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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": 122,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy import linalg\n",
"from IPython.display import Audio"
]
},
{
"cell_type": "code",
"execution_count": 123,
"metadata": {},
"outputs": [],
"source": [
"#a, #b\n",
"E = 10e9 \n",
"L = 0.64 \n",
"height = .04\n",
"base = .02\n",
"width = .04\n",
"T = np.array([7.28,7.22,7.32,8.41,9.03,7.71]) \n",
"M = np.sum(T*9.81*height) \n",
"I = width*base**3/12 "
]
},
{
"cell_type": "code",
"execution_count": 124,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"finite difference A:\n",
"------------------\n",
"[[ 7. -4. 1. 0. 0.]\n",
" [-4. 6. -4. 1. 0.]\n",
" [ 1. -4. 6. -4. 1.]\n",
" [ 0. 1. -4. 5. -2.]\n",
" [ 0. 0. 2. -4. 2.]]\n",
"\n",
"finite difference b:\n",
"------------------\n",
"[ 0. 0. 0. -0.00113216 0.00226432]\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N= 6\n",
"h= L/(N-1)\n",
"\n",
"mu_E1= 0.401e-3\n",
"mu_B= 0.708e-3\n",
"mu_G= 1.140e-3 \n",
"mu_D= 2.333e-3 \n",
"mu_A= 4.466e-3 \n",
"mu_E2= 6.790e-3 \n",
"\n",
"TE= 7.28*9.81 \n",
"TB= 7.22*9.81 \n",
"TG= 7.32*9.81 \n",
"TD= 8.41*9.81 \n",
"TA= 9.02*9.81 \n",
"TE2= 7.71*9.81 \n",
"\n",
"M= (TE+TB+TG+TD+TA+TE2)*height\n",
"\n",
"A= np.diag(np.ones(N-1)*6)\\\n",
"+np.diag(np.ones(N-2)*-4,-1)\\\n",
"+np.diag(np.ones(N-2)*-4,1)\\\n",
"+np.diag(np.ones(N-3),-2)\\\n",
"+np.diag(np.ones(N-3),2)\n",
"A[0,0]+= 1\n",
"A[-1,-1]+= -4\n",
"A[-1,-3]+= 1\n",
"A[-2,-2]+= -1\n",
"A[-2,-1]+= 2\n",
"\n",
"b= np.zeros(N-1)\n",
"b[-1]+= 2*M*h**2/E/I\n",
"b[-2]+= -M*h**2/E/I\n",
"\n",
"w=np.linalg.solve(A,b)\n",
"xnum=np.arange(0,L+h,h)\n",
"\n",
"print('finite difference A:\\n------------------')\n",
"print(A)\n",
"print('\\nfinite difference b:\\n------------------')\n",
"print(b)\n",
"\n",
"x_an= np.linspace(0,L,100)\n",
"w_an= M*x_an**2/2/E/I\n",
"\n",
"plt.figure(figsize=(8,8))\n",
"plt.xlabel('Position on Guitar (m)')\n",
"plt.ylabel('Deflection (m)')\n",
"plt.title('Deflection with Position')\n",
"plt.plot(x_an,w_an,label='Analytical Solution')\n",
"plt.plot(xnum, np.block([0,w]),'o',label='Finite Difference')\n",
"plt.legend(bbox_to_anchor=(1,1));"
]
},
{
"cell_type": "code",
"execution_count": 125,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N= 10\n",
"h= L/(N-1)\n",
"\n",
"mu_E1= 0.401e-3\n",
"mu_B= 0.708e-3\n",
"mu_G= 1.140e-3 \n",
"mu_D= 2.333e-3 \n",
"mu_A= 4.466e-3 \n",
"mu_E2= 6.790e-3 \n",
"\n",
"TE= 7.28*9.81 \n",
"TB= 7.22*9.81 \n",
"TG= 7.32*9.81 \n",
"TD= 8.41*9.81 \n",
"TA= 9.02*9.81 \n",
"TE2= 7.71*9.81 \n",
"\n",
"M= (TE+TB+TG+TD+TA+TE2)*height\n",
"\n",
"A= np.diag(np.ones(N-1)*6)\\\n",
"+np.diag(np.ones(N-2)*-4,-1)\\\n",
"+np.diag(np.ones(N-2)*-4,1)\\\n",
"+np.diag(np.ones(N-3),-2)\\\n",
"+np.diag(np.ones(N-3),2)\n",
"A[0,0]+= 1\n",
"A[-1,-1]+= -4\n",
"A[-1,-3]+= 1\n",
"A[-2,-2]+= -1\n",
"A[-2,-1]+= 2\n",
"\n",
"b= np.zeros(N-1)\n",
"b[-1]+= 2*M*h**2/E/I\n",
"b[-2]+= -M*h**2/E/I\n",
"\n",
"w=np.linalg.solve(A,b)\n",
"xnum=np.arange(0,L+h,h)\n",
"\n",
"x_an= np.linspace(0,L,100)\n",
"w_an= M*x_an**2/2/E/I\n",
"\n",
"plt.figure(figsize=(8,8))\n",
"plt.xlabel('Position on Guitar (m)')\n",
"plt.ylabel('Deflection (m)')\n",
"plt.title('Deflection with Position (N=10)')\n",
"plt.plot(x_an,w_an,label='Analytical Solution')\n",
"plt.plot(xnum, np.block([0,w]),'o',label='Finite Difference')\n",
"plt.legend(bbox_to_anchor=(1,1));"
]
},
{
"cell_type": "code",
"execution_count": 126,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Converges to value 0.014\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N= 50\n",
"h= L/(N-1)\n",
"\n",
"mu_E1= 0.401e-3\n",
"mu_B= 0.708e-3\n",
"mu_G= 1.140e-3 \n",
"mu_D= 2.333e-3 \n",
"mu_A= 4.466e-3 \n",
"mu_E2= 6.790e-3 \n",
"\n",
"TE= 7.28*9.81 \n",
"TB= 7.22*9.81 \n",
"TG= 7.32*9.81 \n",
"TD= 8.41*9.81 \n",
"TA= 9.02*9.81 \n",
"TE2= 7.71*9.81 \n",
"\n",
"M= (TE+TB+TG+TD+TA+TE2)*height\n",
"\n",
"A= np.diag(np.ones(N-1)*6)\\\n",
"+np.diag(np.ones(N-2)*-4,-1)\\\n",
"+np.diag(np.ones(N-2)*-4,1)\\\n",
"+np.diag(np.ones(N-3),-2)\\\n",
"+np.diag(np.ones(N-3),2)\n",
"A[0,0]+= 1\n",
"A[-1,-1]+= -4\n",
"A[-1,-3]+= 1\n",
"A[-2,-2]+= -1\n",
"A[-2,-1]+= 2\n",
"\n",
"b= np.zeros(N-1)\n",
"b[-1]+= 2*M*h**2/E/I\n",
"b[-2]+= -M*h**2/E/I\n",
"\n",
"w=np.linalg.solve(A,b)\n",
"xnum=np.arange(0,L+h,h)\n",
"\n",
"x_an= np.linspace(0,L,100)\n",
"w_an= M*x_an**2/2/E/I\n",
"\n",
"plt.figure(figsize=(8,8))\n",
"plt.xlabel('Position on Guitar (m)')\n",
"plt.ylabel('Deflection (m)')\n",
"plt.title('Deflection with Position (N=50)')\n",
"plt.plot(x_an,w_an,label='Analytical Solution')\n",
"plt.plot(xnum, np.block([0,w]),'o',label='Finite Difference')\n",
"plt.legend(bbox_to_anchor=(1,1));\n",
"print('Converges to value 0.014')"
]
},
{
"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": 127,
"metadata": {},
"outputs": [],
"source": [
"#a\n",
"L = 0.64 \n",
"mu_g = 1.14e-3 \n",
"T_g = 71.81 \n",
"\n",
"mu_e = 0.401e-3\n",
"T_e = 7.28*9.81\n",
"\n",
"mu_b = 0.708e-3\n",
"T_b = 7.22*9.81\n",
"\n",
"mu_d = 2.333e-3\n",
"T_d = 8.41*9.81\n",
"\n",
"mu_a = 4.466e-3\n",
"T_a = 9.03*9.81\n",
"\n",
"mu_E = 6.790e-3\n",
"T_E = 7.71*9.81"
]
},
{
"cell_type": "code",
"execution_count": 128,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 6-element string (Hz)\n",
"f1: 194.4370866109145\n",
"f2: 379.12428580059105\n",
"f3: 544.8006102150752\n",
"Natural frequencies of 30-element string (Hz)\n",
"f1: 195.994645953565\n",
"f2: 391.48617646194407\n",
"f3: 585.9727675700807\n",
"Natural frequencies of 45-element string (Hz)\n",
"f1: 196.04043698528574\n",
"f2: 391.8522995904132\n",
"f3: 587.2072799426845\n",
"Natural frequencies of 60-element string (Hz)\n",
"f1: 196.0568723200582\n",
"f2: 391.9837461956978\n",
"f3: 587.6507093798888\n"
]
}
],
"source": [
"N = np.array([6,30,45,60])\n",
"for i in range(len(N)):\n",
" dx = L/(N[i]+1)\n",
" k = T_g/(dx**2*mu_g)\n",
" A = k*(np.diag(np.ones(N[i])*2)\\\n",
" -np.diag(np.ones(N[i]-1),-1)\\\n",
" -np.diag(np.ones(N[i]-1),1))\n",
" \n",
" e,v = linalg.eig(A)\n",
" isort = np.argsort(e.real)\n",
" e = e.real[isort]\n",
" v = v.real[:,isort]\n",
" x = np.linspace(0,L,N[i]+2)\n",
" v = np.pad(v,((1,1),(0,0)))\n",
" print('Natural frequencies of {}-element string (Hz)'.format(N[i]))\n",
" print('f1:', (e[0]**0.5/(2*np.pi)))\n",
" print('f2:', (e[1]**0.5/(2*np.pi)))\n",
" print('f3:', (e[2]**0.5/(2*np.pi)))"
]
},
{
"cell_type": "code",
"execution_count": 129,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f3480e81eb8>"
]
},
"execution_count": 129,
"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 \n",
"mu = 0.00114 \n",
"N=6 \n",
"dx=L/(N+1)\n",
"\n",
"k = TG/dx**2/mu\n",
"\n",
"A = k*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"e,v=linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e=e[isort]\n",
"v=v[:,isort]\n",
"\n",
"plt.plot(v[:,0],label='Mode 1')\n",
"plt.plot(v[:,1],label='Mode 2')\n",
"plt.plot(v[:,2],label='Mode 3')\n",
"plt.title('Mode shape for 6-Node Guitar String')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 130,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f3480e4ec88>"
]
},
"execution_count": 130,
"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 \n",
"mu = 0.00114 \n",
"N=30 \n",
"dx=L/(N+1)\n",
"\n",
"k = TG/dx**2/mu\n",
"\n",
"A = k*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
"e,v=linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e3=e[isort]\n",
"v=v[:,isort]\n",
"\n",
"plt.plot(v[:,0],label='Mode 1')\n",
"plt.plot(v[:,1],label='Mode 2')\n",
"plt.plot(v[:,2],label='Mode 3')\n",
"plt.title('Mode shape for 30-Node Guitar String')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 131,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f3480db4cf8>"
]
},
"execution_count": 131,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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mG+UNQxnF1MLu7e5FI25xzqxc1bH5mPkalXn9uolZpuLuFevUpihnEaSUmc6OFYcQoi72j+lUQxEpK5aiutnB7kTHys84/xi66iWxYbTQrD1Ijxqta1d44zpYyyjPZx48uy8TTNtOW8pSylullML6oxJ4MhRCRKPsc+qg7L3+iWq1NkB9rKzvlXVGElfvlRI/R8UhpcyWUq6RUj6EUsDPGoc6UbiXuqR4S3Z3vSya3+/mqbLFTfv3yKlZqZQCKeXvKC0lFGUNDLBUSnnKzSysD31xLxJzHPNc1HQHx4tLXxRrHsnmh7OY3yA35C2ElHKnlHI0qgtoMMoL1yrUsEUn4CchxHWe5usKw17CqmzcZ2jQv0kpE6SUKVLKdMOmoNhuXwNXdWw+5uwaRblZv/FuyuMJZpncvVc8nvfsJnVRvTUCWCMunhctsc+bBjhs7Pd4/FJKmY+91VpSHwrF8RRKwamNvWfCGd64DulFjheXvijme3KkB899QjHlmVlr2vbGBwhUHbtDWbufvgHVsLGgPAi+KKXcKKU8IaVMNb1XnCrV5Y2U8hD2xg+ohlJlxqwIFOdLw53vqw1vuHu0DhU0KxJ2hwTjv4ZQHt0cIoRogF27TzAdMm87HScy8nbWOrB2AdUWQjR0IatXkFJmSilXSCmfN5SLjihtW1D4Q+ANOpu257uI566DJ1djcW1N2+bxcXMXm1me8ibBtN3OWSRjrL+VgzSVEsMI2OqcqpC3RynlIBcfwJXulmHYD1ntNB4yWpLOsE6/BBfXwcA6tJZQZL81XNzYcFsn+xNQHzS4uPfEK0gpd2Pv1r1JlM4JkhVrj4+z4T8r9b1Qliusz/EfUsq/HEUw7C9aOTrmQ8yyutsQqqicxz4kXlw9F2crVghvKAXW+cKgNPpvPUhr1qavdxHPvOyrOc0u7BXjqpU92sUxs+ewcu+6Mx4q6wfb2UuspJiXCHU4RiyEaIwad3MHd+rYgpo7a2UVditwX3aNbsD+IXB1r12F/aW71kW80vA36mPk6je7iExdgJtKUNYI7PfBNlcRS8lMVP3WxIXFs2EYaH05O70OhpW49b4seh2s4UGG4aKj9DVRY92OZEhF2bcA3OaB/YSnvGz8V6dwK7WknDT+67g479ao4cGSYB7GclUnoW7EGUPZDAOWBnOjr+g4vvXcy+pe8CrGDJ0NRvAqodbZuAghREs8/K6UWikwrKZbGQV38GSsVUq5FWUlCvC4EOIiDddovf+fEdwm1RQ8a/p87MMWY4QQF3XTGdPj/q/oflMee1HzrQH+KYTo40pmIUSsswfSSfwIIUSjYqJZrcLPuozlOeZW+jVFDxqtyPdx/0G4V6gVyYrm0waYZgR/MizHAZBSXsC+aM5EIYSrDzJCiGhXvUYlxTC6s1rKTxNCtHdQdnWUoypQTlV+8LYchixZUsodrn5G+VZ2G/sLGRQV17NlPE/WqUp5KGczZYKUcg925fYfuO6ytN4P3YQQztwkv46yuIaLF16ba/yHYb9eRXmZwkpxUazGna2AV1wZngkhAks4c2MO9mm29wohni2lAmK10hfYjbttGL1cF01N8wCrgzdw3dtgfa+0dfI+aIDz6+J1hBD/K25GgVDuxx80ghag6LLU1ndvHVF5Vv+09srH42DYzlAUXvE4V+mec4iJuOFIxUnaQaa0gxwcN3s0PIya1lgPNe46FrtXMXc9Gt6LsrCvg92j4TlcezRshN1JSY5Rkb1QY6S1UArPONRLLwsPnOsYFywP5aXtdlRXfW3UmFxv1IvDWj+vOKv3YsqYiwPnFKiP/UHj2AXUjdPcqJvhwHrj2F84d2hivvaHURr2eOP61DO2T5rqzpFHw+ooC1iJeiA/RLXi4lA2Fi1RrcYPjGt4gyf3mHTT+QiFPRqeQa1KaL1XRqLm/FvP9UZXdeGpfKU4H6fPHMrAb51xXXsY9VkD1S3/oOmelsDTpZQnAScOcYrUb1F3tRfFp7BHwzzUss9tUL0MvYzzsqZ/20lZZo+Gn6B6Umqixord9Wg435THCtT7oqFxvzZGedh7wTj3WSWst1jsDmgk9qWTuxnPT3XjHhyC8vVx1hS3sYP81hnHslDvugao98kwVK9cNnZ36I7q3uVzgv1dsBll6xSOslEIMsVpYbrO+416q2fU3USU6+sMV/cMHrreLaaOk1HvlRVGnXRHvZ9qoN7dU0z3gnR0LVHPj/X4v1FKUbBx7oGmeIMo5rl0N67p2MSS5IFq1G82jhWgPIOanyOrI8Hy8WjowQUzn9QgJ3HGUrq1D/rhfO2DbNRUPOsNOtNJHm1QU6ScyWD9WXDgDc+FbPFu5ClRwxgRRdLa6r2YMuY6u+ioLthMF+W+hGsvZ+Zr3xPn6wbkANe7kLEeqtvXnbq4ugQvBqfnUCSeO2sfOPQ86e718MYP95SCb12ch/l8nvGCPNbnZ66b96J0FZ+yX/vgs+LuCVRPxLtu3pOvuFtXTmSdjVKA3CnrT2C4k7wuobDiUPRddxMl9GhoHJ/sQq54U7xHXMTLQin5ruSw3icrvXBvHnIhS9HfB5gUnCL5rHOSZqUpziBH9eEkP5dxTccmliKPRtgbfo5+z6BW3JTAb+7UZ7msK10cUsr5KI3uf6jx1kzj9zdqGl0bKaVThzNSyrUon9Hvo7TkXFSLdgHQS0r5vbO0pjz2ooz+JqA0rBNGPjkozXcJqkXWSHq2it0R1IJNT6G6rA6itOhcQ9bFqAf5cimlWytKeoKUcjXqY74A5Uo6D3vX+Egp5SMukhfNazOqhfMh6rxyjbzmAV2llF+7SHsSNc3tOpRR2hHUSywX1dOwAuVNsKWUcrFnZ+k+UsoVqC7jF1Ct1XRDjkOo8+ospXyjrMr3Mi+g/Mz/grqvzqOUgHPA76ger0uklE86zcH7PENhpzEOkVIeRbXq70O5uU1B3ZsnUcrOKCnlOOnE053xrAxG+bbYjnpfpKLGWe+QUjpbwdWcR66Ucgrqnp6N8muQZsifgqrDl1GOrx52lo8b5WRIKe9GGXw9ifpYHkfdd9moc15tLUtK2UFKucRJXn+hWsJzjDysdTYP5U55YUnlNPJ/D9UruhJVBxYn8V5CNbaWoxpkOSjF8SOgh6t3QRnQCtVT8oIhzzFUvVqv4xbUt6WHlPJOqYadHXElqpG0mzKcKulNjOeoM/Ac6nuZg1IalwHXGs++R7OphKFtaDQOEWpZzzkAUs2j1mg0Gk0lQQixE9XgnSWlvK+4+BWip0Cj0Wg0Go13EULEo3rRAba6k0YrBRqNRqPRVEKEEDVcTEcMRA2bBKCGFb5zJ0+tFGg0Go1GUzkZDuwQQtwjhLhECBEjhKgvhLgaZRdiXen1Velk8bCiVJb5mBqNRqPRaC6mA/Ylvh3xBWrWiVtoQ8NypHbt2jI+Pt7XYnhEcnIyiYnKa3G3bt18LI1Go6mKbN26NVlKWRarp1ZqDM+ft6B8arRE+cUIQflu2ISaDlrs7LtCeWqloPzo3r273LJli6/F0Gg0mkqFEGKrlLK7r+WoCmibAo1Go9FoNIBWCjQajUaj0RhopUCj0Wg0Gg2glQKNRqPRaDQGWinQaDQajUYD+LFSIIQYJ4RYI4RIFUKkCyG2GA4e3D5nIUSwEGKIEOIVIcRGIcRJIUSuEOK4EOIrIcSgMjwFjUaj0WjKFb90XiSEeAuYhlopaxlqJbEhKAcPQ4QQY6SUBW5kNRC1pDGo1QC3olY4bIdaGvR6IcSz5bwKnUZTIgoskqy8ArLzCsjJt6j/PAvpuTkkXjhM9dAa1I2IJSw4kNCggIv+hdDrYdmwWMCS5/x4UGj5yaLReBG/UwqEENejFIJTwAAp5X5jfxxqed7rgHsBd5bHtQBfA29IKdcUKecm4HPgCSHECmNJXo3GJ1gskhOpWexPSufE+SxOX8jhTFo2py/kkGT8n03PwWJ1SxKQSVDkPoIi9xAU+TciMBuAgux65Ke1JT+9LZbsBlg7E8NDAomNCiU2OozYqFDiTP/xtSNoGRtJRKjfvU7sWCxw+k84tFL9EjdAfpbz+NENoNkg9Ws6EKLiykNKjabU+J3zIiHEFtT66BOklJ8UOTYQ5Q/6FNBASulwrXAPyvoAuAP4SEp5R3HxtfMijTc4mZrFnpMX2H86nX2n0zmQlMb+pHQyc113fongZIKidhMUuYfA8ESEcH37W/KjyE9vTUFaW/IzWoEMdhm/QY1qtIyLpGVsJC3jomgZG0nbetGEBQd6fI4VgtRjcGCZUgIOr4LMsyXPK7adSUkYAMHVvCJiVUE7Lyo//EopEEI0BI4CuUANKeVFqrwQ4hjQAOgrpVxfyvLuQQ1J/CqlvKK4+Fop0HhKgUWy99QFtiae4/eEc2xNSOFEaraHuUhCai8jpPYyhHD8vAfKaArIAOFYsbDk1iLr6AQsubEelRwSGECHhtXp3iSGbsavVmQF71o/lwArXoA/FgIu3o8BweBoSMVSAK5GJyPqQP+HofvtepjBTbRSUH74W39fF+P/L0cKgcHvKKWgC1AqpQDlaxrgZCnz0WgAkFKy52QaK/5OYuOhs2w/cp70nHy30saEB9MyLoomNcOJiw4jLjqUmpFB/Hjif6w59dtF8TvU7sDAhgMZ1GgQrWJakZGXwfoT61l1bBVrjq3hXI59UbWAkLPEtfmAKW2eI4qWJKXlcPpCNifPZ3PgTDoJyRnkWy7+gOYWWNiaeI6tifa8mtWOoHt8DANa1aF/yzpUr+a6B6LcSDsNq1+CrXMd2wuE17a39psNhBqNHedTkA8nttuHGo5uKpxfxhlYMgM2zIJBj0HHmyHQ317FmsqKv/UUTEfZCnwrpbzOSZw3gOnAK1LKh0tRVl1gL1AduNqdRSd0T4HGEVm5Baw/mMyyvUms2JvEyWJ6AqoFB9KhQXVa1Y2kVVwULWLVf62IkELGgJl5mTy46kHWHV9n29e5TmdGtxxN/4b9qV2tttMyCiwF/Jn8JyuPrmTe3nlkGePnoYGhvNj/RYY2GVoofm6+hYSzGcaQRhoHktLZffICh5MzXJ5LYICgR3wMQ9rEcVmbWJrXiSh/g8asc7DuTdj0LuRlFj4W3x9aDVeKQGw7CCjBhK3cDGWDcGgF/PUNXDhe+HjtVjD4cWh7teOeB43uKShH/E0p+BfwPPC5lPJWJ3GeB/4FvCelvLuE5QQBS1AzGpZJKYe6iDsZmAzQuHHjbtYVBzVVm9TMPH7adZKlu0+z7kAyOfnOx/fjokPp3qQm3ZrE0CO+Jm3rRREU6PrjlJyVzLTfprEnZY9t37UtruXJ3k8SHOBZy3xX8i7uWXYPKdkpAAgEM3rO4Ja2txSbNjk9x9ZTsCUhhT+Pp5JX4Pyd06RWOIPbxDKyYz26No4pWwWhIF+11te+CtmphY816gVDn4ImfbxbZl42bPkI1rx8sY1Cvc4w/AXvl+kHaKWg/PA3peD/gOeAz6SUtzmJ4w2lwGpgeBToKaU85U463VNQtcnOK2DF3iS+3XGcFXvPkFvgWBGIDgtiYOtYBrWqQ8+mNWkYU82jj+Ph1MNM/W0qx9PtLdIpnaYwrdO0En9kj144ytRlU0m8YFdqb7/kdh7o9gAB7rv+IDuvgD+Pp7LuQDIr9iax81iq07iNa4Zzbef6XNOlAc3rRJZIbqeknYavJkHi2sL74zrAkCeh5bCybbXnpMHGd2D9/yDngn2/CFC9Bn3/UbJeCT9FKwXlh78pBWU+fGBKX2jKoztopaDqYbFINh1O4bsdx/nxz5OkZTu2D2gZG8ngtrEMbh1LtyYxxfYEOGN70nbuW34fqTnqYxsoAnm81+Pc0OqGEp+DlZTsFO5bdh9/JP9h2zei6Qie6/scIYEhJcozKS2blXvPsHxvEmv2nyHDyQyKjg2rc23nBozqVJ86UaU0zjuyEb6YAOkmXb5mM7js/+CS0eX7Mc5MUT0Vm9+HfNOwUesr4dp3oFqN8pOlAqOVgvLD35SCq4HvgO1Syq5O4ixC+Sq4T0o5y8P8XwEeBM4Ag6SUuz1Jr5WCqsO5jFy+2HKUzzYlcjTFsc1rp4bVubpzAy5vF0ejmuGlLnPLqS1M+W0KOQU5AFQLqsbLA19mQMMBpc7bSvuHw9oAACAASURBVFZ+Fo+ufpSVR1fa9vWt35e3hrxFYEDpph7m5Bew6VAKP+86yQ9/OFagAgMEw9rGMb53E3o3r+VZz4eUym7g18fBYs1bwGX/gn7/gEAfGjymHoOv74QjG+z7YprCTZ9B3fa+k6uCoJWC8sPflIJGwBFcT0k8CjQE+kkp1xU97iLv/wKPAGeBIVLKnZ7Kp5UC/+fPY6l8vCGB73eecGgn0KhmNa7r3MDrXeIXci8w+rvRnM48DUDNsJq8NeQt2tf2/gelwFLAC5tfYOHfC2377u96P3d2uNNrZWTnFbDy7yS+2e58qKVFbCTjezdhdNeGRBbnOCknHRbfB38tsu+rVhOu/wBaDPGa3KWiIA+WPgUb37LvC6oGo16HTjf7Tq4KgFYKyg+/UgpA3TxAV7zovEgI8SIwAziHUgi2l0Q2rRT4Jzn5Bfz050k+Xp/IjqPnLzpevVowV3eqz7VdGtC1cY0yMZ6bsXoGPx3+CYAaoTWYd+U8GkU38no5VqSUvLbtNebsmgNAUEAQ866cR9tabb1eltUo85ttx9mckHLR8YiQQK7v1pDxvZvQIjbq4gzO7IMvboMze+376neFGz92Pq3Ql+xaBN/dC3mmmRvd71BGiFXUr4FWCsoPf1QKbgC+RH34+0spDxj7Y1FujtsBD0gp3zCleQE1pPCNlPKfRfJ7FngcOA8MlVJuLalsWinwLzJy8pm36QjvrzlEUlrORcfbN4hmfO94ru5Uv0y9+v18+GceXf2oLfz6oNcZ0qTsW7/5lnwm/DzBZmPQrHozFo5cSFhQWJmVue90Gp9uSGTRtmMO7Q+Gto1l2mUt6No4Ru1I3ACfj4HcNHukbrfDiP9U7A/smb9h4a2QvM++r0lfGPcFhHrZ6LISoJWC8sPvlAIAIcTbwFTUgki/YV8QKRr4FrjBvCCSEGIuMAH4WEo50bTfaqMAsAX4y0mRe6WULxYnl1YK/IPUzDzmrk9gzvrDnM8s7OQmJDCAqzrW47beTejSqGx6BcycyjjF6MWjSTM+ete2uJZn+z5bpmWaSbyQyJjvx9j8GNza9lZm9JxR5uWmZeexaNtxPtmQwMEzF/tC6NO8Fo+1v0CHFbcjctPVzqAwGPkadB5X5vJ5hZw01WOw+1v7vib94JYvICTCd3L5AK0UlB9+qRSAWjoZuAfoAASiHA19BLxTdNjAhVIwEZjjRnGrpJSDiouklYLKzZm0HD5ce5jPNiZe5GUwNiqUCX3iualHI2qXkxtfi7QweelkNp3cBECDyAZ8NeorIkPKtyX5xd9f8OxGuyIye9hs+tQvn7n2Uko2HDzL3PUJLN1zGuvrrLM4wKchLxAllLIiI2IRt34F9TqVi1xeQ0pY+xose9q+r+kAGLsQQkpvnFpZ0EpB+eG3SkFFRCsFlZOUjFxmLT/A55sSLzIebFSzGlMGNuf6rg3LfeGfz3Z/xn9+/w+gHArNHT6XrnEOJ92UKVJK7lt+H6uOrQIgtlosi65ZRPXQ6uUqx/7Tabyz6iCHdq7hk6B/Ey2Ud8JkGc2/ol9gzIhhDG0bWzmXgF73Jix9wh5uNgjGLqgyCytppaD80EpBOaKVgspFRk4+H649zHurD13UM9AyNpJplzVnVMf6JfYpUBoOnDvATT/cRK4lF4A72t/BA90eKHc5rCRnJTP6u9G29RKGxw/nvwP+W/4f4BM7sHx8NQGGn4azMoqxuY+zTyqjy+5NYpgxog094muWr1zeYM2rhXsMmg+Bm+dBcNnZcFQUtFJQfmiXWRpNEXLzLXy8PoGBL63g1aX7CikEHRpU591bu/HLAwO4rktDnygEeQV5/HPtP20KQZuabbin8z3lLoeZ2tVqM7PPTFt4ScIS22yIcuPkH/DJNTaFwBIWw6L2b3EsON4WZUviOca8u4E75v7O36fSnGRUQen/IFz2uD18cJmaVZF/sZGrRlNSdE9BOaJ7Cio2Fovk+z9O8Mqv+ziSUnhhnJaxkTxyRWuGtYvzeffz61tf58NdHwIQEhDCwpELaRHTwqcyWXlq/VMs2q98AUQFR/H11V9TL7Je2Rd8ahd8PAqyjCmLYTVgwmKo14nk9Bzb8I953QUh4LouDXhwWCsaxlSi8fmVL8LKF+zhViPgxk8gqGReJSsDuqeg/NBKQTmilYKKy/Yj55i5+K+LfPHXqx7GP4a14vquDQkM8P1Y9M4zO7ntp9uQqOd2Ro8Z3NrO4dpfPiEjL4MbFt/AsfRjAPSq14v3hr1XtopUymH4YChkJqtwaHWY8B3U71Io2tGUTF5duo9vdxzH/NoLCQpgcv9mTLusOeEhlWAJYylhxfNqmWcr7a6FG+b47XoJWikoP/zzDtJo3ORMWg6PfLmT695eX0ghqF4tmH9d2YYVDw/ixu6NKoRCIKXk1S2v2hSCS+tdyri2FWt6XURwBC/0f8G2SNLGkxtZf2J92RWYkw4LxpkUgmgY/81FCgFAo5rhvHZTZ368rz+DWtex7c/NtzBrxQGGvrKKH/44QYVvKAmh1mno9w/7vt3fqpUXNZpSopUCTZUkr8DCh2sPM/jllXy59Zhtf0hQAFMHNWf1o5cxeUDzcp9R4Ir1J9azLWkboDwIPtX7KY9WKCwvOsd2ZkyrMbbwm9vfLJsPrcUC39wNScYSJIEhcMuX0KCby2Tt6kcz9/aeLJjci04N7TMkTqRmc++87Yx7f1PFtzcQAoY8BT0n2/eteB72/ug7mTR+QcV7o2g0Zcz6A8lc9eYanv1hN2kmI8KhbeP47R8DmTG8DdWr+XBxHAdIKXlz+5u28PUtr6dRVNm5MS4tkztOJjRQ+WvYfXY3y44s834hq1+CvT/YwyNfg8a93E7eq1ktvpnWl/9c34FaEfbx+A2HznLlm2t4+vu/SM3Kc5GDjxECrvi38ltgZdFkSNrjO5k0lR6tFGiqDMnpOUyfv51xH2xi3+l02/5mtSOYe3sPPpjQnca1KqbB2bIjy9h9VrWIQwNDmdxxcjEpfEtseCxj24y1hWdtn0WBxfGyyCVi74+w8t/28KVToYvnthUBAYKbejRm+cODmNgn3jZMVGCRzFmXwJBXVrJ4ZwUeUggMhjEfQ40mKpybDvPHqiWZNZoSoJUCjd8jpeTrrccY+uoqFu88YdsfERLIYyPasOSBAQxqHetDCV1TYClg1nb7Kt83t76Z2PCKK6+VSe0nERGs3PEeTD3ovSmKSXtUi9hK0wFw+XOlyrJ6tWBmXn0JP03vT69mdh8Gyem5TJ+/nTs/3sKJ846XwPY54TVh7Hww6ppzh+GrSVBw8dLTGk1xaKVA49ccTclk/EebeejLnYXWKbimc32WPzyIKQObExJUsR+Dnw7/xMHUgwCEB4VzR4c7fCyRe8SExXBbu9ts4bd3vE2epZTd8ZkpqiVsXc+gRhPVUg70zqyB1nWjmH9XL94a15W60XanQMv2JnH5a6v5dEMCFksF7DWIuwSue8cePrQCfnvKd/JoKi0V+22o0ZSQAovkgzWHuPy11azZn2zb36BGNT6e1JM3bu5CXHTF9wSXZ8nj7R1v28LjLxlPTFiMDyXyjPHtxhMdEg3AsfRjfHvg22JSuKAgX7WAzx1W4eAI1UIO9653QiEEV3Wsx9IHB3Bbrya2/ek5+Tzx3V+Mmb2BA0kV0BCx3TUw0LQY1YZZsHOB7+TRVEq0UqDxO/adTmP02+t47sc9ZOWpcWwhYFLfpvz6jwEMbFWnmBwqDt8e+NY25z86JJrx7cb7WCLPiAqJYlL7SbbwuzvfJaeghB74fntKtYCtXPeuaiGXEVFhwTx7bXu+nNKb5nXsqxJuTTzHlW+s5c1l+8krsLjIwQcMfAxaX2UPL54Ox0u82rumCqKVAo3fUGCRvL/6ECPfXFvI50DruCgWTe3Dk6PaERFaCZzTGOQU5DB752xbeFL7SUSFRPlQopIxts1YalerDUBSZhIL9y70PJO9P6mWr5WBM6Dd1V6S0DU94mvy4/T+TB/cguBAZYiYW2Dh1aX7uP6d9RxISi8mh3IkIEApS3XaqHBBDnw5EbIv+FQsTeVBKwUav+BoSiZj39/I8z/tIddovYUEBvDw5a34/r5+dGlcebrcrXzx9xeczjwNQK2wWoWs+SsT4cHh3NXhLlv4w10fkpmX6SJFEdKTYPF99nDrK1WLuBwJCw7kwctb88N9/encqIZt/x/HUrnqzTXMWXe44tgahEWrhZLCDB8M54/AzzNcp9FoDLRSoKnUSCn5YstRRryxhs2H7dOwOjSozo/T+3Hv4JYV3pDQEZl5mXzw5we28F0d7yI8uGJOl3SHG1rdQL0ItQZCSnYKn+35zL2EUsJ399o9FkbVh2ve8pk739Z1o/h6ah/+dWUbQozFsHLyLTz9/W7Gf7S54sxQqNVc+W2wsnMe/FUKew5NlaHyvS01GoPk9Bwmf7qVR7/6w7aSYWCAYPrgFiya1oeWcZWvq93KZ3s+IyVbKTn1IuoV8hBYGQkJDGFqp6m28Nxdc0nNSXWRwmDLR7D/F3v42re9bljoKYEBgskDmrP4vr60rRdt27/2QDJXvL6ab7cfrxh+DdpfDx1utId/eAAunPSdPJpKgVYKNJWS5XtPc8Vrq1m6+7RtX9PaEXw1pTcPXt6aYB8saewtUnNSmbtrri08tdNUQgIr/wp4o5qPIj46HoC0vDTm/jXXdYLk/fDL/9nDvaZB88vKTD5PaVM3mm/v6cPUQc2xLo2Rlp3PAwt3cO+87RXDG+KVL0F1w/Nl1jn4bppyD63ROKHyvjk1VZLcfAvP/rCbSXO3cDYj17Z/fO8m/Di9ctoOFOXLfV+SlqemvMVHxzOq+SgfS+QdggKCmNZ5mi08b8880nOdGOkV5MGiuyDf6I6v01b5+q9ghAYFMmN4G764uzeNa9qHd3788yRXvrGGbUfO+VA6oFoNZXiIobUcXA6/v+9TkTQVG60UaCoNiWczuOHd9Xy49rBtX1x0KJ9M6skz17SvHMveFkOeJY8Fe+1zy+/qeBdBAZX/vKxcEX8FTas3BSAzP5PvDn7nOOKq/8KJ7Wo7IBiufx+CK65fie7xNfnp/v6M7Wlfj+L4+SxufHcD76466FsjxPh+0MdkqLn0SUja6zt5NBUarRRoKgWLd57gqjfX8odpquGQNrH8fP8ABlQivwPFsfzI8kIzDobHD/exRN4lQARwS5tbbOH5e+djkUW6s49sKrwM8JAnoG6HcpKw5ESGBvHC6I68c0tXosKUIpdvkbz4814mzNnMmbQS+mfwBoMfhzijDvOzYdGdkJ/rOo2mSqKVAk2FJjM3nxlf/cH0+dttxoTBgYInRrbjgwndqRlR+cfazczbM8+2Pab1GL+wJSjKqOajiApWRqCJFxJZd3yd/WBOGnwzGayKQpN+0PteH0hZckZ0qMdP0/vTpbF96uKa/clc+eYa1pq8a5YrQaGqt8VYuZJTfxZeUEqjMdBKgabCsv90GlfPWsfCLUdt+5rUCufrqX24o19ThBA+lM777Dm7h21J2wAIEkHc2OrGYlJUTsKDw7m25bW28Od7P7cfXPIYnEtQ26HRyp9/QGD5CugFGtUM54u7ezNlYHPbvjNpOdz20SZe/uVvCnwxnBDbFobOtIfXvg4J65zF1lRRtFKgqZB8v/ME17y1rpC3uFGd6vPDff3o2LCGi5SVl3l77b0El8dfTp1w/xkWKcrY1mMRhvHbuuPrSEhNgAPLYLvJf8FVr0CNxr4R0AsEBwbw2Ig2fDKpJ7UjVY+PlDBrxQHGf7SJs+k+GE64dAo0G2QEJCy+F/IqiG8FTYVAKwWaCkVegYWnv/+L++ZvJzNXrVsQFhzAf67vwJs3dyYqLNjHEpYNKdkp/HTIvrTwLW1vcRG78tMouhEDGw60hefv/hR+fNAeod210KFy+2awMqBVHX66vz/9WtS27Vt34Cwj/7eW7eU9OyEgAK59B0INb4cph2D1y67TaKoUWinQVBhOX8hm7HsbmbMuwbYvvlY4397Tl5t6NPa74QIzX+/7mlyLMvzqULsDHet09LFEZc+4tuNs29/uX0T6+UQVCKuu5tf70fWOjQrj40k9mT6kpW3fydRsbpy9gU83Jpavs6Po+jBspj287g1I2lN+5WsqNFop0FQINh46y1VvrmVLor3lNKxdHIvv60ebutEuUlZ+8ix5LPjbPg2xsq5x4Cm96vWiWfVmAGTKfL6LMlYiHPYMRMb6ULKyITBA8OCwVsyZ2INoY3ZCXoHkiW938dAXO8kyesbKha4TodGlatuSB98/oJ0aaQCtFGh8jJRqZcNbPthEsjHGGiDg0eGtmX1rN6L9dLjAzLIjy0jKTALUNMQr4q/wsUTlgxCCca3tCtC86CgsjS6FLpVreWhPuaxNLD/c1592JhfJi7Yf57q315GQnFE+QgQEwMjXweoD4+hG2P5J+ZStqdBopUDjM7JyC7h/wQ6e/2mPzRq7VkQIn95xKdMGtSAgwH+6j11hnoZ4Y+sb/XIaojNGXThHlLGq5ZHgYNZeOtFnix2VJ41rhbNoWh/GdGto27f3VBpXz1rL6n1nykeIuHbQ9357eOmTkHbaeXxNlcD/nz5NheTE+SzGzF7P4p0nbPs6N6rBD9P70ddkkOXv7D67m+1JynNfUEBQpV/4yCPSThG+/AWuS7fPMJl3arUPBSpfwoID+e8NHXlhdAfbiosXsvOZOGczH6w5VD52BgMegRjlYZLsVPjlX2VfpqZCo5UCTbmzNTGFq2etY9fxC7Z9Y3s2ZuHdvahXvZoPJSt/zL0EV8Rf4dfTEC9iyWOQk8rNF9IQxvdv3fF1HE497DqdHyGEYGzPxnw5pTd1o5UbZ4uE537cw8Nf/kF2XhnbGQRXg5Gv2sO7voL9v5VtmZoKjVYKNOXKF78f5eb3NtrsB4ICBM9e254XRncgNKjyOakpDWezzvLTYfs0xHFtxrmI7Wfs+xX++gaARvkFDKzV3nZo/t75vpLKZ3RqVIPF9/alq8kL4tfbjnHzextJupBdtoU3H1x4ieUfH4TczLItU1Nh0UqBplzIL7Awc/FfPPr1H+QVqGZhTHgwn915Kbf1auJj6XzD1/u/Js+iltetKtMQAcjNgB8fsoc73sy4btNtwe8OfEdabpoPBPMtsdFhzJ/cq5CdwY6j5xk1ay07j54v28Kv+DeEGQrJ+URY9Z+yLU9TYdFKgabMSc3MY+Kc35m7PsG2r03dKBbf249ezWr5TjAfkmfJY+Hehbawec6+37PyRUg9orarxcAVzxeenpifyXcHnKye6OeEBik7gydHtiPQMLQ9fSGHMbM38M32Y2VXcGQduPxZe3jDLDj9V9mVp6mwaKVAU6YkJGdw3dvrWHvAvhDMiPZ1+XpqHxqZ1p+vaqw8upKkLDUNsXa12lzRpGpMQyRpL2x4yx6+/DmIqI0QopAXx4V/Lyxfhz4VCCEEk/o15ePbe1K9mpqSm5tv4R8Ld/Lqr3+XXb10uQ2a9FXblnz48WHll1lTpdBKgabM2Hw4hWvfXsch09zrB4a25K1xXYkIDfKhZL7n2wPf2rZHtxxNcKD/+2NASvjlnyAN47nGfaCzXREY2WwkEcHKgVHChQR2ntnpCykrDP1a1ua7e/rSMjbStu/N5QeYvmBH2RggCgEjX7P7Ljiy3mb3oak6aKVAUyZ8s/0Yt36wifOZasw8NCiAWeO68MDQVlXG/4AzzmSeYe3xtbbwtS2udRHbj9j3CxxcrrZFAIz4TyFXxuHB4YUcN5kVp6pKfO0Ivp7Wh/4t7dN0v995gnHv2411vUqd1mrRJCtLn9QLJlUxtFKg8SpSSl799W/+sXAnuYZTmtqRISyY3IuRHev7WLqKwfeHvsciVd10j+tOo6hGPpaoHMjPLTwHvusEqHexYaVZQVqSsITMPG0FHx0WzJyJPbi1l33FyG1HznPd2+vYf7oMDDIHPALhhhKSehTW/8/7ZWgqLFop0HiN7LwCpi/YwZvLD9j2tYqL5JtpfenSOMaHklUcpJSFWsBVppdg82xIOai2Q6vD4McdRutcpzPx0fEAZORlsOzIsnISsGITFBjAs9e054mR7WydK0dTshj9znrW7k92ndhTqtUofH3WvAqpZWjkqKlQaKVA4xXOpucw7v2NfG/yUDigVR2+quIGhUX5I/kPm3Oe8KBwhjUZ5mOJyoH0M7Dqv/bwoBkQ4dhrpRCCa1pcYwvrIQQ7Qgju6NeU92/rTniI8umRlp3PhDmbWbD5iHcL6zoe4jqo7fws+G2md/PXVFi0UqApNYlnM7j+nfVsO2KfS31rr8Z8NKF7lVjQyBPMH7kr4q8gPLgKKEzLn4Ucw3tlrZbQ4y6X0Uc1G0WAUK+mzac2czz9eFlLWKkY2i6ukAfEAovksUV/8oo3ZyYEBMKIF+3hP7+EI5u8k7emQqOVAk2p2HH0PKPfXk/CWTX2KwQ8MbIdz17TnqBAfXuZycrPYsnhJbawuUXst5zcCdtMq+9d8W8Icr3gU1xEHL3r97aFFx9YXFbSVVouqV+d7+7tS/sG9pUW/7f8AA99uZPcfC8tgRzfD9qZ7tElM/TyylUA/dbWlJilu09z83sbOJuRC6gZBu/c0o07+jVFiKo9w8ARy44sIz1PLf7TOKoxXWO7+liiMkZKWPJPwGi9thgGrS53K6nZ1uK7g9/ZDDM1duKiw1g4uTcDW9nXy1i07Th3fPw7adl53ilk2LMQGKq2T2yHnVXPBXVVQysFmhLx2cZE7v50C9l56mUdEx7MvLt6Mbx9XR9LVnExDx1c0+Ia/1ecdn8LievUdkCQ6iVwk8saXUZ0iGoFH08/zpZTW8pCwkpPRGgQH0zozk3d7TNY1uxP5sbZGzmV6oU1E2KaQF+7C2qWPQ05Vc8FdVVCKwUaj5BS8t8le3n8211YjAZg45rhfD21D92a6BkGzjiRfoLNJzcDIBBc3fxqH0tUxuRlwa9P2MM9J0OdVm4nDw0M5cqmV9rC2uDQOcGBAbx4fQceHGav3z0nLzD67XXs88aUxb4PQFQ9tZ1+Gta8Uvo8NRUWrRRo3CY338KDX+zk7ZUHbfs6NazOoml9aFYn0kVKzeKDi5FGN3rv+r2pG+HnPSrrZ6k57gDhtWDgox5nYR5CWJq4lPTcdG9J53cIIZg+pCUv3dCRIMM52InUbK5/Zz0bD50tXeahkTD0aXt4w1uQcqh0eWoqLFop0LhFRk4+d36yhW+22y3Bh7SJZf7kXtSODPWhZBUfi7QUWuDH730TpJ2Gta/Zw4MfVwsfeUi7Wu1oUaMFANkF2fyS8Iu3JPRbxnRvxIcTexBhmrI4/qPNLNl1snQZdxgDDXuo7YJcPUXRj9FKgaZYrD4IVu87Y9s3tmdjZt/WjfCQqr2GgTtsPb2VY+nK+UtUSBSDGw/2sURlzKoXIc9Y7yL2EuW9sAQIIS4yONQUz8BWdVh4d2/qRCllPTffwrTPt/H5psSSZxoQAMNNUxR3fwfHtJ2HP6KVAo1Ljp3LZMy7G9h5LNW274GhLfn3dXrKobuYx8OvbHoloYF+3LOSvB+2fmwPD3tazXkvISObjSRIKMVze9J2ElITSilg1aB9g+osmtqHprXVAlMWCf/3zS7e+G1/yX0ZNOwO7Uy9XEuf1Kso+iH6ra5xyt5TF7j+nfW2VQ6FgOeubc8DQ1v5v+W8l8jIy2Bp4lJb+Jrmfu6b4LeZ9lUQ4/tDi6Glyq5WtVr0b9jfFta9Be7TqGY4X03pTceG1W37XvttH09+9xcFlhJ+zIc8aV9FMXEd7FviOr6m0qGVAo1DNh9OYcy7Gzh9Qa3EFhIYwNvjunJrryY+lqxy8WvCr2Tlq1XmmldvTvva7X0sURlyZBPs/cEeHvZMoVUQS4p5CGHxwcUUWMpg2WA/pVZkKPPu6kW/Fna30p9uTGT6/O3k5JegHms1h+6T7OHfZkJBfukF1VQYtFKguYhf/zrFbR9uIi1bPeyRoUHMndSDER3q+ViyykfRxY/8todFStWdbKX99dDAO86Z+jfsT82wmgAkZSax4eQGr+RbVYgMDeKjiT0Y1cm+SumPf57k9jkldHI04FEIMWYbndkLO+d5SVJNRUArBZpCfLX1GFM+20pOvnXZ41AWTO5Fn+aOF7DROOfIhSNsS9oGQKAIZGTzkT6WqAz5+yc4ulFtBwTD4Cdcx/eA4IBgRjaz1515JofGPUKCAnjjps5M7BNv27f+4FnGvb+Js+k5nmUWWQf63m8Pr/g35Oolrv0FrRRobHy09jAPf7nT5pSoSa1wvp7am/YNqrtOqHHIj4d/tG33a9CP2tX8VLEqyC88Ra3HHVCzqVeLMA8hrDi6ggzr7AaN2wQECJ4a1Y5Hrmht2/fn8VRunL2BE+ezPMus9z0QGae2007Cpne8KKnGl2ilQIOUkleX7uOZH3bb9rWtF82XU3rTpFaEDyWrvEgp+enQT7awuaXrd+z4DJL3qe2QKBjwiNeLaBnTklYxymNfTkEOy48s93oZVQEhBPdc1oIXRnewmXscPJPBmHc3cOiMB86hQiJg0GP28NrXIaOUTpI0FQKtFFRxLBbJ09/v5s1l+237ujeJYcHkXsRGhflQssrNnpQ9JFxIAKBaUDUGNhroW4HKitwM1X1spd/9EFE2PSJmt8fmXhiN54zt2ZhZY7sSHKg0g+Pns7hx9gb+OpFaTEoTXcarpbBBLY29+qUykFRT3miloAqTV2DhoS93Mnd9gm3fwFZ1+PSOS6leLdh3gvkB5l6CIY2HUC2omg+lKUM2vK384YPyj9/rnjIrakTTEbbtjSc2cjZLt0xLw1Ud6/HBhB5UC1Z+JJLTc7l59kZ+T0hxL4PAIBg60x7+/QNIOex1OTXli1YKqijZeQVM/WxrIbfFIzvW4/3x3akWUnJnMxoosBTw8+GfbWFz8v9YQAAAIABJREFUC9evyEiGdW/Yw4P+CSHhZVZc/cj6tuWmC2QBvyb+WmZlVRUGtqrDZ3f2JDpM+R5Iy8nntg83sWJvknsZtLkKGl2qti15sPy5MpJUU15opaAKkp6Tz8Q5m/ltj/3BH3dpY964uQshQfqWKC3bkraRlKXqNiY0hl71e/lYojJi1X8h11iFr3Zr6HxLmRdpVrDMvTGaktOtSU0W3t3btoZJdp6Fuz7Zwvc7TxSfWAgY9qw9vOsrOLG9jCTVlAf6C1DFOJ+Zyy0fbGLjIXsX4dRBzXn+2vYEBvjpHPpy5sdD9vHuy+MvJzjAD4diziXClo/s4aEzVXdyGXN5/OU2t8c7zuzgWNqxMi+zKtC2XjRfTelNwxg1zJVvkUxfsJ0vfj9afOLGl0IbkyHtsmedx9VUeLRSUIU4k5bDze9tZOfR87Z9j41ow4zhbfzXqU45k1uQW8it8VXNrvKhNGXIqv+o7mKARr2g9QjX8b1ETFgMvev3toWXJGg3u94ivnYEX03pQ4tY5ZhISnj06z+Ys84NO4EhT4IwPicHl0HC2jKUVFOWaKWginDifBY3zd7A3lOqu9e6jsGUgc19LJl/se74Oi7kXgCgfkR9OtXp5GOJyoAzf8PO+fbwkCe94s7YXa5sZpqFcEjPQvAmdauH8cXdvWnfINq27+nvdzNreTELKdVpDZ3G2sPLntWLJVVStFJQBUhINuYhGwsbBQh4ZUwnvY5BGfDTYfs494imIwgQfviIrXgepPJ4SfMhEN+3XIsf3GgwYYFquuyB8wfYd25fuZbv79SMCGHeXb3o3iTGtu/lX/fxnyV/u1YMBs5Q3ixBebfcv9R5XE2FxQ/fWBoz+06ncePsDRw3PJYFBwrevqUro7s29LFk/kdGXgYrj660hc0tWr/hxHbYbXIzPMR77ozdJTw4nMsaXWYLa4ND7xMdFswnd/QstJDSu6sO8tTiv7A4W2Expgl0v90eXv4MWCxlLKnG22ilwI/581gqN83eQFKa8m0eGhTA++O7M7y9XtioLFh+ZDnZBdlAYQ98foV5ylnbq6F+F5+IYVa4fj78MxapPz7eJjwkiA8mdGdo2zjbvk82JPLwVzvJL3BS3/0fBqtPjlN/wu5vHcfTVFi0UuCnbE1MYdz7GzmXqYzBIkOD+GRSTwa1jvWxZP6LeejAL30TJKyDA7+pbREAl/2fz0TpW78v0SFq3PtExgl2ntnpM1n8mbDgQN65tStXm1ZYXLTtONMXbCc334FiEBUHvabYwyue10srVzK0UuCHrD+YzG0fbiYtRz2M1asF8/mdl3Jps1o+lsx/SclOYcMJ+5K+Zu97foGUsNw01azjzRDbxmfiBAcGc3n85bawNjgsO4IDA3jtps7c3KORbd9Pf55i2udbyc4ruDhBn+kQahgqnj1Q2ChVU+HRSoGfsfLvJG6f8zuZuephrR0ZwoLJvejUqIaPJfNvfk34lQKp6rxLbBcaRDbwsURe5sBvcMRQegKCYdAM38pD4d6YXxN+Jc86RVLjdQIDBC+M7sCkvvbVL3/bk8Rdn2whK7eIYhBeUykGVlb9B/I9XJ5Z4zO0UuBH/PrXKSZ/spUco1svLjqUBZN707ZedDEpNaXFr4cOLBZY9ow93G0ixMT7Shob3eK6ERuuhsPO5Zwr1FOj8T5CCJ4Y2ZZpg+zTmNfsT2bCnM2k5xQZIug1BcINI8XUo7B1bvkJqikVWinwE77feYJpn28j1zAAalCjGl/c3dvmiERTdhxPP872JOXaNVAEFurW9gv2fAen/lDbQdVgwMO+lccgQAQUdnt8WM9CKGuEEDw6vA0PDbMb0W4+nMKtH2wiNcvUUxMaBf0fsodXv6RW1NRUeLRS4Ad8tfUY9y/YTr4xVSi+VjhfTOlNk1oRPpasamBe/Kh3/d7UDKvpQ2m8TEF+4aWRL70bour6Tp4imJWC5UeWk5mX6UNpqg73DWnJ/13Z1hbecfQ8497fSEpGrj1S90kQbQyjZZyBTe+Ws5SakqCVgkrO55sSefjLnVinDreMjeSLu3vToIafLtVbAfHroYM/FkKy4RwoNBr63u9beYrQpmYbmlZX49xZ+VmsOrbKxxJVHe4a0Ixnr7nEFv7rxAVufm8DSWlqWi7BYcqhkZV1b0DWuXKWUuMpWimoxHy09jD/980uW7htvWgWTO5FbHSYD6WqWhw4d4D95/YDEBYYxuDGg30skRfJz4WVL9rDfaYrI7IKhBBCr5zoQ27rHc9/b+ho83K973Q6N8/eyKlUQzHoPA5qGjYI2amw/n++EVTjNlopqKS8u+ogz/yw2xbu1KgGC+7qRS1j+VNN+fBzgn3oYGCjgUQE+9GQzfZPIPWI2g6vVXj+eQXCrBSsPbHWtvaEpny4sXsjXr+ps22V1UPJGdw4ewPHzmVCYDBc9i8VUQRCXpYPJdW4g1YKKiFvLtvPiz/vtYW7N4nhszt6Uj3cD5forcBIKfkl4RdbeES8H/kmyMuC1S/bw30fUMZjFZDG0Y1pV6sdAPmWfJYfWe5jiaoe13RuwFvjuhAcqBSDIymZ3DR7I4lnM+CS0er+ufd3GP6CjyXVFIdWCioRUkpe/uVvXl1qXwCmV7OafDypJ1FhWiEob/ak7CHxQiIAEcER9GvYz8cSeZEtcyDtpNqOjIMed/pWnmIYHj/ctr3ksF5O2RcMb1+Pd2/tRkig+qwcP5/FTbM3cvBsJgx7GmrpFVkrA1opqCRIKXnh573MWnHAtq9/y9rMmdiTiNAgH0pWdTF/fAY3GkxooJ8M3eRmwNpX7eH+D0FIuO/kcYMr4q+wbW88uZFz2dqgzRcMaRvH+xO6ExqkPi2nLmRz0+yN7D+d5mPJNO6ilYJKgJSSp7/fzXurD9n2DW4Ty/vju1MtJNCHklVdpJQsSbArBcObDncRu5Kx+T01hQwguqFyVlTBqR9Zn851OgNQIAtYmqiX7fUVA1vVYc7EHlQLVu+m5PQcbnpvI7tPaFuPyoBWCio4FovkX9/sYu76BNu+Ky6J491buxEWrBUCX7HzzE5OZqju9eiQaHrX6+1jibxE9gU1dczKgIchqHL0gJgVM7PCpil/+rSozSd39CTS6MVMychl7Psb+fNYqo8l0xSH3yoFQohxQog1QohUIUS6EGKLEOIeIUSJztnb+bnLqv1nmL/5iC08smM9Zo3rSkiQ3166SoHZwHBok6EEB/qJTcemd+1zyWPiocutPhXHEy5vcjkCZei25dQWzmSe8bFEVZse8TX59I6eRIUpxSA1K48ZX/+BxepURVMh8csvixDiLeBzoDuwBlgKtAJmAV8JITxqYns7P0+4rHUsDxouRUd3acAbN3chONAvL1ulocBSUEgpMBu5VWqyzsH6WfbwwBlqSlkloU54HbrX7Q6ARPJr4q8+lkjTpXEM8+/qRY3wYOpXD2P2bd0IMKYuaiomfmehJoS4HpgGnAIGSCn3G/vjgBXAdcC9wBtOMynD/ErC9CEtaV03iqFt42xzgTW+Y1vSNs5kqVZozbCa9Kjbw8cSeYn1syDH6N6t1QI63OhbeUrA8Pjh/H7qd0AZgt7S9hYfS6Rp36A68+/qRbXgQBrVrNgGqxr/7Cn4p/E/w/oBB5BSngamGsHHPOj293Z+JeKKS+pqhaCCYJ51MKzJMIIC/EC3zkiGje/Yw4P+CYGV77yGNRlGoNFxt+PMDk6mn/SxRBpQ3lbja/uRYy8/xq+UAiFEQ6AbkAt8WfS4lHIVcByoC/Qq7/w0lZ98S34hy3a/GTpY9zrkGavYxbZTDmcqITFhMfSqZ38UzcM8Go2meCpfU8A1XYz/v+T/t3fe4VFVaQP/nWQmk56QkEAMgYSAUgSUUBRRAihVYhRQimBwVZRPl7XwrayCq2JX3AU+cVFXBARElA4ivShIlSYiEAm9JKT3mbnfH3cyJT0hybTze5557j33nHPnvWfKfe85b1GUiuJp7gUiTW1/buDzSZycPZf2kF6oGuKF+4TTuUlnO0t0Y+j1eq5fOkOmdyf0/ZeoB/0aw4kTdpXrRniyyZMMDx4OgLZIy/Hjx+0skaQEjUZDUFAQISEhaDSudvtxDVztU4kxbVMqaVNiyh9TSZv6Op/EybHOddA/pj8e9btqVK8YjUbOnTuHzlhI8+hYvDxBePlC41swZ7hxQgxGAyfST6AoqpV7y0YtXSewlBOjKApFRUWkpaVx7tw5WrRogYeH8/5+XBVX+0T8TdvcStrkmLbVCeR+w+cTQjxlcl/cd+2adJFyZooMRWxK2WQuO/vSQXp6OhoPiPAuQqcRCCEgIMKpFQIATw9P/LX+5nJWoQya4wgIIdDpdERERKDRaEhPl1EnHRFXUwpK/s3qyhH2hs+nKMocRVG6KIrSJSwsrI7EktiDny/+THaxGq410j+SDo072FmiGyMnJ4dgL4NFB9D6gi7QrjLVFYFW15FZJAPmOBJCCIKDg8nNrexZS2IvXE0pKAmw7V9Jm5K66gTjruvzSZyYdX9aLR1E91efrJ2YgtxsfA1WX1sXmCUoIUAbYP58CvWFFOgL7CyRxBpfX1/y82UaZUfE1ZSCM6Zti0raRJVq25Dnkzgp+fp8tp7bai4PjHH+NMnG/Aw8hGkSzMvfYVMj1wZPD08CvCzXk1UklxAcCQ8PD4xGo73FkJSDqykFB03b9kIInwradC3VtiHPJ3FSdpzfQZ4+D4DowGhuaXSLnSW6QVJPQlGeZbbDhWYJSgjyCjLvZxZmmg0PJfbH2WfZXBmXUgoURTkHHAC8gOGl64UQvYBmqNEJdzX0+STOS+mMiE7/p7b1HcymMroA0FW2Quac+Hv5m71DigxFFBjkEoJEUhUupRSYeMe0fU8I0arkoBAiHPjEVHxXURSjVd07QojfhRDvUJYan0/iWuQW57L9/HZz2dm9DrjyGxz93lIOiLCfLPWIh/CwWULILJQGhxJJVbicUqAoylJgNmqUwSNCiFVCiO+Bk0A7YDlqIiNrIoBbTNu6OJ/Ehdh8djOFhkIAWgW3IjY41s4S3SBb38YySxAIXq4bfjZIZ1lCyCrMkksIEkkVuJxSAKAoygRgNOrUfy+gP3AKNXHRUEVRDPY8n8S5sPY6GBQzyI6S1AEXf4XjqyxlF50lKMFP62fOhVBsLCZfX32L9+joaIRQ4zdMnjy50rajR482t42Pj78RkatNUlISQgjmzp1b7+914MAB3n//fR5++GFiYmLM17pv3756f29Jw+JqEQ3NKIqyEFhYzbZJQFJdnU/iOmQUZLDrosVcZECMky8dbHnbsq/1BS/XzlrnITwI1AWSXqAGyskszMRXW/NrnjdvHtOmTcPTs2yW9KysLJYtW3bDsjoyb7zxBitWrLC3GJIGwCVnCiSSumLD2Q3oFT0AHRt3JCogqooeDsy5PXCyJEGQAO+gSpu7CoFetoGMarqE0KVLFy5evMiGDRvKrV+8eDH5+fl07eoiKbTL4c477+TVV19l2bJl5hDFEtfEZWcKXI6CTCjOh4Cm9pbErbBeOnD62ARb3rLsdxgGnlr7ydKA+Gn90Hho0Bv1GIwGcotz8feqvrdFUlIS+/btY+7cuQwYUHamaO7cuXh6ejJmzBj27t1bl6I7DH//+9/tLYKkgZAzBY5OUR7s/Bf8qyP88LK9pXErruReYd9ldc3UQ3jQP7q/nSW6Ac7shOSt6r7whF7u810SQtxQ2OPu3bvTrl07VqxYQUZGhk3diRMn2LVrF/379ycionL7jGPHjjF27FiioqLQ6XQ0btyYQYMGsW7dugr75Obm8sorrxAbG4tOpyMqKooJEyaQlpZWpdzr168nISGBJk2a4OXlRUREBCNHjuTIkSPVu3CJWyKVAkfn2nHY+BoUZMCxZXDpkL0lchvWn1mPYrLS79qkK2G+Tpq7QlFg8zRLudNIaNyq4vYuiHUgo6zCLIw19CBOSkqioKCARYsW2RwvMfIbN25cpf1XrlxJXFwc8+fPJygoiKFDh9KuXTvWr1/PoEGDmDJlSpk+ubm59O7dm7fffpvU1FQGDhxIt27dWLx4Md27d680odDEiRMZMGAA69atIzY2lsTERCIiIli8eDHdunVj7dq1Nbp+ifsglw8cncg4aHM//L5aLW+eBqO/ta9MboL10oFTGxie2ghnTcaSHlroNala3aJfXlOPQtUvZ94dbFP20fig9dRSbCjGqBjJKcqxmT2oijFjxjB58mTmzp3LM888A4DBYGDevHmEhISQkJDAypUry+17+fJlxowZQ2FhIR999BEvvPCCuW7r1q0MHjyYadOm0bNnT/r3t8xGTZ06lb1799KhQwc2btxIeHg4ABkZGQwePLjC9/v000+ZMWMG7du3Z+nSpbRp08Zct3z5coYPH87o0aNJTk6mUaNG1R4DiXsgZwqcgT6vYk7YePJHSJHBE+ubc1nnOJp2FACNh4b7WtxnZ4lqidEIm96wlOOSoFG0vaSxG0II29mCGuZCaNq0KQMGDGDPnj0cP34cgB9//JGLFy8yatQovLy8Kuz72WefkZWVRY8ePWwUAoD4+HieffZZAD788EPz8fz8fObMmQPAjBkzzAoBQHBwMLNnzy43qqbBYOCNN9TPe8mSJTYKAUBiYiLjx48nIyODBQsW1GQIJG6CVAqcgfC20PERS3nzm+qUsKTeWHfGMktw10132QTBcSqOr4DLh9V9jQ/c85J95bEj1p9hdlE2BmPNwoskJSUBliWDkm3J8YrYtm1bpe0ef/xxAHbu3InBoMq0f/9+cnJyiIyMLDfuQceOHenYsWOZ47/++iuXLl2iffv2tGvXrtz369WrFwC7dsmHC0lZ5PKBsxD/MhxdCkY9pPwEpzdDq772lsplcQmvA4MeNlt5HHQfXyPvldJT8M6OzlOHzlNHoaFQXUIozqmRspeQkEBoaCjz589n0qRJrFixgg4dOhAXF1dpvwsXLgAQExNTbn1MTAweHh4UFBSQlpZGeHg458+fr7QPqMGVDh2ytTFKTk4GVKPGqvJzXLt2rdJ6iXsilQInwKgYOVh8ncxbB9LnsCka3aY3ILaPy2W2cwT+SP+DUxmnAPD29KZ3VG87S1RLDn8DaSfVfV0g3DXRvvLYGSEEQbogruZdBdRARjVRCry8vBg1ahQzZ85k3LhxFBYWVmlgCJjjIjREEq2SmYbIyEjuvffeStuWXlqoLwxGAxmFGQTpgtB4yFuOoyM/IQcnOTOZZzY8w8Xci0T6NqG3xhuhL4BLpnC17RLsLaLL8cOfloyI8VHxtYqAZ3f0hbD1XUu5x1/BN8R+8jgIgbpAs1KQU5yD3qiv0Y0qKSmJmTNnsnr1ajQaDaNHj66yT7NmzThx4gTJycn07Vt2du/MmTMYjUa8vb0JCVE/o8jISHNdRZRXFxWlBteKiIhokPDH1SG7OJvLuZe5nHuZEO8QIvxdO7S2syNtChycKP8ocopzALiQd4Vfbxtqqdw8DWq4LiqpHEVRXMPrYP9XkHlW3fdtDHc8bV95HASdpw4fjQ+gftbZRdk16t+5c2d69uxJaGgow4cPtzEArIiSNfx58+aVW//ll18C0LNnTzQaVUGJi4vDz8+P8+fPs3379jJ9jh49yuHDh8sc79atG6GhoRw8eJBTp05V+7rqE+vslHKmwPGRSoGDo/XU2gTNWR3UCErSwaaegMNL7CSZa3Ik9Qjnc9T13ABtAHdH3m1niWpBUS5s/8BSvvtF0AVU3N7NsAlkVIt0yjt27CA1NZWFC6uXCuXJJ58kICCAnTt3MmPGDJu67du3M3PmTABefPFF83FfX1+eeOIJQI05YL3+n5mZyYQJE8oN16zVapkyZQoGg4HExET27NlTpk1ubi6LFi0ye1HUJ8XGYnKKcsxlpzXYdSOkUuAE3N/yfvP+D+e3UnznBEvl1rdBX2QHqVwT61mCvi364uVZsauZw/LLfyBXnSInMBK6PG5feRwMa9fE3OJcio3F9fp+TZs2Zf78+eh0OiZOnEjHjh0ZNWoU8fHx9O7dm9zcXF599dUyIZSnTZtG586d+fXXX2nVqhUPPvggw4YNo2XLlly4cIGEhPKXDidOnMjzzz/PsWPH6N69O506deKhhx4iMTGRuLg4wsPDGTVqFCkpKdW+hjVr1nDHHXeYX5cuXQLUoE0lxx588MEy/bIKLa6fvlpf5/w9uRlSKXACbgu/jUh/dY0xqyiLHc07gW+oWplxFg58ZUfpXAeD0cAPZyz2BE7pdZCfAT/9y1Lu9XfQettPHgdE66m1sROxvnHVFw888AD79u3j0UcfJS0tjaVLl3LkyBH69evHmjVrePPNN8v08ff3Z9u2bbz88suEhISwdu1adu/ezbBhw/jll18qDTw0ffp0tm3bxogRI0hPT2fNmjVs3bqVvLw8hgwZwtdff83dd1d/FuzatWv88ssv5ldRkfogcvToUfOxgwcPlulnPRMjZwmcA1HTjGGS2tOlSxeltvnHZxyYwWdHPgPgvhb3Md0rBn58Va30bwJ//dXl0+DWN3su7eEvP/4FgBDvEDYN3+R8a6Cb3oQdpiA4IbHwP79UmPjo+PHjtG3btgGFcxyuF1znUo76tOuj9aFlUEs7S+R6FOoLzV48QghubnSzze+pJt8/IcR+RVG61IugEhvkTIGTMLilxWd827ltZHcaAQEmK96cK7Bnjp0kcx3W/mmJB9+vRT/nUwhyrsHu2ZZy73+4TSbEmhLoFYgwRQnNL86nyCCX4Ooa68RT/lp/5/s9uSlSKXASYoNjaRuiatVFxiI2XtwJvf7X0mDnx5BfcYIUSeUUGYrYkLLBXB7UcpAdpaklOz6E4lx1v8mt0P4h+8rjwGg8NPh5+ZnLtTE4lFSMoihkFFoySgbrgu0ojaQmSKXAibA2OFydvBpuHwONTBHPCjJUxUBSK3ac32GOh3+T3010CutkZ4lqyPVk2PuFpdznVfCQP+/KsDY4zCzMLNeaX1I78vX5FBtUA04P4YG/l7+dJZJUF/mv4UQMjBmIh1A/sr2X93K5IA36TrU02P0pZJ63k3TOzcrTloxz98febx5np2HTm1BiRd+8B9zspPEVGpAArwDz51xoKKRAX2BniVwH61mCIF2Q8/2e3Bj5STkRYb5hdG/aHQAFRV0Db/8g3NRZbWAohC1v21FC5yS9IJ3tFywBYoa0HGJHaWrBhf1w7HtL+b43ZPjrauDp4UmglyVmgfWNTFJ7jIrRJgul9DpwLqRS4GTcH1tqCUEI9SZQwq8L4coxO0jmvPxw5gf0Rj0AHcM6Eh0UbV+BaoKiwIbXLOW2CRDV1X7yOBnWN6zMokyMitGO0rgGucW55gyUWg8tvhrpFeVMSKXAyejbvC/enqrf+cn0k5y4fgJi7obW/UwtFNj4T7vJ54ysOr3KvJ/Q0slySZzaCGd2qPvCE/q+Vnl7iQ1+Wj+0HqqHhsFosIm+J6kdpZcOGiIRlKTukEqBk+Gn9aN3c0vWvjV/rlF37v0nmFysOPkj/Fk2XrqkLMmZyRxJPQKoFulOlevAaIANVjYlcUnQuJXdxHFGSjInliC9EG4Mg9Fgk09CLh04H1IpcEKsvRDWJK9RpzybtIfbRlkabZgKRjkVWhWrT68278c3i3euP7FDi+Hqb+q+1g/iX7avPE6KtbtcdnG2eSlJUnOyirLMXhzeGm+8NTKaprMhlQIn5M6b7qSRTg1xejXvKvsum6Ik9v4HlPwILx6E35bZSULnwKgYWZVsWToYEutEBobF+bDlLUu5x3PgX3XGPklZdBrbzIkNEfbYVZFhjZ0fqRQ4IVoPrc009+pk09NuUDPoPt7ScNMbMllSJey9vJfLuZcB9WnRqTIi/vIfyLqg7vuFQY9n7SuPk2N9A8sokl4ItaHYUExuSfAsbONASJwHqRQ4KdZLCBtSNlh8rHs+D96m6dD0M7D/y4YXzkmwjk0wMGYgWmcJCZx3HXZOt5R7/V2mRr5BrA3i8ovzKdQX2lki58M6rLGf1s95fk8SG6RS4KR0aNyB5gHNAcgpzmHb+W1qhU8juOclS8Nt70GBnA4tTV5xnk1Y44RYJ/I62PERFJj+gENiVQNDyQ2h8dDgr7VE3ZOzBTVHLh24BlIpcFKEEDZJktYkr7FUdn0SglSFgbw0+OnfDSyd47Pp7Cby9fkAtAxqSfvQ9naWqJpknLVNfnXvazLpUR1hbXCYWSDDHteEAn2BebZSCGETFEriXEilwImxVgp2nN9BWn6aWtB6q7HvS9g1CzLONbB0jo11bIIhsUOcx5d6w2tQktGvWVc1WJGkTvD38sfTwxOAYmMx0THRCCEQQjB58uRK+44ePdrcNj4+vv6FBZKSkhBCMHfu3Hp9n7y8PFatWsWECRPo0qULYWFh6HQ6oqOjGTt2LAcPHrSJTRDgFWAeR4nzIZUCJ6ZFYAtuC7sNAL2it7nR0WE4NO2o7usLYKMMalPCldwr7L60GwCBsLHPcGhSfi4VzvhNGc64DvEQHjZPuNbRDefNm4fBYCi3X1ZWFsuWua6nz8KFC0lISGD27NmkpqZy1113MWTIELRaLfPnz6dr167M+cwyeyUzIjo3Uilwch5qbUmP+93J7yxTnh4eMPA9S8Oj36k3FQlr/lyDgjpO3SK60dSvqZ0lqgZGA6z7u6Xc/iFocaf95HFRrG9oJUpBly5duHjxIhs2bCi3z+LFi8nPz6drV9cML63Vann88cc5cOAAZ86cYfny5SxdupQ//viDjz76CIPBwJv/+yZnTp8pY5shcT6kUuDk9I/uj59WzQt/JusMB64esFS26KHePEr44WW3D2ikKAorT1m8DpzGwPDXr+HyYXVf422b70JSZ/hofPDy9LI5lpSUBFDhNP3cuXPx9PRkzJgx9SydfXjsscf44osvuP32222OCyF44YUXuKvXXej364fkAAAgAElEQVSL9fyw/AcaeTdynqU4SblIpcDJ8dX6MihmkLn8/cnvbRvc94YloNGlQ+rNxY05fv04pzNPA+oN4N7m99pZompQkKXGnCjhrokQHGU/eVwYIUSZ6e/u3bvTrl07VqxYQUaGrVfCiRMn2LVrF/379yciIqLScx87doyxY8cSFRWFTqejcePGDBo0iHXr1lXYJzc3l1deeYXY2Fh0Oh1RUVFMmDCBtLS0Kq9l/fr1JCQk0KRJE7y8vIiIiGDkyJEcOXKkyr7VpchQROtbWwNw5eIVuXTgAkilwAUY2nqoef/HMz/apC0lOEq9iZSw6XW3dlG0tru4t/m9+GqdIIPb9g8g95q6Hxhp+3lK6pzS7nR6g56kpCQKCgpYtGiRTV3J7MG4ceMqPefKlSuJi4tj/vz5BAUFMXToUNq1a8f69esZNGgQU6ZMKdMnNzeX3r178/bbb5OamsrAgQPp1q0bixcvpnv37qSnp1f4fhMnTmTAgAGsW7eO2NhYEhMTiYiIYPHixXTr1o21a9dWczQqJ6Mwg7PJZwG46aabysyySJwPjb0FkNw47ULb0SakDb9f/50CQwFrk9cyos0IS4O7JsLBBWoEvNxr6k2m35v2E9hOFBmKbFw3nSKscdpp2D3bUr7vDfDya5j3/qcT+5r/s/aJjbw8vcxLcqDmQxgzZgyTJ09m7ty5PPPMMwAYDAbmzZtHSEgICQkJrFy5stzzXb58mTFjxlBYWMhHH33ECy+8YK7bunUrgwcPZtq0afTs2ZP+/fub66ZOncrevXvp0KEDGzduJDxcDWOdkZHB4MGDK3y/Tz/9lBkzZtC+fXuWLl1KmzZtzHXLly9n+PDhjB49muTkZBo1alTrcVIUhd0HdrN9w3aEEAx7aFitzyVxHORMgQsghLAxOCyzhODlB/e+binvnq3ebNyMDSkbSC9Un64i/CLo1rSbnSWqBj++CsZidT+qO9w6tPL2kjrBeho8qyiLJk2aMGDAAPbs2cPx48cB+PHHH7l48SKjRo3Cy6viJ+TPPvuMrKwsevToYaMQAMTHx/Pss2qI6g8//NB8PD8/nzlzVIv+GTNmmBUCgODgYGbPnl3u2r3BYOCNN9SlpiVLltgoBACJiYmMHz+ejIwMFixYUK2xqIjL6Zd56amX0Ov1PDjqQXp06XFD55M4BlIpcBEGxQxC56kD1HXzY2nHbBt0GKbeVEC9yfz4Ku7GkhNLzPvDbh7m+L7UpzbBCatp3gHvShfEBiJQZ3FN1Bv15BTnlDE4LNmWHK+Ibdu2Vdru8ccfB2Dnzp1mt8f9+/eTk5NDZGRkuXEPOnbsSMeOHcsc//XXX7l06RLt27enXbt25b5fr169ANi1a1elcldGcXExIx8ZycnjJ2lzaxs+mP4BHkLeTlwBuXzgIgTpgujXop8569/3f3xP+zutovQJod5UPuutlk+shdObIbaPHaRteP5I/8PsmaERGpuZFYfEoIf1/7CUb3sUIjs3rAw3MAXv7HgID5ubXHpBOgkJCYSGhjJ//nwmTZrEihUr6NChA3FxcZWe68IFNXFVTExMufUxMTF4eHhQUFBAWloa4eHhnD9/vtI+ANHR0Rw6dMjmWHJyMqAaNVblBXDt2rVK6ytCr9fz8CMPs23jNlre3JL/LPkPkSGRtTqXxPGQSoEL8VDrh8xKwdo/1/JilxdtDekiO6s3l19N04Y/TIanfwJP1/8afHviW/N+n+Z9aOzT2I7SVIN9/4Vrv6v7Xv7Qd6p95XFDrJWC7KJsmvo1ZdSoUcycOZNx48ZRWFhYpYEhYI4d0hCueiUzDZGRkdx7b+WeNaWXFqp7/tGjR7N82XKaxzTn8+8+J+qmKHQaXa3klTgern83cCPimsQRHRjNmawz5BTn8GPKjyS2SrRt1Hcq/LYcinLUm86+L2zTLbsgecV5ZmUJ4JFbHrGjNNUg7zpsectSvuclCGhiP3ncFIHtTTy9MJ2kpCRmzpzJ6tWr0Wg0jB49usrzNGvWjBMnTpCcnEzfvn3L1J85cwaj0Yi3tzchISGAelMvqauI8uqiolRX1YiIiDoPf2wwGBgzZgxLliyhWYtmfLHsC8KbhtNIV3tjRYnjIReBXIgqDQ5BvblYZ1Hc/BZkX24A6ezHmj/XmPO8RwdG07Wpg0ee2zAVCkz+8I1i4I4J9pVHAkBGQQa33X4bPXv2JDQ0lOHDh9sYAFZEyRr+vHnzyq3/8ks1vXnPnj3RaNTntLi4OPz8/Dh//jzbt28v0+fo0aMcPny4zPFu3boRGhrKwYMHOXXqVLWvrSqMRiNjx45l0aJFNG/RnP8u+y8RkRFqaGidTH7kSkilwMUYEjsEjVD/WA5ePcjpjHK8DO6YoKbcBSjMVCMduiiKotgsHTx8y8OOHXHtzE9wcL6lPOAdkFOzdsVTqAapeqOe7KJsduzYQWpqKgsXLqxW/yeffJKAgAB27tzJjBkzbOq2b9/OzJkzAXjxxRfNx319fXniiScANeaA9fp/ZmYmEyZMKDeLo1arZcqUKRgMBhITE9mzZ0+ZNrm5uSxatMjsRVEVRqORcePGsXDhQpo3b86iVYu4KeomQLVlkgaGroVcPnAxGvs0Jj4qno1nNwLqbMGkrpNsG2l0cP/HMM8U4vfYMug0Cm7u18DS1j9HUo9w/Lr656fz1Dl2WGN9Iaz+m6XcdgjcMtB+8kgAW0+E9IL0MsGNqqJp06bMnz+fRx55hIkTJ/L5559z6623cvHiRXbs2IHRaOTVV19lwIABNv2mTZvGjh07OHDgAK1ataJPnz54enqyZcsWgoODK4yNMHHiRFJSUvj444/p3r07HTt2JDY2FqPRyLlz5/j999/Jy8tj3bp1tG3btkr5Z82aZZ7liGkZw/tvv48pdYhNRsSePXuaFRmJ8yKVAhdk6M1DzUrBqtOrmNh5YtlIYy17QaeRcMgUoW3NixC9u+EC4zQQ35z4xrw/IHpAjf/QG5Sd/4LUP9R9rwAY+L595ZEAEKi1KAW5xbkU6gtrbFj3wAMPsG/fPt577z02b97M0qVLCQgIoF+/fjz33HMMGjSoTB9/f3+2bdvGW2+9xeLFi1m7di1hYWEMGzaMt956i5deeqmcd1KZPn06iYmJzJ49m59++ok1a9bg4+NDREQEQ4YMISEhgbvvvrtasl+/ft28v23rtkrbSqXA+RHlTUFJ6ocuXboo+/btq/f3MRgNDPh+AJdzVVuBD3p9wIDoAWUb5qbBrC6Qb/rR9/irS0U6zCzMpO+3fSk0FAKwcNBCOoR1sLNUFZB6CmbfCYYitTzwA+j+VL2+5fHjx6v1pCiBs1lnyS7KBiDUJ9Q5MmvWMYqicDrzNIV69fcU4RdBiE9Irc9Xk++fEGK/oihdav1mkmojF4NcEE8PTx5s9aC5vPSPpeU39AuFftMs5V3/B5fKGi85KytOrTArBG1D2nJr41vtLFEFKIq6bFCiEETGQde/2FcmiQ2NvC0W9hkFGea0yu5Evj7frBAIIRx71k1Sa6RS4KI82OpBs0vVL5d+4WT6yfIb3jYKok3TiIoBVk0Eo6GBpKw/FEXh2z+cxMDw14VwZoe6Lzzh/n+Bo0dbdDP8tf5oPbUAGBQDWYXul1TseoFlGSHIK8jxI4JKaoVUClyUCP8I7m1hCV7y1bGvym8ohGp0WGJzcPEA7P2iASSsX/Zc3sOZrDOA+odunV7aochNsw05fecEiCgbvlZiX4QQhHhbpsqvF16vpLXrUWQoIrPQEuHyRpYNJI6NVApcmMfaP2beX/PnGq7kXim/YePWcLeV0dKmNyDrYj1LV79YGxje3/J+x02R/OMrFpuOoOYQP9m+8kgqJFgXbJ5tyi/OJ1+fb2eJGg7rWQI/rR8+Gh87SiOpT6RS4MJ0CuvE7eG3A6qP9cLfK/Gr7vk3aHyzul+UDev+twEkrB+u5V1jy9kt5rLDRjBM3mbx/gAY/JHLeX+4EhoPDYFetu6J7oDBaLC51lCfUDtKI6lvpFLg4ljPFnx74ltzZL8yaHTqWnYJx1fB72vqWbr64fuT36NX9AB0Du9Mq0at7CxRORQXwOrnLeX2D7pknAhXw9rgMLMwE4ML2N9URXphutmwUuepw1/rb2eJJPWJVApcnPhm8bQIbAFAdnF2+aGPS4i+C25/1FJe/TzkptazhHVLoaHQZung4VsetqM0lbDpdbhuijapC1IzWEocHl+NrzlGgVExkl7o2rMFRsVIWn6auRzqE+q4BruSOkEqBS6Op4cnY9uNNZfn/zYfvVFfcYf73gQ/Uzz3nCuqN4ITxbJYfnI51/LVkLDhPuHc1+I+O0tUDqc3w+5PLOX7XocA9/N7d0ZKGxym5ae5tHtiVmGW+f9C46GRbohugFQK3IAhsUPMmcwu5V5iQ8qGihv7hsAD/2cp/74aDi6oZwnrhmJjMV8ctXhOJN2aVDaSo73Juw7LrRIcte4PcUl2E0dSc4J1wWg81GCweqOejJLkVS6GoiikFlhmCkO8Q2SeAzdAfsJugI/GhxFtRpjLXx79stxkKmZu7gddrcKV/vAyXE+uRwnrhtWnV3Mp9xIAjXSNGNp6qJ0lKoWiqEsy2aqM+DaGB2apbqESp8FDeNDYp7G5nJqf6pKzBSUhnUG9Zmt7ConrIpUCN2FEmxHoPNW10OPXj7PvShXhlu97E0Jbq/tFOfD9eDBUsuxgZwxGg80swdj2Yx3PDfHwN/Dbcks5YSb4V516V+J4NPJuZA7eU2wstvHhdxVS8y2zBMHeltkRiWsjlQI3IcQ7hAdiHzCXvzz6ZeUdvHzhoTlQ8kdwfg/s/LgeJbwxfkz5kZSsFEDN3DbilhFV9Ghg0lNgrVW2ys6PQRsHDagkqRIP4UGot8U1LzU/tfLZNycjX59v46lkfa0S10YqBW7EmHZjzKGPd1zYwan0U5V3iOwM8S9bylvfgQv761HC2mFUjMw5PMdcHt12NP5eDuQ2ZTTAsqehJDRuSEvo/7Z9ZZLcMCHeIXgKdbagyFBEVpHrhD629jgI1AU6nm2OpN6QSoEbER0UTe+o3ubyvN/mVd3pruchqru6rxjg+6egqIJYB3Ziy7ktnMpQFRwfjQ+j24y2s0Sl+HkGnP1Z3Ree8OAc0DmQ0iKpFZ4enjbhfq/lX3OJ2YJiQ7FNbofG3o0raS1xNaRS4GYk3Zpk3l+dvJpredcq7+CpgQf/AyVP3mmnbGP12xlFUWxmCUbcMoJg72A7SlSKS4dg81uW8j2TIKqr/eSRVJvo6GiEEAghmDy5/PDTJRb5f3/677Ru1BoPDw/i4+MbRL6kpCSEEMydO7dOz5tWkIaCqtz4an3x1njz5ptvkpiYSOvWrQkODkar1RIREcGQIUNYtWpVnb6/xL5IpcDNuC3sNjqGqQl3io3FlYc+LiEkBga+Zynv+y/8vraeJKwZP138id/SfgPUaGtj24+tokcDUpQL3z0JxmK1HBkH97xUeR+JQzJv3jwMhrLRCzUeGrRFWjat3WQHqeqe0iGNG/s0xmAwMHXqVNavX0+jRo2Ij48nMTGRiIgIVq9eTUJCAs8995wdpZbUJVIpcDOEECS1TzKXvz7+NVfzrlbd8bbR0HaIpbxsPKRWkI65gSg9SzC09VAbVzG7oihqPILUE2pZ6wsPfQam9LsS56FLly5cvHiRDRvKj++xYcUGCvILuPX2WwE1tbKzYu1e6eXphb/WH09PT7Zu3UpGRgZ79uxh+fLlfPvttxw4cICtW7fi5+fHrFmz2LJlSxVnlzgDUilwQ/pE9aFVsJoPIF+fz6yDs6ruJATc/28IbKaWC7Ng0UgosJ8r1r4r+zh49SCgPrGNu3Wc3WQpw46PbN0PB74PobH2k0dSa5KSkgAqnKafP28+np6eDBmuKs3FhmKntC0oMhSRVmAxMAzzDTMvn/Tq1QudTlemT69evXjkETXhWEVKk8S5kEqBG+Lp4cmkrhb3uOWnlnM87XjVHf1CYcTXoPFWy2knTdPj9nkysp4leCD2AZr6OUio4BPrYPM0S7nrk9B5jP3kkdwQ3bt3p127dqxYsYKMDNvohSdOnGDXrl3069ePsKZhgDpTkKfPK3OeY8eOMXbsWKKiotDpdDRu3JhBgwaxbt26Ct87NzeXV155hdjYWHQ6HVFRUUyYMIG0tLQK+5Swfv16EhISaNKkCV5eXkRERDBy5EiOHDlSbvsreVfMyoyPxocgr+qFNNZoVLdlb2/varWXODZSKXBTetzUg3ua3QOAgsIH+z6o3tPNTbfZhkE+ud72BthAHL52mN2XdgOqz/hfbv1Lg8tQLtdOqIqSyVCLFj1hwDt2FUly4yQlJVFQUMCiRYtsjpfMHjz++OP4aS1pr0sb8K5cuZK4uDjmz59PUFAQQ4cOpV27dqxfv55BgwYxZcqUMu+Zm5tL7969efvtt0lNTWXgwIF069aNxYsX0717d9LTK07GNHHiRAYMGMC6deuIjY012wAsXryYbt26sXatrU1QXnGejcdBU7+m1Up8tH//fr755huEEAwePLjK9hLHR4aocmNe7PIiP1/4Gb2iZ+/lvWw+t5m+zftW3bHDMLh8BH4ypVreOR2a3gq3NkxYYUVRmHFghrk8KGYQUYFRDfLelZKfoS6pFGWr5aDm8PBXTmtH0OGrDvYWodYceaz8p+HaMmbMGCZPnszcuXN55plnADAYDMybN4+QkBASEhL4frklA2lucS45RTn4e/lz+fJlxowZQ2FhIR999BEvvPCCud3WrVsZPHgw06ZNo2fPnvTv399cN3XqVPbu3UuHDh3YuHEj4eFq9MuMjAwGDx7MypUry5X1008/ZcaMGbRv356lS5fSpk0bc93y5csZPnw4o0ePJjk5mUaNGqEoCpdzL5vbBOoCK4wG+sEHH3Ds2DEKCgo4c+YMe/bsQavVMmvWLOLi4moxshJHQ84UuDEtg1rapBaevm86xYbi6nXuOxVaWWUgXP4/cOlwHUtYPquTV/PL5V8AdZbgiQ5PVNGjATAa4Lu/WNIha33VpRY/BzF8lNwQTZs2ZcCAAezZs4fjx9Wlth9//JGLFy8yatQovLy8yoQBvpR7CaNi5LPPPiMrK4sePXrYKAQA8fHxPPvsswB8+OGH5uP5+fnMmaMuj82YMcOsEAAEBwcze/bscp/kDQYDb7zxBgBLliyxUQgAEhMTGT9+PBkZGSxYoCY6yyzKJF+fD6iGyE18m1Q4DuvXr+err77im2++4ZdffsHHx4eZM2cyfvz4SkZP4kxIpcDNeabTMwR4BQBwNvssi35fVEUPEx6eMPRzCFUNFtHnw+JRkJtaeb8bJLMwkw/3Wf48R7cdTWywAxjwbXodTm20lBM/gYiO9pNHUueUNjgs2ZYcL6EkamiRoYjU/FS2bdtWbrsSHn/8cQB27txpdnvcv38/OTk5REZGlhv3oGPHjnTsWPb79euvv3Lp0iXat29Pu3btyn2/Xr16AbBr1y6MipEruVfMdaHeoZVGL9y4cSOKopCdnc2BAwcYOXIk48ePp1+/fmRnZ1fYT+I8yOUDNyfYO5inOz7NB/s+AODTw5+SEJtQvQBAPsEwYhF83lf1Rsg8B0vGwtgV9TZl/vH+j7lecB2AJr5NePa2Z+vlfWrE4W/hp39byne/BO0ftJ88dURdT8E7OwkJCYSGhjJ//nwmTZrEihUr6NChQ5lpc+ubamp+KucvnAcgJiam3PPGxMTg4eFBQUEBaWlphIeHc/585X1ADa506NAhm2PJyWo202PHjlVpE3Dt2jVS81PRG9VEZ54entV26fX39+f222/n888/x8fHh1mzZvHaa68xffr0avWXOC5SKZAwss1IlvyxhJSsFLKLsvnk0Cf8o/s/qtc57GZ1xmDhI4ACKT+pMQwenKNGQ6xDDlw5wHcnvzOX/9H9H/bPhHhqE6z4H0v55oHQ+xX7ySOpN7y8vBg1ahQzZ85k3LhxFBYWMm5cWTdYjYcGH40P+fp8FEUxL8lVx3DvRimZaYiMjOTee++ttG3rm1vb5DgI9w03Z36sCUlJScyaNYvvvvtOKgUugFQKJGg9tbwQ9wITt0wEYMmJJYy4ZQQtg1tW7wQ391dtDDa9rpaPfqdmV0ycrS4z1AHFhmLe2PWGudw7qjd9mvepk3PXmuSt6pKJQc05T+ObTZkl5aqcq5KUlMTMmTNZvXo1Go2G0aPLz7Nxk/9NnM5Q7UvCI8JJPplMcnIyffuWNeQ9c+YMRqMRb29vQkLUXAqRkZHmuooory4qSjW4jYiIqDL88YWcC2QUqC6WOo2ORrpGlbaviLAw1RXz6tVqBEGTODzy30sCqDfZbk27Aaqf9Uf7P6rZCXo+D12tDP4OfwMrnq2zGAZf/fYVpzPVP1kfjU/1ZzLqiz+3w8IRoC9Qy0FRMPpb8A60r1ySeqVz58707NmT0NBQhg8fbmMAaI23xptQHzXdcJceXQD4at5X5bb98ks1jXnPnj3NPv9xcXH4+flx/vx5tm/fXqbP0aNHOXy4rGFvt27dCA0N5eDBg5w6VXEW1Hx9vlkhAGjqWz0XxPLYvHkzAK1bt65Vf4ljIZUCCaBObU7qOslsJLX9/HZ+vvBzTU4AAz+AOKvp1EMLYdVfwWi8IdnOZZ3j00OfmsvP3vasfQMVnflJXS4xWWwTGAmPrYJG0faTSdJg7Nixg9TUVBYurDxvSJhPGFoPLcMeHYafvx8/7fyJGTNm2LTZvn07M2fOBODFF180H/f19eWJJ1Qle+LEiVy7Zol7kJmZyYQJE8qNK6LVapkyZQoGg4HExET27NlTpk1OTg5zvprD6T9UJTvAK6DSVOMrV65k5cqV5eZ+WLNmDS+9pObzeOqppyo8h8R5kMsHEjNtQtqQ2CqRZaeWATDl5yl8c/831c8n4OEBg6erKZYPmNIyH1ygpgu+/1+1mlZXFIW3fnmLQtMUfduQtoxqO6rG56kzzu6Gr4dDsSliXUCEqhCEVGwQJnFPPD08ifCPoLhJMe988g4vPfkSEydO5PPPP+fWW2/l4sWL7NixA6PRyKuvvsqAAQNs+k+bNo0dO3Zw4MABWrVqRZ8+ffD09GTLli0EBweTkJBQbqyCiRMnkpKSwscff0z37t3p2LEjsbGxGI1Gzp07x++//05eXh6fLv6UVje3qtQFEeDAgQO8/vrrhIWF0blzZxo3bsz169c5ceKE2bDxySefZMKECXU3eBK7IWcKJDY8d/tzBHqpU+BX867y0raXKDZWM3YBqDf++/8Ntz1qOXbgK1j7kpokqIb8cOYHfrr4E6C6ek29c2oZf/AG49weWDAUinPVsn9TeGy1zGkgqZAArwACvQLpM7AP32z4hoSHE0hLS2Pp0qUcOXKEfv36sWbNGt58880yff39/dm2bRsvv/wyISEhrF27lt27dzNs2DB++eUXGjWq2AZg+vTpbNu2jREjRpCens6aNWvYunUrObk53NPvHt779D0639GZEJ8QdJqyOQ2sGTp0KJMmTaJ169YcOXKEb7/9lq1bt+Lh4cGjjz7K5s2bmTNnDh7SlsYlEM6YuMNZ6dKli7Jv3z57i1ElOy/sZMLGCeac6qPbjublbi/X7CRGg2qVf8gq7kG3p9TEQNVcu8wqyiJhWYI5ScuoNqOY3L38vPb1zvl9MC/REq3QLxyS1qjeF07K8ePHadu2rb3FcHmKDcWcyjhlzj4Y7htOmG9Yg8tRZCgiOTMZg8nOx0frQ3RgNB7CPjfzmnz/hBD7FUXpUs8iSZAzBZJy6BnZk792/qu5/PXxr1l1elXNTuLhqeZI6DDccmzPHPjm0WplVtQb9byy8xWzQhDuE85zt9spZ/vhJTD3fotC4NtYXTJwYoVA0nBoPbWE+1oMEq/lXyO3KLdBZTAqRs5lnzMrBBoPDVH+UXZTCCSOi8t9I4QQtwghFgghLgohCoUQKUKI2UKIiFqe63khxDohxCkhRIEQIlMIsUsI8TchRMWhv5ycv9z6F+5tbvFzfn3X6/yW9lvNTuLhCYmf2uZE+H01zOkNVyo+l1Ex8trPr7H13FbzsZe7v1ypMVS9oC+CNS/B909ajAp9Q1WFILxN5X0lEitCvEPwNmUXVRSFs9lnyS/Ob5D3VhSFizkXKTB5ygghiAqIQuukOTkk9YtLKQVCiF7AQWA0cAlYBuQBTwOHhBA1fbTbBEwH4q3Otx+4DfgY2C2ECKkT4R0MIQTTek6jZZAaq6DQUMjftvyN9IKKM7OVi6dGDWTU/WnLseun1SiIh78t01xRFN7f+z4rT1sMqMa1H8d9Le4r07ZeybwAcwfB3s8sx0Jbw7h10KT88LESSUWU3IhL7GGMipGU7BTzjbo+uV5wncxCy+xcU7+m9g/6JXFYXEYpEEL4AYsBH+A5RVHiFEUZoShKW+AjIAxYJGrmjHsC+AsQpijK3YqijFQUpQ/QFjgG3I6qHLgkflo//t373/hr1Sf0S7mXmLR9kjksarXx1MDA92DoF1CSXrY4D75/Atb+r/pEbuLTQ5/y9fGvzeWhrYfyfNzzN3wtNSJ5G/znHji/13Ks3QPw5GYIu6VhZZG4DF6eXrQIbGGOGmgwGkjJSqHIUFRFz9qTW5xrkwEx2Du41kGKJO6ByygFwDigKbBVUZRZper+DpwGOgMDq3tCRVH6KoryX0VRckodP4M6+wDwsCsvI0QHRfPu3e+ay79c+oV/H/h3JT0qocMweHKT+sRdwp7/wNzBkHWRBb8t4JNDn5ir+rXox5Q7pjRIeFhA9Y7Y+THMT4Q8U2In4Qn93oLhX8nARJIbxlvjTYuAFua1fL1RT0pWSs08fKpJsaGYc9nnzGUfjQ8RfhEN93uSOCWupBQkmrYLSlcoimJAnUWwbnejHDRtvYHQOjqnQ9IrqhcTOll8kOcem8ucw3PMRks1Iryt+sTddvaohKgAAA0QSURBVIjl2Pk9rPyyF+/tfc986K6b7uLdu9+tVSz2WnF+P3w1BDb+E0xW4viFq/YDPZ6ttseERFIVPlofmgc0N9+ciwxFpGSl1HwGrhIK9YWkZKeYf6OeHp5EBUjDQknVuNI35HbTdm8F9XtLtbtRSh53i4DrdXROh2V8p/HEN4s3l2cenMm49eNsnkSqjXcgPDwf7nsThCebfX2YGmTxlb7NN5Lp93zQMIZQV4/D4tHweR84s8NyPOoOGL8dou+qfxnsiHRJtg9+Xn40829mLhfqCzmbfbZ2irYViqKQlp/G6czTFOrVgF8CxzMslN87x8UllAIhRCBQYvCXUkGzs6ZtXYWeK3HcX60oSmEdndNh8RAevH3323QK62Q+dvDqQYauHMrSP5bW/EcuBFldk/ik11NMCm+MwfTUdHNhEbOO78b3sz7w24paBTyqFukpsOxp+ORO1SPCLJcn3PksJK2GwBo7rDgVHh4eGG8wBLWk9gTqAon0jzSX84vzSclKIacop1Y3zWJDMWezz3I597K5vxCCCP8I/EpseRwEo9Eogx05KC4RvEgIcRNwwVTUKopSZh5OCNEa+AMoUhSl8hBeVb9fEvAlqmdDZ0VRTlTS9ingKYDmzZvHpaRUpLM4B3qjns+OfMZ/Dv0Hg2J5qunVrBf/7PHPaoVEzizMZMHxBXz929dkF2ebjzfXG/nqwkUaW9+oIm6Du1+ElvE3vqZvNMKVo3BwPuz7Ekqv47Z/UE173Ng9ErukpKQQEhJCQECAvUVxa9Ly02yMAQF8tb6E+YThp/Wrlg1AZmEml3Iu2fwmdRodkf6R+Gh86lzmGyU7O5v09HSaN29erfYyeFHD4RBKgRDifSChFl37KopyQQgRCZw3HatXpUAI0RdYC2iBsYqilLFhqAhniWhYHY6lHmPyzsn8mfmn+VgjXSMmdZ1Ex7COhPmElXF7yizMZP5v8/n6+NfkFNvYbhIbFMv/3f0+kUeWwc8zLYGCShCe0Kyrqhy0jIdmXaA606EZZ+H0FjXN8Z/bIC+tbJtW90KfKXDTbdW5dJchLS2NvLw8mjVrJo3P7ExqfipXc6+ao4iW4KP1IdwnvIxyoCgKekWP3qgnLT/NxuUQINQnlHDfcIe0IVAUhfPnz+Pr60toaPXMsaRS0HA4ilKwADW2QE2JURTljGn5oORXEawoSpmQeUKI24EDQJqiKNXM8FPmHD2BHwA/4K+KosysSX9XUgoACvQF/OvAv2xcCK3x0/oR5hNGmG8Ywbpgfr74M7nFtpHcogOjearjUwyMGWjJaZCbBjunw57PwFDByoyXP7S4C4Kjyq8vzoezu+B6csUXENUd+r7m8nYDFWE0GklJSUGn0xEaGoqXl5dUDuxIkaGI1PxUMgozyiwf+Gh80HhoKDYWozfqKzRK1HpoiQyIdLjlAlCVgaKiItLS0igsLKRFixbVXkKQSkHD4RBKQV0ghEhDtSvopChKmUTjQogEYAVQqy+XEKIHqkIQAPxdUZT3a3oOV1MKSth1cRev/vQqV/OuVrtPdGA0T3d6mgHRAyr2MMi8oAYPOrUJLpfNHV8rfBtDzD3QaSS0vs/tvQr0ej3Xr18nMzMTvb7urN8ltcdgNJBdnE1+cX6ZmYPK8NX4EqgLdMjZgRI0Gg1BQUGEhISg0VQ/sZlUChoOV1IKNgJ9gScURfminPppwCvA54qiPFnDc98BrAcCgVcVRXmrNjK6qlIA6tLAnMNzOHTtENfyrnEt/1q5vtctg1oyvuN4+kf3r5m7YW4q/LldXQZI3qIuC1QHjY86E9AyXn2Ft69VCmeJpKG5lHOJL45+wfcnvy/3txSkCyLMJ4wIvwgevuVh4qPiG17IBkIqBQ2HKykFzwEzgC2mqIPWdZ6o0QljgcGKoqytwXm7ARtQFYJ/Koryem1ldGWloDSKopBZmMnV/Kuk5qVyNf8q4T7hdI/ofuOxBxQF0v+ElF1qZMSKCGsDUd2gitSwEokjczn3Mnsv70XnqTNnWGzs0xidp/t8r6VS0HC4klLgD5xEjWr4rKIo/2dV9wHwEmrAoTjF6qJNN/15AIqitCl1zjjU/AdBwJuKoky9ERndSSmQSCSSukIqBQ1H9Rd1HBxFUXKEECOAdcAsIcQ4VCWhE2quglRgpFJWC/IFKgpovwFVIcgAmgsh5lbQ7iVFUVJv8BIkEolEIrErLqMUACiKss3kZTAV1b6gA3AF+A/wuqIol2p4ypLMIcHAY5W0+yeq0iGRSCQSidPiUkoBgCmQULXdGxVF2QqUa4KuKIp7m6ZLJBKJxK2QZtgSiUQikUgAqRRIJBKJRCIxIZUCiUQikUgkgFQKJBKJRCKRmHCZOAXOgBDiGhWndq4OjZFeDqWRY1IWOSZlkWNSFmcakxaKooTZWwh3QCoFToQQYp8M4GGLHJOyyDEpixyTssgxkZSHXD6QSCQSiUQCSKVAIpFIJBKJCakUOBdz7C2AAyLHpCxyTMoix6QsckwkZZA2BRKJRCKRSAA5UyCRSCQSicSEVAokEolEIpEAUilweIQQo4QQO4QQmUKIHCHEPiHE/wghXPKzE0LcIoSYKIRYIIT4XQhhFEIoQohh1ejrkmMlhNAKIfoKIT4SQuwWQlwSQhQJIS4IIZYKIeKr6O+q4/KcEGKJEOK4ECJNCFEshLgmhNgohHhUCFFhQjNXHZPSCCHeNv1+FCHES5W0c4vxkFQDRVHky0FfwP8BCpAPrAaWAVmmY98DnvaWsR6u+V+m6yv9GuauYwXcazUOl0zX9w1wxOr4G244LueBIuAAsApYDOwCjKbrWw54uNOYlLrOroDeajxecrfviHzV4ntjbwHkq4IPBoZa3QRaWx1vAvxmqptobznr4bqfAN4HHgZiga1VKQWuPlZAH2ApcHc5dY+Y/vgVoLebjUtPwK+c4+2By6brG+dOY2J1PTrgGHDBdJMvVylwl/GQrxp8d+wtgHxV8MHAPtMPcmw5db2sfshlnoRc6VVNpcCtxwr43HSNX8hxMV/fFNP1LXTHMQHeM13LEGBuJUqBW4yHfFX/JdeLHBAhRDMgDnVq9NvS9YqibEN9AmgK3NGw0jkWcqwAOGjaNis5IMcFvWlbUHLAXcZECNEdeBFVIVpVSTu3GA9JzZBKgWNyu2l7TFGU/Ara7C3V1l2RYwWtTdtLVsfcdlyEEDHA06ai9U3R5cdECOENfAVcByZW0dzlx0NSczT2FkBSLjGmbWUZFc+WauuuuPVYCSGaAkmm4ndWVW4zLkKIcahT3VrU2ZIeqA887yiKssyqqTuMyVvALcAIRVGqyoDoDuMhqSFSKXBM/E3b3Era5Ji2AfUsi6PjtmMlhNAAC4AgYFOpqWJ3Gpe7gMesynpUm4Lppdq59JgIIXoAfwOWK4ryTTW6uPR4SGqHXD5wTEr8q2UM6qpx57H6FOgLnAMeLVXnNuOiKMoTiqIIwBfV8+BfwD+B3UKIm6yauuyYCCF8gC9RXQknVLebaety4yGpPVIpcEyyTVv/StqU1GVX0sYdcMuxEkL8G/gLqutdX0VRLpdq4nbjoihKvqIovymKMgmYDHQCZlk1ceUxeRu4GXhBUZRLVTU24crjIaklcvnAMTlj2raopE1UqbbuyhnT1m3GSgjxEfBX4BqqQnCynGZnTFu3GZdSfAl8CAwRQmgVRSnGtcfkQdQgRY8JIR4rVdfGtH1GCHE/cEpRlCdw7fGQ1BKpFDgmJS5m7YUQPhVYBnct1dZdcauxEkK8D7wApAH3KYryWwVN3WpcyiED1bZAA4QAV3D9MfFANbisiJamV7Cp7OrjIakFcvnAAVEU5Rxq6FYvYHjpeiFEL1Qr68uoYV3dFncaKyHEu8AkIB1VIThUUVt3GpcKuAdVIcgAUsG1x0RRlGhFUUR5L1QXRYBJpmO3mfq47HhIao9UChyXd0zb94QQrUoOCiHCgU9MxXcVRTE2uGSOh8uPlRDiTeDvqDe5+xRFqc6Tm8uOixDibiHEaCGErpy6u4AvTMUvFEUxWFW77JjUEjkeEhuEokjDU0dFCPEJ8AxqVLaNQDGqtXkgarKXYaX+8JweIURnLH9GAO1Q3aFOogZkAUBRlDtK9XPZsRJCJAArTMV9qDHty+N3RVHeLdXXJcdFCJGEajeQgfq0exn1exKL+p0BWAMMLz0t7qpjUhFCiLmoLpuTFEX5sJx6txoPSeVIpcDBEUKMAv4H6AB4Ar8D/wVmu6L2bkoDvKWqdqZp0dJ9XXKsrG6AVbFNUZT4cvq73LiYohaOA+4GWgGNUV3sLqMqTgsURVleSX+XG5OKqEopMLVxm/GQVI5UCiQSiUQikQDSpkAikUgkEokJqRRIJBKJRCIBpFIgkUgkEonEhFQKJBKJRCKRAFIpkEgkEolEYkIqBRKJRCKRSACpFEgkEolEIjEhlQKJRCKRSCSAVAokEolEIpGY+H/zkx4TkOyxZAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"TG = 71.81 \n",
