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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": 2,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy import linalg"
]
},
{
"cell_type": "code",
"execution_count": 120,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Matrix A =\n",
" [[ 7. -4. 1. 0. 0. 0.]\n",
" [-4. 6. -4. 1. 0. 0.]\n",
" [ 1. -4. 6. -4. 1. 0.]\n",
" [ 0. 1. -4. 6. -4. 1.]\n",
" [ 0. 0. 1. -4. 5. -2.]\n",
" [ 0. 0. 0. 2. -4. 2.]]\n",
"\n",
"Matrix B =\n",
" [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" -7.86390528e-05 1.57278106e-04]\n"
]
}
],
"source": [
"#Constants\n",
"L = 0.64 #m\n",
"g = 9.81 #m/s^2\n",
"bh = 0.004 #m\n",
"a = (0.04*0.02) #m^2\n",
"I = (0.04*0.02**3)/12 #m^4\n",
"E = 10e9 #Pa\n",
"N = 6 #steps\n",
"h = L/N\n",
"\n",
"# String Density (kg/m)\n",
"de = 0.401e-3\n",
"dB = 0.708e-3\n",
"dG = 1.140e-3\n",
"dD = 2.333e-3\n",
"dA = 4.466e-3\n",
"dE = 6.790e-3\n",
"\n",
"#String Tension (N)\n",
"te = 7.28*g\n",
"tB = 7.22*g\n",
"tG = 7.32*g\n",
"tD = 8.41*g\n",
"tA = 9.03*g\n",
"tE = 7.71*g\n",
"\n",
"d_net = de+dB+dG+dD+dA+dE\n",
"t_net = te+tB+tG+tD+tA+tE\n",
"M_net = t_net*bh\n",
"\n",
"x = np.linspace(0,L,100)\n",
"t = np.linspace(0,0.64,1000)\n",
"w = (M_net/(2*E*I))*x**2\n",
"\n",
"A = np.diag(np.ones(N)*6)\\\n",
"+np.diag(np.ones(N-1)*-4,-1)\\\n",
"+np.diag(np.ones(N-1)*-4,1)\\\n",
"+np.diag(np.ones(N-2),-2)\\\n",
"+np.diag(np.ones(N-2),2)\n",
"\n",
"A[0,0]+=1\n",
"A[-1,-1]+=-4\n",
"A[-1,-2]+=0\n",
"A[-1,-3]+=1\n",
"A[-2,-2]+=-1\n",
"A[-2,-1]+=2\n",
"\n",
"b = np.zeros(N)\n",
"b[-2] = -M_net*(h**2)/(E*I)\n",
"b[-1] = 2*M_net*(h**2)/(E*I)\n",
"\n",
"#Numerical solution\n",
"w_nu = np.linalg.solve(A,b)\n",
"x_nu = np.arange(0,L+h,h)\n",
"\n",
"#Analytical solution\n",
"x = np.linspace(0,L,100)\n",
"w = (M_net/(2*E*I))*x**2\n",
"\n",
"\n",
"print('Matrix A =\\n',A)\n",
"print('\\nMatrix B =\\n',b)"
]
},
{
"cell_type": "code",
"execution_count": 121,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1A) Deflection of the Guitars Bridge = 1.4155029504000065 mm\n"
]
}
],
"source": [
"#1A\n",
"defl = w_nu[-1] #m\n",
"print('1A) Deflection of the Guitars Bridge =', defl*1000, 'mm')"
]
},
{
"cell_type": "code",
"execution_count": 122,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 576x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize = (8,4))\n",
"plt.plot(x_nu, np.block([0,w_nu]), 'o', label = \"numerical solution\")\n",
"plt.plot(x, w, '-', label = 'analytical solution')\n",
"plt.xlabel('Position on Bridge (m)')\n",
"plt.ylabel('Deflection(m)')\n",
"plt.title('6 Step Guitar Bridge Deflection')\n",
"plt.legend(bbox_to_anchor=(1,1));"
]
},
{
"cell_type": "code",
"execution_count": 123,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N = 24 #strings\n",
"h = L/N\n",
"\n",
"x = np.linspace(0,L,100)\n",
"t = np.linspace(0,0.64,1000)\n",
"w = (M_net/(2*E*I))*x**2\n",
"\n",
"A = np.diag(np.ones(N)*6)\\\n",
"+np.diag(np.ones(N-1)*-4,-1)\\\n",
"+np.diag(np.ones(N-1)*-4,1)\\\n",
"+np.diag(np.ones(N-2),-2)\\\n",
"+np.diag(np.ones(N-2),2)\n",
"\n",
"A[0,0]+=1\n",
"A[-1,-1]+=-4\n",
"A[-1,-2]+=0\n",
"A[-1,-3]+=1\n",
"A[-2,-2]+=-1\n",
"A[-2,-1]+=2\n",
"\n",
"b = np.zeros(N)\n",
"b[-2] = -M_net*(h**2)/(E*I)\n",
"b[-1] = 2*M_net*(h**2)/(E*I)\n",
"\n",
"#Numerical solution\n",
"w_nu = np.linalg.solve(A,b)\n",
"x_nu = np.arange(0,L+h,h)\n",
"\n",
"#Analytical solution\n",
"x = np.linspace(0,L,100)\n",
"w = (M_net/(2*E*I))*x**2\n",
"\n",
"plt.figure(figsize = (8,4))\n",
"plt.plot(x_nu, np.block([0,w_nu]), 'o', label = \"numerical solution\")\n",
"plt.plot(x, w, '-', label = 'analytical solution')\n",
"plt.xlabel('Position on Bridge (m)')\n",
"plt.ylabel('Deflection(m)')\n",
"plt.title('24 Step Guitar Bridge Deflection')\n",
"plt.legend(bbox_to_anchor=(1,1));"
]
},
{
"cell_type": "code",
