfKqVMFELUApZIKZ8RQnQC9gOhQE7uqdOllL8V1H9FDfh3ycrJIik9ibi0uHszkLvPFqYWjGo6ijqVS5gelp4CFw4qwf9mXq/1e9jXgwbdoE57MNeeSZSxB7SC0MdHITo5mtXhq8mW2fd+OTtZO1HNqhpO1k7YW9hX+OUbgwV8Q1PRA75O4dED2uPRx0fnLo8L+Or/VtfR0dHRKRP0gK9TbtDyr1E10cdFp7DoAV+nXGBpaUlCQoIe3B5CSklCQgKWltq776KjPUpqraCjUya4uLgQExNDfHzJdldWRCwtLXFxcVFbhk45QA/4OuUCc3Nz6tWrp7YMHZ1yjb6ko6Ojo2Mk6AFfR0dHx0jQA76Ojo6OkaDpjVdCiHjgQjFPrwYUvqyQcaCPSV70McmLPiZ5KU9jUldKWT2/NzQd8EuCECL4UbvNjBV9TPKij0le9DHJS0UZE31JR0dHR8dI0AO+jo6OjpFQkQO+n9oCNIg+JnnRxyQv+pjkpUKMSYVdw9fR0dHReZCKPMPX0dHR0bkPPeDr6OjoGAkVLuALIXoLISKFEGdzyy4aJUKIZUKIOCFE2H3HHIQQO4UQZ3Kf7dXUWNYIIeoIIfYIIcKFECeFEJNzjxvtuAghLIUQfwshTuSOyezc40Y7JncRQpgKIY4JIbbkvi73Y1KhAr4QwhT4HugDNANGCiGaqatKNZYDvR86NhXYLaVsBOzOfW1MZAH/klI2BdoDr+f++zDmcbkDdJdSegEtgd5CiPYY95jcZTIQft/rcj8mFSrgAz7AWSlllJQyA1gDDFRZkypIKfcBiQ8dHohSUJ7c52fLVJTKSCmvSimP5v59E+U/c22MeFykwt3K7Oa5D4kRjwmAEMIF6Assue9wuR+TihbwawOX7nsdk3tMR6GGlPIqKMEPcFJZj2oIIdwAb+AwRj4uuUsXx4E4YKeU0ujHBPgGeA/Iue9YuR+TihbwRT7H9LxTnQcQQtgCG4C3pJQpautRGylltpSyJeAC+AghPNTWpCZCiH5AnJTyiNpaSpuKFvBjgDr3vXYBrqikRYvECiFqAuQ+x6msp8wRQpijBHt/KeXG3MNGPy4AUsobQBDKvR9jHpOOwAAhxHmUZeHuQohVVIAxqWgB/x+gkRCinhCiEjAC+FVlTVriV8A3929fYJOKWsocIYQAlgLhUsqv73vLaMdFCFFdCFE1928roAcQgRGPiZRympTSRUrphhJD/pBSjqYCjEmF22krhHgGZf3NFFgmpfxYZUmqIIQIAJ5EsXWNBWYCvwBrAVfgIjBUSvnwjd0KixCiE7AfCOX/a7PTUdbxjXJchBCeKDcgTVEmgGullHOEEI4Y6ZjcjxDiSeAdKWW/ijAmFS7g6+jo6OjkT0Vb0tHR0dHReQR6wNfR0dExEvSAr6Ojo2Mk6AFfR0dHx0jQA76Ojo6OkaAHfB0dHR0jQQ/4Ojo6OkbC/wD18lLq2vwcLAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#A string\n",
"k45A = TA/dx45**2/dA\n",
"\n",
"A45A = k45A*(np.diag(np.ones(N45)*2)\\\n",
" -np.diag(np.ones(N45-1),-1)\\\n",
" -np.diag(np.ones(N45-1),1))\n",
"print('K=T/mu/h^2*')\n",
"e45A,v45A=linalg.eig(A45A)\n",
"isort = np.argsort(e45A.real)\n",
"e45A=e45A[isort]\n",
"v45A=v45A[:,isort]\n",
"\n",
"print('First 3 Natural frequencies of {}-element string (Hz)'.format(N45))\n",
"print(e45A.real[:3]**0.5/2/np.pi)\n",
"f145A=np.sqrt(e45A.real[0])/2/np.pi\n",
"fn45A=np.sqrt(e45A.real[-1])/2/np.pi\n",
"print('\\nLongest time period ={:1.3f} ms\\nshortest time period ={:1.3f} ms'.format(1/f145A*1000,1/fn45A*1000))\n",
"plt.plot(v45A[:,0],label='Mode 1')\n",
"plt.plot(v45A[:,1],label='Mode 2')\n",
"plt.plot(v45A[:,2],label='Mode 3')\n",
"plt.title('First Two Vibration Modes for 45-Node Guitar A String')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 281,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"K=T/mu/h^2*\n",
"First 3 Natural frequencies of 45-element string (Hz)\n",
"[ 82.43894585 164.78177157 246.93246912]\n",
"\n",
"Longest time period =12.130 ms\n",
"shortest time period =0.414 ms\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fe797335278>"
]
},
"execution_count": 281,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#Second E string\n",
"k45E2 = TE2/dx45**2/dE2\n",
"\n",
"A45E2 = k45E2*(np.diag(np.ones(N45)*2)\\\n",
" -np.diag(np.ones(N45-1),-1)\\\n",
" -np.diag(np.ones(N45-1),1))\n",
"print('K=T/mu/h^2*')\n",
"e45E2,v45E2=linalg.eig(A45E2)\n",
"isort = np.argsort(e45E2.real)\n",
"e45E2=e45E2[isort]\n",
"v45E2=v45E2[:,isort]\n",
"\n",
"print('First 3 Natural frequencies of {}-element string (Hz)'.format(N45))\n",
"print(e45E2.real[:3]**0.5/2/np.pi)\n",
"f145E2=np.sqrt(e45E2.real[0])/2/np.pi\n",
"fn45E2=np.sqrt(e45E2.real[-1])/2/np.pi\n",
"print('\\nLongest time period ={:1.3f} ms\\nshortest time period ={:1.3f} ms'.format(1/f145E2*1000,1/fn45E2*1000))\n",