"mu = 0.00114 \n",
"N=45\n",
"dx=L/(N+1)\n",
"\n",
"k = TG/dx**2/mu\n",
"\n",
"A = k*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
"e,v=linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e3=e[isort]\n",
"v=v[:,isort]\n",
"\n",
"plt.plot(v[:,0],label='Mode 1')\n",
"plt.plot(v[:,1],label='Mode 2')\n",
"plt.plot(v[:,2],label='Mode 3')\n",
"plt.title('Mode shape for 45-Node Guitar String')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 132,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f3480d35f98>"
]
},
"execution_count": 132,
"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 \n",
"mu = 0.00114 \n",
"N=60 \n",
"dx=L/(N+1)\n",
"\n",
"k = TG/dx**2/mu\n",
"\n",
"A = k*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
"e,v=linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e3=e[isort]\n",
"v=v[:,isort]\n",
"\n",
"plt.plot(v[:,0],label='Mode 1')\n",
"plt.plot(v[:,1],label='Mode 2')\n",
"plt.plot(v[:,2],label='Mode 3')\n",
"plt.title('Mode shape for 60-Node Guitar String')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 133,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"45 nodes necessary\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"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": [
"N = np.array([6,30,45,60])\n",
"for i in range(len(N)):\n",
" dx = L/(N[i]+1)\n",
" k = T_g/(dx**2*mu_g)\n",
" A = k*(np.diag(np.ones(N[i])*2)\\\n",
" -np.diag(np.ones(N[i]-1),-1)\\\n",
" -np.diag(np.ones(N[i]-1),1))\n",
" \n",
" e,v = linalg.eig(A)\n",
" isort = np.argsort(e.real)\n",
" e = e.real[isort]\n",
" v = v.real[:,isort]\n",
" x = np.linspace(0,L,N[i]+2)\n",
" v = np.pad(v,((1,1),(0,0)))\n",
" \n",
" colors = ['silver', 'orange', 'green', 'pink']\n",
" shapes = ['s' , 'o', 'g','-']\n",
" plt.figure(1);\n",
" plt.xlabel('Time (s)')\n",
" plt.ylabel('y-position (m)')\n",
" plt.title('First Mode Convergence')\n",
" if N[i] == 45:\n",
" plt.plot(x,v[:,0]/np.max(v[:,0]),shapes[i] ,color = colors[i] , label = 'N ='+ str(N[i]))\n",
" else:\n",
" plt.plot(x,-v[:,0]/np.max(-v[:,0]),shapes[i] ,color = colors[i] , label = 'N ='+ str(N[i]))\n",
" plt.legend(bbox_to_anchor=(1,0.5),loc='center left');\n",
" \n",
" plt.figure(2);\n",
" plt.xlabel('Time (s)')\n",
" plt.ylabel('y-position (m)')\n",
" plt.title('Second Mode Convergence')\n",
" if N[i] == 45:\n",
" plt.plot(x,-v[:,1]/np.max(v[:,1]),shapes[i] ,color = colors[i] , label = 'N ='+ str(N[i]))\n",
" else:\n",
" plt.plot(x,v[:,1]/np.max(v[:,1]),shapes[i] ,color = colors[i] , label = 'N ='+ str(N[i]))\n",
" plt.legend(bbox_to_anchor=(1,0.5),loc='center left');\n",
" \n",
" plt.figure(3);\n",
" plt.xlabel('Time (s)')\n",
" plt.ylabel('y-position (m)')\n",
" plt.title('Third Mode Convergence')\n",
" if N[i] == 45 or N[i] == 6:\n",
" plt.plot(x,-v[:,2]/np.max(-v[:,2]),shapes[i] ,color = colors[i] , label = 'N ='+ str(N[i]))\n",
" else:\n",
" plt.plot(x, v[:,2]/np.max(v[:,2]),shapes[i] ,color = colors[i] , label = 'N =' + str(N[i]))\n",
" plt.legend(bbox_to_anchor=(1,0.5),loc='center left');\n",
" \n",
"print('45 nodes necessary')"
]
},
{
"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": 134,
"metadata": {},
"outputs": [],
"source": [
"N = 60\n",
"dx = L/(N+1)\n",
"x = np.linspace(0,L,N)\n",
"\n",
"k_e = T_e/(dx**2*mu_e)\n",
"k_b = T_b/(dx**2*mu_b)\n",
"k_d = T_d/(dx**2*mu_d)\n",
"k_a = T_a/(dx**2*mu_a)\n",
"k_E = T_E/(dx**2*mu_E)\n",
"\n",
"A_e = k_e*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
"e_e,v_e = linalg.eig(A_e)\n",
"isort_e = np.argsort(e_e.real)\n",
"e_e = e_e.real[isort_e]\n",
"v_e = v_e.real[:,isort_e]\n",
"\n",
"A_b = k_b*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
"e_b,v_b = linalg.eig(A_b)\n",
"isort_b = np.argsort(e_b.real)\n",
"e_b = e_b.real[isort_b]\n",
"v_b = v_b.real[:,isort_b]\n",
"\n",
"A_d = k_d*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
"e_d,v_d = linalg.eig(A_d)\n",
"isort_d = np.argsort(e_d.real)\n",
"e_d = e_d.real[isort_d]\n",
"v_d = v_d.real[:,isort_d]\n",
"\n",
"A_a = k_a*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
"e_a,v_a = linalg.eig(A_a)\n",
"isort_a = np.argsort(e_a.real)\n",
"e_a = e_a.real[isort_a]\n",
"v_a = v_a.real[:,isort_a]\n",
"\n",
"A_E = k_E*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
"e_E,v_E = linalg.eig(A_E)\n",
"isort_E = np.argsort(e_E.real)\n",
"e_E = e_E.real[isort_E]\n",
"v_E = v_E.real[:,isort_E]"
]
},
{
"cell_type": "code",
"execution_count": 135,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 60-element E string (Hz)\n",
"f1: 329.66287320010764\n",
"f2: 659.1071584966114\n",
"f3: 988.114412923938\n",
"Natural frequencies of 60-element B string (Hz)\n",
"f1: 247.0748304582595\n",
"f2: 493.98583425108916\n",
"f3: 740.5692933408752\n",
"Natural frequencies of 60-element D string (Hz)\n",
"f1: 146.89843350538408\n",
"f2: 293.69946380512823\n",
"f3: 440.30575227830343\n",
"Natural frequencies of 60-element A string (Hz)\n",
"f1: 110.01731758315341\n",
"f2: 219.96168653677248\n",
"f3: 329.76020660099965\n",
"Natural frequencies of 60-element bottom E string (Hz)\n",
"f1: 82.44585723617439\n",
"f2: 164.8370475123807\n",
"f3: 247.11894011639782\n"
]
}
],
"source": [
"print('Natural frequencies of {}-element E string (Hz)'.format(N))\n",
"f_e = np.array([e_e[0],e_e[1],e_e[2]])**0.5/ (2*np.pi)\n",
"print('f1:', f_e[0])\n",
"print('f2:', f_e[1])\n",
"print('f3:', f_e[2])\n",
"\n",
"print('Natural frequencies of {}-element B string (Hz)'.format(N))\n",
"f_b = np.array([e_b[0],e_b[1],e_b[2]])**0.5/ (2*np.pi)\n",
"print('f1:', f_b[0])\n",
"print('f2:', f_b[1])\n",
"print('f3:', f_b[2])\n",
"\n",
"print('Natural frequencies of {}-element D string (Hz)'.format(N))\n",
"f_d = np.array([e_d[0],e_d[1],e_d[2]])**0.5/ (2*np.pi)\n",
"print('f1:', f_d[0])\n",
"print('f2:', f_d[1])\n",
"print('f3:', f_d[2])\n",
"\n",
"print('Natural frequencies of {}-element A string (Hz)'.format(N))\n",
"f_a = np.array([e_a[0],e_a[1],e_a[2]])**0.5/ (2*np.pi)\n",
"print('f1:', f_a[0])\n",
"print('f2:', f_a[1])\n",
"print('f3:', f_a[2])\n",
"\n",
"print('Natural frequencies of {}-element bottom E string (Hz)'.format(N))\n",
"f_E = np.array([e_E[0],e_E[1],e_E[2]])**0.5/ (2*np.pi)\n",
"print('f1:', f_E[0])\n",
"print('f2:', f_E[1])\n",
"print('f3:', f_E[2])"
]
},
{
"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": 136,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from IPython.display import Audio\n",
"N= 10000\n",
"dt= 2/N\n",
"t= np.linspace(0,2,N)\n",
"out_file=0\n",
"for n in range(0,18):\n",
" out_file+= np.sin(2*np.pi*frequencies[n]*t)\n",
" \n",
"samplerate= int(1/dt)\n",
"Audio(data=out_file,rate=samplerate)\n",
"\n",
"plt.plot(np.arange(0,len(out_file))*dt*1000,out_file)\n",
"plt.xlim(0,200)\n",
"plt.xlabel('Time (ms)')\n",
"plt.ylabel('Input Signal (a.u.)')\n",
"plt.title('Audio Signal of 18 Frequencies');"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}