"execution_count": 124,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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cuHD+tdde+xPAJZdccsjdd9+9cuHChfM7duyYP2TIkCbxfD5t27Yt7N+/f86gQYPWfffdd/NPP/30neKdstoNBoM2Z86cBaNGjVoxfPjwuN6vSCKnnlcCzWJeNwVWx1kmLY66xXUD/mBm9wAZQNjMtrv7Q7vQdxERkYSKzW5uaasYU3A3hQT48oTxnHjiqUw/eW/3sGQ5eQVpFbker8zMzIJjjjkmH6BLly7bli5dWq28Osccc0xenTp1wnXq1AnXqlUr1Ldv31yATp06bfv2229rbtq0KWnWrFm1+vbt27KoTmFh4Y7BqD59+mxMSfllKPTZZ5+lv/LKK0sAUlJSOOigg0IAo0aNajh58uQMgLVr16bOmzeveqNGjUpc7tauXbuCFStWVBswYECzs846a9M555yz+aeffkrOy8tLPvPMM7cAXHnllT/17dv30Ap8TCUqr92+fftujH5eW2+66aYK/ZwSGSh+DbQ2s0OAVUA/4IJiZd4CBkfXIHYDNrn7GjPLiaPuTty9R9H3ZjYM2KIgUURE9lVF2c3tbRnPpo3AMc4rvI0tX6Yw/cS93bvS1U+vVvhjCUFh/fRqhb+m3bS0tB0zh8nJyZ6fn58EkJKS4qFQZKugbdu2WWl1kpKSqF69uhd9HwwGLRQKkZ6eHvzuu+9i8yN2qFWrVjje/k2aNCl92rRp6TNmzPguPT093LVr17ZFfSxJ/fr1Q3Pnzp3/+uuvH/jII480eOmll+qOHTt2RWnlYyUnJ3s4HOlaWe8Rr6LPJSUlhVAoVNKsbakSNvXs7kFgMDAVWAC87O7zzGyQmQ2KFptCJPlkEfA4cE1ZdQHM7BwzWwl0Byab2dREPYOIiEiirM7N53D7gRfS7iJACucV3k62N9/ns5uvP7n1qmopSTsFWNVSksLXn9x6VSLer1mzZgVfffXVAQATJ04sdzo6Vt26dcNNmzYtfOqpp+oAhMNhPv/883Kzgo499ti80aNH14fIWsMNGzYk5ebmJteuXTuUnp4enjVrVvXZs2cfUFYba9asSQmFQlxyySW5d91116o5c+bUPOigg0IHHnhgqGid4JNPPnlQ9+7df7FkrmnTpoXTp0+vCfDyyy/veOb09PRQXl7eL6a74213VyR0H0V3n+Lubdy9pbv/I3ptrLuPjX7v7n5t9H4nd59RVt3o9dfdvam7V3P3hu5+WgnvO8zd703ks4mIiPwapx+4hIlpd7PZa9K38A4We2Tp2L6U3VySi44+eMPtv+uwrEF6tUIDGqRXK7z9dx2WJSrreejQoeuefPLJ+l26dGm3fv36Cs+EvvDCC4vHjx9fr23bth1at27d8dVXX80or86jjz66fNq0aelt2rTpcNhhh3X43//+V+Pcc8/dFAwGrU2bNh1uvfXWJp07dy5zh5WlS5emHnfccW3btWvX4bLLLjtk+PDhKwHGjx+/ZMiQIU3btGnT4dtvv60xcuTIXyytu+OOO1bffPPNzY866qi2ycnJO0ZNzz333NzJkydnFCWzxNaJp91dYZGdaaqmrKwsnzFjRvkFRUREdqcfPiT4/PmsCNbh/IJbWUtkK7waqckJT1wxs5nuvtOBFbNnz17auXPn9Ql7U9mnzZ49u17nzp1blHRPR/iJiIgkWOzZzX9M/5a7Q/eRUr8tC7o8SvLH67E9d6azSIUoUBQREUmg2Ozm3ydN5x+FjzKXQ1l55GOc2a0jvY7e2z0UKV1C1yiKiIhUdUXZzecnf8A/Ux/h63A7Lii4hbs/Wre3uyZSLo0oioiIJNDq3HwGJr/Nrakv8GHoCK4O/IkC0ti2j2c3i4ACRRERkcRx528HvMYloVd4O3Q0NwauIRD9q3dfz24WAQWKIiIiiREOwztDuCT0Cv8On8SQwGWEoyu+9qWzm0XKojWKIiIiu0Hsuc2/HfEey8dfAl89Bt0Hk9r7QRpnHLBPnt28vxkzZsxB/fv3b15emaVLl6YWvT7vvPMOnjlzZvWKvtekSZPSTzzxxFa70s9YNWvW7FJemeHDhzfIy8vbEbcdf/zxrdavX1/qWdO7i0YURUREfqXYzOZqFHL7tvtovmImC9pdR/tT/05vM3of2XRvd1OinnvuuXpHHHFEfosWLQIAL7300rK93afyjBs3ruGVV165IT09PQwwbdq0RXvifTWiKCIi8isVZTYfQD7jU++hZ/JM7ggM4IqlJ4FV6GjdKuuUU05p2bFjx/atWrXqeO+999Yrul6zZs0u1113XWbbtm07dO7cud2KFStSAJ5//vnahx9+eLv27dt3OOaYY9oUXS+ycePGpMzMzE4FBQUGsGHDhqTMzMxOTz31VJ25c+fW7N+//6Ht2rXrsGXLFuvatWvbTz75pCbAK6+8cmCHDh3at23btkP37t3bAHz00Uc1u3Tp0q59+/YdunTp0m727NnVynqWGTNmVO/UqVP7du3adWjTpk2HOXPmVAMYNmxYw9atW3ds3bp1x+HDhzcoXq/4CGX//v2bjxkz5qC77rqrwY8//ph6/PHHt+nWrVsbgMzMzE5r1qxJKa3d7OzstEMPPbRjv379Dm7VqlXHY489tvWWLVsq/MuoEUUREZFfaXVuPnXYzNNp99DRlnJD4TW8GT4Oq4yZzW9c24wf59fcrW026LCN3g+vKKvIxIkTlzZs2DC0ZcsW69KlS4eLLrpoY6NGjUL5+flJ3bt33/Lggw+uGjRoUNMHH3yw/j333LOmZ8+eW/r16/ddUlIS999/f73hw4c3evzxx1cWtVenTp1w9+7d815++eXaF198ce5TTz1Vt1evXhsvu+yyjWPHjm1w7733rvjtb3+7LbYPq1evThk8eHCLjz/++Lt27doVrlu3Lhmgc+fO27/66qvvUlNTeeONN9JvvvnmplOnTv2htGd58MEH619zzTXrrr766g3bt2+3YDDIf//735rPP//8QTNnzlzg7hx11FHtTz755Lxjjz223F+S22677cdHH3204bRp0xY2btw4GHuvtHbr1asXWr58efXnnntu8THHHLOsV69eh06YMKHONddcU6GjFhUoioiI/EpH1N7KPfl/p5n9yFWBP/NB+ChAmc0VMWrUqIaTJ0/OAFi7dm3qvHnzqjdq1Ghramqq9+vXbxPAUUcdtfX9998/EGDJkiVpvXv3bpqTk5NaWFiY1KxZs4LibQ4cODBn1KhRjS6++OLc5557rt7jjz++tKw+fPzxxwd07do1r127doUADRs2DAFs2LAh+bzzzjtk6dKl1c3MA4FAmSNz3bt333rvvfc2XrlyZVq/fv02durUqeDjjz+u1atXr9wDDzwwDHDmmWdu/Oijj9LjCRTL6XOJ7fbt2zc3MzOz4JhjjskH6NKly7alS5eWORJaEgWKIiIiv0bOQiYm3U7INjGgcChfenugEmc2lzPylwiTJk1KnzZtWvqMGTO+S09PD3ft2rVtfn5+EkBKSoonJUVWyqWkpBAMBg1g8ODBzW+44Ya1F1544aZJkyalDx8+vEnxdk899dSt1113XbXJkyfXCoVC9pvf/GZ7Wf1wd6yEpQJDhgzJPP744/Pee++9H7Kzs9NOOumkMn+wgwYN2tCjR4+tr7/+eu0zzjijzSOPPLLU3cv9HFJTUz0cDu94XTRtXl6fS5OWlrbjZnJyshd9phWhNYoiIiIVEJvdfPnd4yh4vCc1k0LMOOFZVtY+UpnNuyA3Nze5du3aofT09PCsWbOqz549+4Dy6uTl5SU3b948APD0008fVFq5fv36/XTppZceetFFF60vularVq3Qpk2bfpExfOKJJ2798ssv07/77rs0gKKp582bNyc3bdq0EGDcuHH1itcrbv78+Wnt27cvuO2223489dRTc7/55psaJ5100pYpU6Zk5OXlJW3evDlpypQpdU488cS82HotW7YsWLRoUY38/Hz76aefkj/99NMDi+4dcMABoU2bNv0iboun3V9DI4oiIiJxis1uPiZpLv8quJ8c0lnQYwI9exzD9BP3dg8rp3PPPXfTY489Vr9NmzYdWrZsub1z585by6vz17/+dfX555/fsmHDhoVZWVlbly9fXuK06uWXX/7TqFGjMi+//PIda/P69++//rrrrjv4pptuCs+YMWNB0fUmTZoEx4wZs/Scc85pFQ6HOeiggwKfffbZ90OGDFl7xRVXHDJmzJhGPXr02Fxe35599tm6//73vw9KSUnx+vXrB0aMGLG6YcOGoQsuuOCnI488sj3AxRdfnFN82rlVq1aBs846a2P79u07HnLIIds7duy4Yw3lgAED1p9xxhmtGzRoEPjyyy8XFl0/7rjjtpXUbnZ2dlp5/YyHxTMUur/KysryGTNm7O1uiIhIJXHsyA9ZlZtPr6QveCD1EZZ4Y/oXDiU1ownTh560t7sXFzOb6e5Zsddmz569tHPnzutLq1OZjR8/vs6bb76Z8cYbbyzZ233ZV82ePbte586dW5R0TyOKIiIicVqdm89Fye8xPOVpZngbrij8PzZTq3JmN1cBAwYMaPbRRx/VnjRp0vd7uy+VlQJFERGReLhz2wFvcnnoJd4LHcngwPUUEJndU3bzvumZZ55ZAezx5Jz9iZJZREREyhMOweQbuTz0Eq+GT2BQ4M87gsRKm928s3A4HNbO4FVQ9OceLu1+QgNFMzvdzLLNbJGZDS3hvpnZmOj9b83syPLqmllfM5tnZmEzy4q53tPMZprZnOiflWOxiIiI7JOKspvbDn2dj+/qBTOegmP/RHLvh2mUUWt/y26em5OTU1vBYtUSDoctJyenNjC3tDIJm3o2s2TgYaAnsBL42szecvf5McXOAFpHv7oBjwLdyqk7F+gDjCv2luuBs9x9tZkdBkwFKv1/uSIisucVZTenBjYzIe0+fhPK5m4fQId6A+ndJXO/O7c5GAxesXbt2ifWrl17GJptrErCwNxgMHhFaQUSuUaxK7DI3RcDmNmLwNlAbKB4NjDBI6nXX5hZhpk1BlqUVtfdF0Sv7fRm7j4r5uU8oLqZVXP3X+zULiIiUpbRU7OpHfiRp9Pu4VBbzfWBwUwKdydzavb+MHr4C0cdddSPwO/3dj9k35PIfzVksvMC0pX8coSvtDLx1C3LucCskoJEMxtoZjPMbEZOTk4FmhQRkaqi5qbvebXaMDJtPQMCQ5kU7g5Esp5FqpJEBoolrXMovmljaWXiqVvym5p1BEYBV5V0390fc/csd8+qX79+PE2KiEhVsuwzXq12J6mE6Fd4O5+HO+64pexmqWoSOfW8EmgW87opsDrOMmlx1P0FM2sKvA70d/cfdqHPIiJSlc1/E169EqvVhPM33cgP/vPJcPtJdrNIhSQyUPwaaG1mhwCrgH7ABcXKvAUMjq5B7AZscvc1ZpYTR92dmFkGMBm4xd2n795HERGR/dEbs1Yxemo2q3Pzua7WR/w5+ATW9DekX/AS12Xn77jXJKMGN53Wdr9cnyhSloQFiu4eNLPBRLKPk4Gn3H2emQ2K3h8LTAF6AYuAbcClZdUFMLNzgAeB+sBkM/vG3U8DBgOtgNvN7PZoN0519x8T9YwiIlJ5FWU2bw8EGJLyEoOCb/OBZ7Gt86OcVbMuvbugwFCqPJ31rLOeRUSqpGNHfkhO7mbuTR3L75M/59ngKQwLDqBRRq1Kc27zrijprGeR0ugIPxERqZLyctczIe1+jk5awKhAPx4NnQWYMptFYihQFBGRqid3BW/UGE7T8GpuKLyGN8PH7bilzGaRnylQFBGR/V5s0soJB67mURtJs+TtXBm8lY/D7XeUU2azyM4UKIqIyH6tKGklPxDihKRZPFQwhg2ks+CkifQ+sDXfK7NZpFQKFEVEZL82emo2+YEQFya/z/CU8cz3g7ms8CbSPg8zfWimAkORMihQFBGR/dqa3K0MTXmJQSlv82HoCAYHrmcb1TElrYiUS4GiiIjsvwL5PFnzYU4M/7z9TYhkQEkrIvFQoCgiIvunLTnwQj9OCM9kZPhixgZPBwxQ0opIvBQoiojIfqMou7nGpkU8U/1eGiZtIuW8Z2m3/UgylbQiUmEKFEVEZL9QlN3cJTSbsWn/pCCcyvnB27lw+5H07qKkFZFdkbS3OyAiIrI7jJ6azYYxLloAACAASURBVNnh93gmdRSr/CB6Fwzn68AhjJ6avbe7JlJpaURRREQqv3CIAVueYGDqZD4Kdea6wHVsoSaAjuQT+RUUKIqISOVWsAVev4qBKZN5JtiT4cH+OzKbQdnNIr+GAkUREalUYo/j61x7K09Xv4+MzQv59rBbGDn7CEKEdpRVdrPIr6M1iiIiUmkUJaysys2nk/3AY9tvIiV3GZ91e4TD/zCUEX06kZlRAwMyM2owok8nJbGI/AoaURQRkUqj6Di+XklfcH/qo+R4BhcFbmHrNw2ZfjrKbhbZzRQoiohIpbE6dxs3JL/Gn1NfZUa4DVcV/pmfqK3j+EQSRIGiiIhUDoXbeKLmI5wcns6roR7cEriCQlIBJayIJIoCRRER2SfFJq0cXnsbT1d/gJPC8xkdvpCHA73QcXwiiZfQZBYzO93Mss1skZkNLeG+mdmY6P1vzezI8uqaWV8zm2dmYTPLKtbeLdHy2WZ2WiKfTUREEic2aaWzLeKx7X8hLfcHvuz2EK3P+SuZGTWVsCKyByRsRNHMkoGHgZ7ASuBrM3vL3efHFDsDaB396gY8CnQrp+5coA8wrtj7dQD6AR2BJsD7ZtbG3UOIiEilUpS00jvpU0alPs46z6B/YChbZjdh+hlKWBHZUxI59dwVWOTuiwHM7EXgbCA2UDwbmODuDnxhZhlm1hhoUVpdd18QvVb8/c4GXnT3AmCJmS2K9uHzBD2fiIgkyNrcrQxNeZFBKZP4PNSBawLXs5EDlbQisoclcuo5E1gR83pl9Fo8ZeKpuyvvh5kNNLMZZjYjJyennCZFRGSP276JZ2s+wKCUSUwI9uTiwFA2ciCgpBWRPS2RI4q/GPIDPM4y8dTdlffD3R8DHgPIysoqr00REUmw2KSVow/cwGNp93G0r2BY+AqeDp60o5ySVkT2vEQGiiuBZjGvmwKr4yyTFkfdXXk/ERHZhxQlreQHQpyQNIsxBQ9RWJDKN8c9xRH1ssiMBpBNMmpw02lttTZRZA9LZKD4NdDazA4BVhFJNLmgWJm3gMHRNYjdgE3uvsbMcuKoW9xbwPNmdj+RZJbWwFe77WlERGS3iyStBBmU/DY3p7zEAm/OwMIbYWY604cqaUVkb0tYoOjuQTMbDEwFkoGn3H2emQ2K3h8LTAF6AYuAbcClZdUFMLNzgAeB+sBkM/vG3U+Ltv0ykWSZIHCtMp5FRPZtG3M38lDqY/wu+QveDh3NTYGr2E41Ja2I7CMsknBcNWVlZfmMGTP2djdERKqmDUtY9ODZHBJezj3BfowL/Y6i5eaZGTWYPvSksuvLLjGzme6eVX5JEZ3MIiIie0BswkqTjBrc0+Unjp31F5qnhLlq+1DeD3XaUVZJKyL7DgWKIiKSULEJK+D8Lu9ljv7sRTYd2IraA1/md8uqsUBJKyL7JAWKIiKSUEWnrBxAPvekjuPM5K+YFDqafxZez/t1D6V3XRQYiuyjFCiKiEhCrc7N5xBbw7jU+2lpq/lH4AIeD52JbdrbPROR8sQVKJpZdeB3QA8iW8/kEzlzeXJRNrKIiEhJ/pg+h78W/pMgyVwcuIXPwocBOmVFpDIoN1A0s2HAWcDHwJfAj0B1oA0wMhpE/p+7f5u4boqISGUQm7TStHYaTxz8HqMC45jHIQws+BOrqA8oYUWksohnRPFrdx9Wyr37zawB0Hz3dUlERCqj2KSVDPL4x7aHaLtwDkubn8sPh98G7y/FlLAiUqmUGyi6++Ry7v9IZJRRRESqsKKklcNsMWPT/kl9chkSuJJPf+zF9KxD+X3WoXu7iyJSQXEns5hZFvBX4OBoPQPc3Q9PUN9ERKQSWZ27jfOTP2RYyjPkkEHfwr/xrbfUKSsilVhFsp4nAjcBc4BwYrojIiKVUuE2Hq75BL3CHzEtdDg3BK4ll3RASSsilVlFAsUcd38rYT0REZFKIzZppeuBG3ms+hjOCC/kwfAfeCDQmzBJgJJWRCq7igSKfzOzJ4APgIKii+7+2m7vlYiI7LNik1ZOT/qK0QXjCBUk83n3sTRr2IPGOmVFZL9RkUDxUqAdkMrPU88OKFAUEalCRk/NJhgo4I6U57ks5R1mhVtxbeH12DcNmD40U4GhyH6kIoFiZ3fvVH4xERHZr+Wu4KW0MRyZtIingqczIngBAVKUtCKyH6pIoPiFmXVw9/kJ642IiOzbFk5lSvVbSfIQ1xRez5Tw0TtuKWlFZP9TkUDxOGCAmS0hskZR2+OIiOzHYhNWmtVO5Ylm79Bm0ZN47Xb03TCI78INdpRV0orI/qkigeLpCeuFiIjsU2ITVhrxE/flP0ibRQtZ0uKPHHLhgwya+9OOIFJJKyL7r3jOeq7l7lvcfVl5ZXZv10REZG8pOmXlxKRZ3Jf6KGkEub5wMDPXnsz01Or07qKkFZGqIJ4RxTfN7BvgTWCmu28FMLNDgROBPwKPA68krJciIrJH5eTmcWvKSwxMmcz88MFcG7ieJd5YCSsiVUxSeQXc/WQieydeBcwzs81m9hPwHNAIGODuJQaJZna6mWWb2SIzG1rCfTOzMdH735rZkeXVNbO6ZvaemX0f/bNO9HqqmT1jZnPMbIGZ3VLRD0NERICNy3i9xl0MTJnMhGBPzim8kyXeGFDCikhVE9caRXefAkypSMNmlgw8DPQEVgJfm9lbxbKmzwBaR7+6AY8C3cqpOxT4wN1HRgPIocAQoC9Qzd07mVlNYL6ZveDuSyvSbxGRqiY2aeWC9FkM87G0