"plt.plot(v45E2[:,0],label='Mode 1')\n",
"plt.plot(v45E2[:,1],label='Mode 2')\n",
"plt.plot(v45E2[:,2],label='Mode 3')\n",
"plt.title('First Two Vibration Modes for 45-Node Guitar Second E String')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 282,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First 3 Natural frequencies of 45-element First E string (Hz)\n",
"[329.63523775 658.88613556 987.36880161]\n",
"First 3 Natural frequencies of 45-element B string (Hz)\n",
"[247.05411832 493.82018258 740.01047461]\n",
"First 3 Natural frequencies of 45-element G string (Hz)\n",
"[196.04043699 391.85229959 587.20727994]\n",
"First 3 Natural frequencies of 45-element D string (Hz)\n",
"[146.88611909 293.60097554 439.97350639]\n",
"First 3 Natural frequencies of 45-element A string (Hz)\n",
"[110.00809489 219.88792527 329.51137616]\n",
"First 3 Natural frequencies of 45-element Second E string (Hz)\n",
"[ 82.43894585 164.78177157 246.93246912]\n"
]
}
],
"source": [
"#Natural Frequencies\n",
"print('First 3 Natural frequencies of {}-element First E string (Hz)'.format(N45))\n",
"print(e45E.real[:3]**0.5/2/np.pi)\n",
"print('First 3 Natural frequencies of {}-element B string (Hz)'.format(N45))\n",
"print(e45B.real[:3]**0.5/2/np.pi)\n",
"print('First 3 Natural frequencies of {}-element G string (Hz)'.format(N45))\n",
"print(e45.real[:3]**0.5/2/np.pi)\n",
"print('First 3 Natural frequencies of {}-element D string (Hz)'.format(N45))\n",
"print(e45D.real[:3]**0.5/2/np.pi)\n",
"print('First 3 Natural frequencies of {}-element A string (Hz)'.format(N45))\n",
"print(e45A.real[:3]**0.5/2/np.pi)\n",
"print('First 3 Natural frequencies of {}-element Second E string (Hz)'.format(N45))\n",
"print(e45E2.real[:3]**0.5/2/np.pi)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"c. Create an audio signal that has the 18 frequencies (6 strings $\\times$ 3 modes) in an array and display it using the `from IPython.display import Audio` library. \n",
"\n",
"_Hint: you don't need to solve the differential equations here. You can use the calculated frequencies to add sine-waves together:_ $\\sin(f_12\\pi t)+\\sin(f_22\\pi t)+...$"
]
},
{
"cell_type": "code",
"execution_count": 283,
"metadata": {},
"outputs": [
{
"data": {
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\" type=\"audio/wav\" />\n",
" Your browser does not support the audio element.\n",
" </audio>\n",
" "
],
"text/plain": [
"<IPython.lib.display.Audio object>"
]
},
"execution_count": 283,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Audio\n",
"samplerate=20000\n",
"t=np.arange(0,3,1/samplerate)\n",
"out_file_E = 100*(np.sin(t*e45E.real[0]**0.5)+np.sin(t*e45E.real[1]**0.5)+np.sin(t*e45E.real[2]**0.5))\n",
"out_file_B = 100*(np.sin(t*e45B.real[0]**0.5)+np.sin(t*e45B.real[1]**0.5)+np.sin(t*e45B.real[2]**0.5))\n",
"out_file_G = 100*(np.sin(t*e45.real[0]**0.5)+np.sin(t*e45.real[1]**0.5)+np.sin(t*e45.real[2]**0.5))\n",
"out_file_D = 100*(np.sin(t*e45D.real[0]**0.5)+np.sin(t*e45D.real[1]**0.5)+np.sin(t*e45D.real[2]**0.5))\n",
"out_file_A = 100*(np.sin(t*e45A.real[0]**0.5)+np.sin(t*e45A.real[1]**0.5)+np.sin(t*e45A.real[2]**0.5))\n",
"out_file_E2 = 100*(np.sin(t*e45E2.real[0]**0.5)+np.sin(t*e45E2.real[1]**0.5)+np.sin(t*e45E2.real[2]**0.5))\n",
"Audio(data=out_file_E+out_file_B+out_file_G+out_file_D+out_file_A+out_file_E2,rate=samplerate)"
]
},
{
"cell_type": "code",
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