SXZuKPgzbwZ/s6OcElZEqp6KJLNgZpnAwbH13P2TUop3BRa5++Jo3ReBs4HYQPFsYIK7O5HtdzLMrDHQooy6ZwMnROs/A3xMJFB04AAzSwFqAIXA5oo8n4hIVVOUtBIO5HNXyrNcGPiA2d6KdT0f5sQDmjFDCSsiVVrcgaKZjQLOIxKshaKXHSgtUMwEVsS8Xklk1LC8Mpnl1G3o7msA3H2NmRXtz/AKkSByDVAT+LO7byjhOQYCAwGaN29eStdFRKqG0VOzaRpcxkNpY2ibtJKxwbO4N9iXhp9u0ykrIlKhEcXeQFt3Lyi3ZISVcM3jLBNP3eK6EglgmwB1gP+a2ftFo5I7GnF/DHgMICsrq7w2RUT2X+6ckPc2t6c9Sx41uLhwKP8NR7bGXa2kFRGhYoHiYiLnPMcbKK4EmsW8bgqsjrNMWhl115lZ4+hoYmPgx+j1C4B33D0A/Ghm04GsaL9FRKq82LWIbWsHearuBP6R+j7TQofzl8AgcsjYUVZJKyICcWQ9x9gGfGNm46KZymPMbEwZ5b8GWpvZIWaWBvQD3ipW5i2gfzT7+WhgU3Rauay6bwEDot8PILJtD8By4KRoWwcARwPfVeD5RET2W0VrEVfl5tPVFvDU9j9Rb/VHTGkymKu5ZacgUUkrIlKkIiOKb/HLQK9U7h40s8HAVCAZeMrd55nZoOj9sUQyqXsBi4gEopeWVTfa9EjgZTO7nEhw2Dd6/WFgPDCXyNT1eHf/tgLPJyKy3xo9NZtAoIC/pLzKNclvsdQb0idwJxs3dOTuPm11yoqIlMgiCcdxFo6M7rWJvsyOTvNWWllZWT5jxoy93Q0RkYQ74ZYn+WfqQxyRtJgXgycwPNifbVTHgCUjz9zb3ZM9yMxmunvW3u6HVA4VyXo+gch2NEuJjNg1M7MBZWyPIyIie5s7fDORKdVupdCTGVT4J94Jd91xW2sRRaQsFZl6vg841d2zAcysDfACcFQiOiYiIhUXm7DSrnaAJ+pOJHPNu2yt15U/rhvAknCdHWW1FlFEylORZJbUoiARwN0XEsmCFhGRfUBswspxSd/y9PYbqL/6A+Z2+D/qX/MON/Q5kcyMGhiQmVGDEX06aS2iiJSpIiOKM8zsSeDZ6OsLgZm7v0siIrIrRk/NJhzI546UF7ks5R0WhjO5NHAzmxa3Z3pSMr27aANtEamYigSKVwPXAtcTWaP4CfBIIjolIiIVV2fTfJ5Oe4TWSasYHzyNkcHzKSAN0+bZIrKL4g4Uoyey3B/9EhGRvSh2LWKz2mmMPeQT3qj2MOv9QC4qvIVPw512lFXCiojsqnIDRTN72d3/aGZzKOEYPXc/PCE9ExGREhWtRcwPhDjY1nJ//qN0+O57vs04mYE/XcDa8M+BoRJWROTXiGdE8Ybon79LZEdERCQ+o6dmkx8IclHy+9ya8jwBkrm+cDAzt5/MUG2eLSK7UbmBYvRIPYBr3H1I7D0zGwUM+WUtERFJlHDuSiakPsZvk+cwLXQ4NwcGso66WG6+ElZEZLeqSDJLT34ZFJ5RwjUREdlNYtciNqldnTEdsnm3+t9J8hB/DVzGxNDJRPILtRZRRHa/eNYoXg1cA7Q0s9izk9OBzxLVMRGRqi52LWJ9chm27UmOmjWTZQd04srNV7AwVH9HWa1FFJFEiGdE8XngP8AIYGjM9Tx335CQXomIyI61iGclfc7w1KepQQF/D1zIu8Fz+L8+HbQWUUQSLp41ipuATWb2L2CDu+cBmFm6mXVz9y8T3UkRkaqoMHctj6SOp1fyV8wKt+Ivgav4wTOxTYVaiygie0RF1ig+ChwZ83prCddEROTXcoe5r/Je9Zup4dsZGejH46EzCZEMaC2iiOw5FQkUzd137KPo7mEzq0h9EREpQWzCymG1tzOuzkSarP2AcJ3D6bN+APNCjXeU1VpEEdmTkipQdrGZXW9mqdGvG4DFieqYiEhVUJSwsip3G+ckfcKz26+j7ppPmNvxL9S97mOu7HMGmRk1MCAzowYj+nTSlLOI7DEVGREcBIwBbiNyQssHwMBEdEpEpKoYPTWbOoF1PJr6JCckz+brcBuGBAZS8ENLpiclay2iiOxVFTnr+UegXwL7IiJStYTDnJD3NkOrvUASYe4IDODZUE+cJCw3f2/3TkQk/kDRzNoQSV5p6O6HmdnhwO/d/a6E9U5EZD8Suxbx6AM38GD6eP6ROpNPQx0ZGrySld5gR1klrIjIvqAiaxQfB24BAgDu/i3ljDCa2elmlm1mi8xsaAn3zczGRO9/a2ZHllfXzOqa2Xtm9n30zzox9w43s8/NbJ6ZzTGz6hV4PhGRhClai7guN4+rk9/g6YI/k7r+O15rdgtXcvtOQaISVkRkX1GRQLGmu39V7FqwtMJmlgw8TOSYvw7A+WbWoVixM4DW0a+BREYsy6s7FPjA3VsTWSc5NFonBXgOGOTuHYETiAa1IiJ72+ip2bQJZvN22m3cnPoy74e7cErBaO7L6cqIPocrYUVE9kkVSWZZb2YtiSSyYGZ/ANaUUb4rsMjdF0fLvwicDcyPKXM2MCG67c4XZpZhZo2BFmXUPZtIEAjwDPAxkfOmTwW+dffZAO7+UwWeTUQkcQryuHzLOC5Jm8qPZDCw8M+8G/4NAJabr4QVEdlnVSRQvBZ4DGhnZquAJcBFZZTPBFbEvF4JdIujTGY5dRu6+xoAd19jZkXzNW0AN7OpQH3gRXe/p3inzGwg0Wzt5s2bl9F9EZFdE7sW8dz0eQxPeZJLUtbxXPAURgfPI4+aO8pqLaKI7MsqkvW8GDjFzA4AkoqO8iuDldRMnGXiqVtcCnAc8BtgG/CBmc109w92asT9MSIBL1lZWeW1KSJSIUVrEdMD63ko9RnODHzFosKmfNDmEf75XV3yCe0oq7WIIrKvKzdQNLMbS7kOgLvfX0rVlUCzmNdNgdVxlkkro+46M2scHU1sDPwY09Y0d18f7d8UIscL7hQoiogk0n3vzOcP4f9wU7WXSCPIPYE/8njodzRYkc6IPm13jDQ2yajBTae11ZSziOzT4hlRTN/Ftr8GWpvZIcAqIhnSFxQr8xYwOLoGsRuwKRoA5pRR9y1gADAy+ueb0etTgZvNrCZQCBwPPLCLfRcRqbg1s3kwfwhHpP7AJ6FO3B68lGXeCIDVWosoIpVQPIFiTXcfYmZ93f3f8Tbs7kEzG0wkgEsGnnL3eWY2KHp/LDAF6AUsIjJdfGlZdaNNjwReNrPLgeVA32idjWZ2P5EA1YEp7j453v6KiFRE7DrEVrWdsZn/oeWS52melM71hdfyVvgYYlfRaC2iiFRGFkk4LqOA2RwiU7hfuvuRZRauZLKysnzGjBl7uxsiUskUrUPMDwQ5M+lL7kidQH02sfSQfizocAN/eXsZ+YGd1yJqyxvZV0TX72ft7X5I5RDPiOI7wHrgADPbTOSfyEUJJ+7uByawfyIi+5zRU7NpFFzJnalP89vkOcwNt2Bg4EbWr+3E9EvaE0g9UGsRRWS/UG6g6O43ATeZ2ZvufvYe6JOIyL6rcBvnb3mGK9MmUUAadwQGMDF0CiGSd5zPrLWIIrK/qMj2OGeb2cFAa3d/38xqAClxbJMjIlJp/bwWcRvnpc/hjpQJDE5Zzauh4xgRuJD11N5RVusQRWR/E3egaGZXEtmoui7QksiWNWOBkxPTNRGRvatoLWKj4ErGp07ghMBsFhY245PWD3JfdgPtiSgi+72KnPV8LXAssBnA3b8HGpRZQ0SkEnvonW+4zicyNe1mjkxayJ2Bi+lV8A/Gr2zKiD6ddD6ziOz3KnKEX4G7FxZttG1mKZR/WoqISKUQu91Nk9rV+ddhi3hu+wgapWzk1VAPRgbOJ4cMQHsiikjVUZFAcZqZ3QrUMLOewDXA24nplojInvPzdjchOtpShuU/TdbMhcy3Q7mm4Ab+5212Kq+1iCJSVVQkUBwKXA7MAa4isln2E4nolIjInjR6ajY1Axu4PeVl+iV/zAbSuTlwJe+lnsL2FCCgtYgiUjVVJOs5bGZvAG+4e04C+yQisucECzkz798MrvY6NShkfOh0/hXsw2YOwEIhHjjvCO2JKCJVVrmBokUWJf4NGExkk20zsxDwoLsPT3D/RER2m+LrEO/rvJqjFz3Arak/8GHoCO4KXsRib7KjfJOMGlqLKCJVWjwjin8iku38G3dfAmBmhwKPmtmf3f2BRHZQRGR3iF2H2N6Wcdu25zj6q3nk1TqUOUeP49rpGeS7pphFRGLFsz1Of+D8oiARwN0XAxdF74mI7PNGT82mVuAnRqY8xuS0W2mftIzbA5dwZmAUx5zeT9vdiIiUIJ4RxVR3X1/8orvnmFlqAvokIvKr7DTFnFGDoSc349y8iVxV7W1SCfJU6HTGBM9hM7WwTQFAx+6JiJQknkCxcBfviYjscbFTzEmE6Z73Dl0nvcxZqRuZEurKPcHzWOqNd5TXVjciIqWLJ1DsbGabS7huQPXd3B8RkV9l9NRs8gNBfpv0LbekvED7pOXMCrdiiN3Il7TROkQRkQooN1B09+Q90RERkd0hY9MCRqY+T4/kuSwP12dw4XVMCh+NYTxwXidtdSMiUgEV2XBbRGSfErsW8agDN/NAg0lMrjaJDV6LYYH+TAydQiD6vzltdSMiUnEKFEWkUipai1gzsIE7Ut7gwoL3Ca1IZlrDi/jLmpPJCVXbUVZTzCIiu0aBoohUSg+/M4ur/FWuqDaF6hTycugE/hk8l9TNTfhrn7aaYhYR2Q0SGiia2enAv4Bk4Al3H1nsvkXv9wK2AZe4+//KqmtmdYGXgBbAUuCP7r4xps3mwHxgmLvfm8jnE5HEK77VzZBTDub3hf/hpe0jqJuyhSmhrtwb/OOOE1UsN19TzCIiu0nCAkUzSwYeBnoCK4Gvzewtd58fU+wMoHX0qxvwKNCtnLpDgQ/cfaSZDY2+HhLT5gPAfxL1XCKy58RudZNCkB55k+n69mtgG/g++Qjuyv8Dc/zQnepouxsRkd0nnpNZdlVXYJG7L3b3QuBF4OxiZc4GJnjEF0CGmTUup+7ZwDPR758Behc1Zma9gcXAvEQ9lIjsOaOnZlMQCNA76VPeT7uJkalPsNrrMjj176w563kWpbTeqbzWIoqI7F6JnHrOBFbEvF5JZNSwvDKZ5dRt6O5rANx9jZk1ADCzA4iMLPYE/lJap8xsIDAQoHnz5hV7IhFJmOJTzDed2prOmz/m6bRXaJ20innhg7m08CY+Ch+BFRoPRaeWtRZRRCRxEhkoWgnXPM4y8dQt7k7gAXffEln6WDJ3fwx4DCArK6u8NkVkD4idYgan4+ZPaPfmDfROW8734UyuLryBd8K/waOTIEXTy1qLKCKSWIkMFFcCzWJeNwVWx1kmrYy668yscXQ0sTHwY/R6N+APZnYPkAGEzWy7uz+0W55GRBKm6DSVk5JmcWPKKxyWtJTF4Ubcatfzpndna/jnf9NpellEZM9JZKD4NdDazA4BVgH9gAuKlXkLGGxmLxIJ9DZFA8CcMuq+BQwARkb/fBPA3XsUNWpmw4AtChJF9j2/nGJuQ4fNn/Jo2mscnrSEZeEG/F/hIN4IH0uYZB44r7Oml0VE9pKEBYruHjSzwcBUIlvcPOXu88xsUPT+WGAKka1xFhHZHufSsupGmx4JvGxmlwPLgb6JegYR2b1ip5iNMB03f0KbN/9M77SlLAs34KbAQF4PHUcw+r+mTJ2mIiKyV5l71V2ml5WV5TNmzNjb3RCpMo4d+SFrcrdyRtJXDE55g/ZJy1kabshTSefyeuhY8gI/ry+ukZrMiD6dFCSK7GZmNtPds/Z2P6Ry0MksIrJnhIJ03fwe16a9Qauk1fwQbsyNhYN4c8cU8xGaYhYR2ccoUBSR3S52HeLBtVP4Z7t5HLH8GR5IW8p34WYMLryOKeFuhKNZzJpiFhHZNylQFJHdqmgdogW2clnyBwzcPpmGs3PZmNGJhV3HcOnn9dmmLGYRkUpBgaKI7LJfZDCf1pbH3/mKQf4mA6q9S4ZtZXqoI38OXcOy/Cym9zqZuxv/so5GEkVE9k0KFEVkl+y8STbYpuXkvT6OV+xDaqQUMjWUxdjgWczy1tH72wFtki0iUpkoUBSRXRLZJDtER1vCVSmT6JX0JWGMN8PHMTb4O37wnYPBotNURESk8lCgKCLlKmmT7NabP+ee1MkcmzyPPK/Bk6EzGB88nbUcRI3UZIiONILWIYqIVFYKFEWkTLFTzNUo5Li8jzjszevonbaStV6HuwPn80LoZPKoCUQymG86ra3WIYqI7AcUKIpImUZPzaZmYANXJn/AxSnvUt82Mz98MH+1wbwd7s7m0M6bZBcFhQoMRUQqPwWKIgKUnMHcu/EGbtjyT86uNp1qFuSjUGceD53JZ+GOGKZNskVE9nMKFEVkp+nlZEIctvkTGr/xV7D5nJVSjZeCJ/J06DQWe5MddZpok2wRkf2eAkURYfTUbNICm+if/BEXp7xHU1vPSq/Hwyn9adHzakZMWk6+KzlFRKSqUaAoUsUUn2K+q1uQG7Y8xO+rfUZ1C/B5qAN/D13M++EjCRcks6RbBwJptTXFLCJSBSlQFKlCiqaYw4F8eid9Sf9t79Fl2iLyU6rxWrAHE0Kn8p0331E+M7r3oaaYRUSqJgWKIvuhEhNTumTy/H8+5k8+mb7VplHXtvBDuDF3Bi7m/dSTWW81NL0sIiI7UaAosp8pfrTeutw8PnztCY757AteLvyMQHIy74aPYmLoFD4Pd8BJwkLwwHmdNL0sIiI7UaAosp8pOlqvua2jX/JH9E2eRn3bxNqcejyWcgGPbzmWHOrsVEcZzCIiUhIFiiKVWPEp5iGntCBr8/uMTv2IY5LnE/QkPgx34fnQSfw33Jn7zjuSLa/N0fF6IiISFwWKIpXUz1PMQTraUvpumcbxb0/n92lbWR6uz72Bvvw7dDzrqAtEElOKRgw1xSwiIvFIaKBoZqcD/wKSgSfcfWSx+xa93wvYBlzi7v8rq66Z1QVeAloAS4E/uvtGM+sJjATSgELgJnf/MJHPJ7KnlJSc8vg7X3F++AP6pk2jfdJyCjyFd8JdmZx8Cp96e7aFfEf92FFDTTGLiEi8EhYomlky8DDQE1gJfG1mb7n7/JhiZwCto1/dgEeBbuXUHQp84O4jzWxo9PUQYD1wlruvNrPDgKmA/jaUSi82OSWVIIdt/oRab9zN6/yPtNQQs8OHclvgUt4OdWcTtbAAPHBeZ40aiojIr5bIEcWuwCJ3XwxgZi8CZwOxgeLZwAR3d+ALM8sws8ZERgtLq3s2cEK0/jPAx8AQd58V0+48oLqZVXP3gsQ8nsjuVdqWNqPf+Y42wWzOSfmU3yd/Rl3bQo7XZkLoNP4d+i3ZMfseghJTRERk90lkoJgJrIh5vZLIqGF5ZTLLqdvQ3dcAuPsaM2tQwnufC8wqKUg0s4HAQIDmzZsXvy2yVxTf0mZVbj6PvPYebbO/57n8Vzik2loKPJV3w0fxaqgH/w0fTohkaqQmKzFFREQSJpGBopVwzeMsE0/dkt/UrCMwCji1pPvu/v/t3XmUnFWZx/Hvr3pJOhsdyEJWwhJ2wmIIazCMyEDwGBEcXI6i4nFwBh1mjgcFDw5n5jiizoyiqJwMojguoJBgFAiMIJshZCc7IQkhdBITQvakk3RXPfNHvR0qleruqtjVne7+fc7p013v+9637tMVkofnvvfeycBkgLFjxxZ1T7Nya1rSZiDbuKZiJpMqZnBuaiWZ5WJ+5Rn8aN8HmZ4ex056HWgzLKk6eojZzMzKpZyJYh0wIuf1cGB9kddUt9B2o6QhSTVxCLCp6SJJw4GpwKciYlWbRGHWxvKHmO+4fDCX7nyCD1S9zMWpJVQoWJo5jm82fIzfpy/mthvexx+mLKI+fWjl0EPMZmZWTuVMFGcDoyUdD6wDPgp8PO+aacAtyTOIFwDbkwTw7RbaTgNuJDvD+UbgdwCSaoHHgdsj4s9ljMvssDUNMVc27OTa1Bw+sHsm459YxDVVadZkBnNv+kNMS1/Mqsgmf17SxszMOlLZEsWIaJR0C9nZxxXAAxGxRNLNyfn7gCfILo2zkuzyOJ9pqW1y67uB30i6CVgLfCQ5fgtwEnCnpDuTY1dGxIGKo1l7OrRyeCyL//gr7uUlLu2xiB5qpC4GZNq44wAAEcZJREFU8JP01TxfeSkLYhT1jZkD7b2kjZmZdTRlJxx3T2PHjo05c+Z0dDesC2qqHPZq2ML7K+ZyVWo2l6QWU6U0dTGAJ9PjeCJ9AfPjJEAI+O4N57hqaGZlJ2luRIzt6H5Y5+CdWcz+CgWXtBnVwJuP38PPNIPze7xGSsHazEAeSF/F9MyFzM+cQP58LS9pY2ZmRyInimZFKJQQAgdtoXflrrmc+tgc0Fr+CXiN4fwgfS3T0+ezLEbSlBzWVFUcWAan6bWXtDEzsyORh5499GytyF/jEKC2Ks34yiVc2DCbv6mYzxBtIR1iTpzCrOoLeTE1jlk7ag+5l5e0MbOO5qFnK4UrimY5ClUOm9Y4HMbbXF6xgAmpBVySWkJN7GdXRU9eyIzhvzLn8mz6XLbQD+3PPm+4KC+59JI2ZmbW2ThRNEvkVw43b9vOtCm/5MZYwITqBZycWgfAm5lBPJyewDOZ83glcxr7qTroPkO9pI2ZmXURThSt22lpT+VhjW8yvmIR41OLuDC1jF7ax76oZHbmFB5uuJw/Zc5hdQwBRG1NFRWNmWa30HPl0MzMOjsnitat5FcNG7atZ8bUZzh3Xh2P7H2BIT22APBGZjAPpyfwQmYMMzOnQVXvQ3ZGueuDZwCuGpqZWdflRNG6rEKVw8nTZ3NZej4XVy7h4tRSRifDydvf6sOcijHcs+90XsqcRV0MPHCf1iagODE0M7OuyomidXotLV1T07CVK1PLuXDXMk59bBlPaC1Uw57owazMqfym4b3MyJzJshjJf99wHr/znspmZmYHOFG0TqG55woPHkoOtP1NZkx9hnGp15impYzuma0Y1kc1czIn84e4gRnp01gUJ9CQ88ffeyqbmZkdyomiHfHynytct62e26csQpn9PP7UU3wss5jzqlZwfuo1BmsbADuiF3PiZB5tGM+szKkHJYY1VRU0eAKKmZlZq5wo2hGl+XUMGxmutzlHqzg7tYrz9Dpn/n4Nk2iAKqiLAbycOZ05mVOYkzmFFTGcDKlD7u8Fr83MzIrnnVm8M0uHaHlLvDSD2MpZqdWcV7mG02IVY1KrGaAdAOyNKhbF8SzIjGZNzRn8cedINnL0QfevraliX2PmkAWvv/nhs5wUmlm35p1ZrBSuKFrZFPtcYWr7Gp6d8iJnVazhh6zmjB5rDgwhp0OsYhjPps/l1TiRBZkTeS1G0EjlgerglCmLDlnL0EvXmJmZ/fWcKNpfrbXqIGSfK/zGlFc4eks1K15+kdtjFadVv8mpeou+qgegMVKs1DBeypzJ4szxLMycwNI4jnp6UlNVQX1j4dnI0HxC6MTQzMzs8Hno2UPPRSsmIQQYVLWX0yrXM2j/WkZrHaNVx8mpOobpnQPX7IgalsdIlmVGsiyOY2nmOF6LEeyj+pD39XOFZmZtx0PPVgonik4UD1LccDFU0chJVe8wunIjA/e/xYnawAmpDZygDQxKho0B9kUVq2MIy2MEKzIjWBHD2dZnNHN39AF00Hv7uUIzs/Jzomil8NBzF9dS4tdydTDYs20j/ztlOUPX92Td/PncGXWMqNrEKG1kqDZToYAAqmBr9GFVDOW59NmsjiG8HsN4PYZTFwMPmn3cVB1cmleF9HOFZmZmRx5XFI/AimIpyV1rx/OHhWuqKrjuPcOYPvd1jmrczGBtZQhbGFm5heGpdzgmvZmh2swwbaa39h3Ur3eiL2/FINbGIN6IY1mTOZY3YzBvxLFspd9B17ZWHWyuz2ZmVl6uKFopypooSroKuAeoAO6PiLvzzis5PxHYA3w6Iua11FbS0cDDwChgDfB3EbE1OXc7cBOQBr4UEU+11L+2TBTbI7l7dO66Fo430o891GoXQyt3cetF/fnTvGVU1G9moLYxUNsZqG0MYDuDtZU+2ntIDJujHxviaNbFQNbFAOpiQPJ9EA39RvL6dh3SpqWEEFwdNDM70jhRtFKULVGUVAGsAN4P1AGzgY9FxNKcayYCXySbKF4A3BMRF7TUVtK3gS0RcbekrwL9I+Irkk4Hfg2MA4YCfwROjoh3M5g8bZUoHm5yt7ehgR400JP91Fal+dqVo/jFi8vZuXMHvbSPXuylN3vprb30Uz292UNf6jlKu+nHbvppD0exm1rtopZdVCpTsH87ooa3o5bNHMXbUcvG6M/G5Psm+rM+juEvcXTBiSTw7nBxoRidEJqZdS5OFK0U5XxGcRywMiJWA0h6CJgELM25ZhLw88hmqzMl1UoaQrZa2FzbScCEpP2DwHPAV5LjD0XEPuANSSuTPrxcxhiBbJJU27CJadV3I+LAV2oe/L3SpHpkqCRNBRmqaKRqfpq7Ug1U9sxL7J7JZsb0KPw+DVHBTmrYHr3ZQW92RC/+Qn+2ZfqylT5sjT5si768Q1+2xFFU9hvI0u3V7M27YYVEusD/IDRXHfQyNGZmZt1TORPFYcBbOa/ryFYNW7tmWCttB0fEBoCI2CBpUM69Zha410EkfR74PMDIkSNLCKd567fVcwyVrIhhBCkCDqSLjaRIZypIkyJDiv1Usp9KGqikISrZRxV7qWYv1eyPKmp69+Wt3WJP9GAPPdlNT3ZFDXvUi/qoJH+mcHNJX24VMH8x6uYqna1NJvE+yGZmZt1LORPFQx9oy86RLeaaYtoezvsREZOByZAdem7lnkUZWlvDum3wjw23HnS8uSSuteRuymE9o1haFXDscUe7OmhmZmYtKmeiWAeMyHk9HFhf5DXVLbTdKGlIUk0cAmwq4f3Kornn99oruWst6SuU+Lk6aGZmZq0p52SWSrITUt4HrCM7IeXjEbEk55prgFt4dzLL9yNiXEttJX0HeCdnMsvREXGbpDOAX/HuZJZngNHtMZkF2m7Ws5mZWTl5MouVotzL40wEvkd2iZsHIuIbkm4GiIj7kuVx7gWuIrs8zmciYk5zbZPjxwC/AUYCa4GPRMSW5NzXgM8CjcCtEfFkS/07UtdRNDMzKxcnilYKL7jtRNHMzLoRJ4pWilTrl5iZmZlZd+RE0czMzMwKcqJoZmZmZgU5UTQzMzOzgrr1ZBZJbwNvtvFtBwCb2/ienYVj7766c/zdOXbo3vF31tiPi4iBHd0J6xy6daJYDpLmdNfZZI69e8YO3Tv+7hw7dO/4u3Ps1n146NnMzMzMCnKiaGZmZmYFOVFse5M7ugMdyLF3X905/u4cO3Tv+Ltz7NZN+BlFMzMzMyvIFUUzMzMzK8iJopmZmZkV5ETxMEi6StJrklZK+mqB85L0/eT8QknndUQ/y6WI+E+V9LKkfZK+3BF9LJciYv9E8pkvlDRD0tkd0c9yKCL2SUncCyTNkXRpR/SzXFqLP+e68yWlJV3fnv0rpyI++wmStief/QJJX++IfpZLMZ998jtYIGmJpOfbu49mZRMR/irhC6gAVgEnANXAq8DpeddMBJ4EBFwIvNLR/W7n+AcB5wPfAL7c0X1u59gvBvonP1/dVT77ImPvw7vPPY8Blnd0v9sz/pzrngWeAK7v6H6342c/AfhDR/e1A+OvBZYCI5PXgzq63/7yV1t9uaJYunHAyohYHRH7gYeASXnXTAJ+HlkzgVpJQ9q7o2XSavwRsSkiZgMNHdHBMiom9hkRsTV5ORMY3s59LJdiYt8VEU2z43oDXWmmXDH/3QN8EXgU2NSenSuzYmPvqoqJ/+PAlIhYC9m/A9u5j2Zl40SxdMOAt3Je1yXHSr2ms+rKsbWm1NhvIltZ7gqKil3StZKWA48Dn22nvrWHVuOXNAy4FrivHfvVHor9c3+RpFclPSnpjPbpWrsoJv6Tgf6SnpM0V9Kn2q13ZmVW2dEd6IRU4Fh+5aSYazqrrhxba4qOXdLlZBPFrvKcXlGxR8RUYKqky4B/B64od8faSTHxfw/4SkSkpUKXd1rFxD6P7P7BuyRNBB4DRpe9Z+2jmPgrgfcA7wNqgJclzYyIFeXunFm5OVEsXR0wIuf1cGD9YVzTWXXl2FpTVOySxgD3A1dHxDvt1LdyK+lzj4gXJJ0oaUBEbC5778qvmPjHAg8lSeIAYKKkxoh4rH26WDatxh4RO3J+fkLSj7rZZ18HbI6I3cBuSS8AZwNOFK3T89Bz6WYDoyUdL6ka+CgwLe+aacCnktnPFwLbI2JDe3e0TIqJv6tqNXZJI4EpwCe7WDWhmNhPUpIlJTP9q4Gukii3Gn9EHB8RoyJiFPAI8A9dIEmE4j77Y3M++3Fk/23pNp898DtgvKRKSb2AC4Bl7dxPs7JwRbFEEdEo6RbgKbKz4R6IiCWSbk7O30d2xuNEYCWwB/hMR/W3rRUTv6RjgTlAPyAj6VayswR3NHvjTqDIz/7rwDHAj5J/NxsjYmxH9bmtFBn7dWT/B6kBqAduyJnc0qkVGX+XVGTs1wNfkNRI9rP/aHf67CNimaTpwEIgA9wfEYs7rtdmbcdb+JmZmZlZQR56NjMzM7OCnCiamZmZWUFOFM3MzMysICeKZmZmZlaQE0UzMzMzK8iJotkRTFJa0gJJiyX9NlmjrdR73C/p9OTnO/LOzWirvh4uSaMk1SdxvipphqRTmrl2qKRHmjn3nKQ2WYpI0rmS7i+xzUOSuspuJGZmgBNFsyNdfUScExFnAvuBm0u9QUR8LiKWJi/vyDt3cRv0sS2sSuI8G3iQvH4CSKqMiPURcX079OcO4AcltvkxcFsZ+mJm1mGcKJp1Hi8CJwFI+pekyrg4WdAcSb0lPZ5U5RZLuiE5/pyksZLuBmqSyt0vk3O7ku+S9J2k3aKcthOS9o9IWi7pl007cOSSdI6kmZIWSpoqqX/Oe39L0ixJKySNLyLOfsDWpP2nk0rq74Gnk+rj4uRcTVLFWyjpYbJ77Db156bk/Z6T9D+S7k2OD5T0qKTZydclBWLpC4yJiFeT13dJelDS05LWSPqwpG8nv6fpkqpyPp8rJHkjAzPrMvwXmlknkCQfVwPTJb2H7G4/FwACXpH0PHACsD4irknaHJV7j4j4qqRbIuKcAm/xYeAcsvvTDgBmK7tfLcC5wBlk97f9M3AJ8FJe+58DX4yI5yX9G/CvwK3JucqIGCdpYnL8igLvf6KkBUBfoGkLtCYXkU3ctkgalXP8C8CeiBij7P7a85K4hwJ3AucBO4FngVeTNvcA342Il5TdbvEp4LS8vowF8nfVOBG4HDgdeBm4LiJukzQVuAZ4LCIyklYmv8O5BWI0M+t0XFE0O7LVJAnUHGAt8BPgUmBqROyOiF1k95YeDywiW9H6lqTxEbG9hPe5FPh1RKQjYiPwPHB+cm5WRNRFRAZYAIzKbZgkpLUR8Xxy6EHgspxLpiTf5+a3zdE09Hwi2QRzcs65/4uILQXaXAb8AiAiFpLdPg1gHPB8RGyJiAbgtzltrgDuTX6n04B+SQUx1xDg7bxjTyb3WkR2G7fpyfFFeTFtAoY2E6OZWafjiqLZka0+vwJYaOgXICJWJNXGicA3JT0dEf9W5PsUvGdiX87PaUr/e6OpfbFtpwE/zXm9u4VrC+1B2lIsKeCiiKhv4Zp6oGfesX0ASdWwIWcf4wwHx9QzaW9m1iW4omjW+bwAfEhSL0m9gWuBF5Mh1z0R8QvgP8kOveZryHmmLv+eN0iqkDSQbLVuVjGdSSqXW3OeP/wk2Yrk4boUWFXEdS8AnwCQdCYwJjk+C3ivpP7JkP11OW2eBm5peiGp0DD8MpJnQQ/DycCSw2xrZnbEcUXRrJOJiHmSfsa7idz9ETFf0t8C35GUARrIPsOXbzKwUNK8iPhEzvGpZJ8FfJVsle62iPiLpFOL7NaNwH3KLt+zmuwzlKVoekZRZGd3f66INj8GfippIdkh8VkAEbFO0n8Ar5B9rnIp0DQM/yXgh0mbSrLJ5kEzySNiuaSjJPWNiJ3FBiBpMNkK8IZi25iZHen07giKmVnXIKlPROxKKopTgQciYmoJ7f8Z2BkRRa+lmLTZERE/Kb3HZmZHJg89m1lXdFdSoVwMvAE8VmL7H3Pws5nF2EZ2Io+ZWZfhiqKZmZmZFeSKopmZmZkV5ETRzMzMzApyomhmZmZmBTlRNDMzM7OCnCiamZmZWUH/D3GG87eIGznQAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 576x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N = 64 #strings\n",
"h = L/N\n",
"\n",
"x = np.linspace(0,L,100)\n",
"t = np.linspace(0,0.64,1000)\n",
"w = (M_net/(2*E*I))*x**2\n",
"\n",
"A = np.diag(np.ones(N)*6)\\\n",
"+np.diag(np.ones(N-1)*-4,-1)\\\n",
"+np.diag(np.ones(N-1)*-4,1)\\\n",
"+np.diag(np.ones(N-2),-2)\\\n",
"+np.diag(np.ones(N-2),2)\n",
"\n",
"A[0,0]+=1\n",
"A[-1,-1]+=-4\n",
"A[-1,-2]+=0\n",
"A[-1,-3]+=1\n",
"A[-2,-2]+=-1\n",
"A[-2,-1]+=2\n",
"\n",
"b = np.zeros(N)\n",
"b[-2] = -M_net*(h**2)/(E*I)\n",
"b[-1] = 2*M_net*(h**2)/(E*I)\n",
"\n",
"#Numerical solution\n",
"w_nu = np.linalg.solve(A,b)\n",
"x_nu = np.arange(0,L+h,h)\n",
"\n",
"#Analytical solution\n",
"x = np.linspace(0,L,100)\n",
"w = (M_net/(2*E*I))*x**2\n",
"\n",
"plt.figure(figsize = (8,4))\n",
"plt.plot(x_nu, np.block([0,w_nu]), 'o', label = \"numerical solution\")\n",
"plt.plot(x, w, '-', label = 'analytical solution')\n",
"plt.xlabel('Position on Bridge (m)')\n",
"plt.ylabel('Deflection(m)')\n",
"plt.title('64 Step Guitar Bridge Deflection')\n",
"plt.legend(bbox_to_anchor=(1,1));"
]
},
{
"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": 125,
"metadata": {},
"outputs": [],
"source": [
"L = 0.64\n",
"dG = 1.140e-3\n",
"tG = 71.81"
]
},
{
"cell_type": "code",
"execution_count": 126,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"6 node G string Natural Frequencies\n",
"--------------------------------\n",
"1st natural frequency: 194.437 Hz\n",
"2nd natural frequency: 379.124 Hz\n",
"3rd natural frequency: 544.801 Hz\n"
]
}
],
"source": [
"#6 node nat frequencies\n",
"N = 6\n",
"x = np.linspace(0,L,N)\n",
"dx = L/(N+1)\n",
"k = tG/(dG*dx**2)\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",
"e = e[isort]\n",
"v = v[:,isort]\n",
"\n",
"freq1 = e.real[0]**0.5/2/np.pi\n",
"freq2 = e.real[1]**0.5/2/np.pi\n",
"freq3 = e.real[2]**0.5/2/np.pi\n",
"\n",
"print('6 node G string Natural Frequencies\\n--------------------------------')\n",
"print('1st natural frequency:', freq1.round(3), 'Hz')\n",
"print('2nd natural frequency:', freq2.round(3), 'Hz')\n",
"print('3rd natural frequency:', freq3.round(3), 'Hz')"
]
},
{
"cell_type": "code",
"execution_count": 127,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#6 node plot\n",
"plt.figure(figsize = (8,4))\n",
"plt.plot(x, v[:,0], label = \"1st Mode\")\n",
"plt.plot(x, v[:,1], label = \"2nd Mode\")\n",
"plt.plot(x, -v[:,2], label = \"3rd Mode\")\n",
"\n",
"plt.xlabel('Guitar Bridge Location (m)')\n",
"plt.ylabel('Displacement (m)')\n",
"plt.title('First Three modes of G-string (6 steps)')\n",
"plt.legend(bbox_to_anchor=(1,1));"
]
},
{
"cell_type": "code",
"execution_count": 111,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"30 node G string Natural Frequencies\n",
"--------------------------------\n",
"1st natural frequency: 195.995 Hz\n",
"2nd natural frequency: 391.486 Hz\n",
"3rd natural frequency: 585.973 Hz\n"
]
}
],
"source": [
"#30 node nat frequencies\n",
"N = 30\n",
"x = np.linspace(0,L,N)\n",
"dx = L/(N+1)\n",
"k = tG/(dG*dx**2)\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",
"e = e[isort]\n",
"v = v[:,isort]\n",
"\n",
"freq1 = e.real[0]**0.5/2/np.pi\n",
"freq2 = e.real[1]**0.5/2/np.pi\n",
"freq3 = e.real[2]**0.5/2/np.pi\n",
"\n",
"print('30 node G string Natural Frequencies\\n--------------------------------')\n",
"print('1st natural frequency:', freq1.round(3), 'Hz')\n",
"print('2nd natural frequency:', freq2.round(3), 'Hz')\n",
"print('3rd natural frequency:', freq3.round(3), 'Hz')"
]
},
{
"cell_type": "code",
"execution_count": 112,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#30 node plot\n",
"plt.figure(figsize = (8,4))\n",
"plt.plot(x, v[:,0], label = \"1st Mode\")\n",
"plt.plot(x, v[:,1], label = \"2nd Mode\")\n",
"plt.plot(x, v[:,2], label = \"3rd Mode\")\n",
"\n",
"plt.xlabel('Guitar Bridge Location (m)')\n",
"plt.ylabel('Displacement (m)')\n",
"plt.title('First Three modes of G-string (30 steps)')\n",
"plt.legend(bbox_to_anchor=(1,1));"
]
},
{
"cell_type": "code",
"execution_count": 113,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"45 node G string Natural Frequencies\n",
"--------------------------------\n",
"1st natural frequency: 196.04 Hz\n",
"2nd natural frequency: 391.852 Hz\n",
"3rd natural frequency: 587.207 Hz\n"
]
}
],
"source": [
"#45 node nat frequencies\n",
"N = 45\n",
"x = np.linspace(0,L,N)\n",
"dx = L/(N+1)\n",
"k = tG/(dG*dx**2)\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",
"e = e[isort]\n",
"v = v[:,isort]\n",
"\n",
"freq1 = e.real[0]**0.5/2/np.pi\n",
"freq2 = e.real[1]**0.5/2/np.pi\n",
"freq3 = e.real[2]**0.5/2/np.pi\n",
"\n",
"print('45 node G string Natural Frequencies\\n--------------------------------')\n",
"print('1st natural frequency:', freq1.round(3), 'Hz')\n",
"print('2nd natural frequency:', freq2.round(3), 'Hz')\n",
"print('3rd natural frequency:', freq3.round(3), 'Hz')"
]
},
{
"cell_type": "code",
"execution_count": 114,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#45 node plot\n",
"plt.figure(figsize = (8,4))\n",
"plt.plot(x, -v[:,0], label = \"1st Mode\")\n",
"plt.plot(x, -v[:,1], label = \"2nd Mode\")\n",
"plt.plot(x, -v[:,2], label = \"3rd Mode\")\n",
"\n",
"plt.xlabel('Guitar Bridge Location (m)')\n",
"plt.ylabel('Displacement (m)')\n",
"plt.title('First Three modes of G-string (45 steps)')\n",
"plt.legend(bbox_to_anchor=(1,1));"
]
},
{
"cell_type": "code",
"execution_count": 115,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"60 node G string Natural Frequencies\n",
"--------------------------------\n",
"1st natural frequency: 196.057 Hz\n",
"2nd natural frequency: 391.984 Hz\n",
"3rd natural frequency: 587.651 Hz\n"
]
}
],
"source": [
"#60 node nat frequencies\n",
"N = 60\n",
"x = np.linspace(0,L,N)\n",
"dx = L/(N+1)\n",
"k = tG/(dG*dx**2)\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",
"e = e[isort]\n",
"v = v[:,isort]\n",
"\n",
"freq1 = e.real[0]**0.5/2/np.pi\n",
"freq2 = e.real[1]**0.5/2/np.pi\n",
"freq3 = e.real[2]**0.5/2/np.pi\n",
"\n",
"print('60 node G string Natural Frequencies\\n--------------------------------')\n",
"print('1st natural frequency:', freq1.round(3), 'Hz')\n",
"print('2nd natural frequency:', freq2.round(3), 'Hz')\n",
"print('3rd natural frequency:', freq3.round(3), 'Hz')"
]
},
{
"cell_type": "code",
"execution_count": 116,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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End/AttkQt89YVrYS+LUGv7vBr5VRVN2IvSM4uoDrfzMS2OGfr9OTIHaPUXQd+x22z4HNXxgFW8hDENYNfBvqli5NKwAHEg4wZ+8cfjzyIxYs3FPzHvqH9ifMK9e+w1e1q9mOdjXbAZCelc7e+L1sO7uNr/d9Td+f+tKhVgeebvQ0vuV8C+NpaDZ03333JR84cOA/14TfeuutSjNnzvS2t7dXAQEBaRMmTIiZM2eOt52dnfr2228rfvTRRyc6dOiQnHOfpk2bJm/atKlcenq6pKWlybFjx5xDQ0NTstf/8MMPbi+++GL1rKwsIiIiUubMmXPc1dVVLVq0yP25556r7unpmRkeHn51+0uXLtkNHjy4xr59+1yzsrLk5ZdfPv3oo4/mfkknD0Sp0tMfrnHjxkrf6/DfLMrCiiMr+Hj7x5xNOUv7mu35v4b/l79Lf0BKRgqLDy1m7t65nEo+RS33WoxsOJL2NdvDmZ2wZTrsXmS0QPk2hrCuRoFVKbhwip30JDjwE+z5Hg79CpYMKF8T6j0CTYdBWa+Cz6BpJdyRxCO8v/l9Np7eiKuDK93qdqNPcB+qud3kA9RNpGSkMDNqJrP2zMKiLPQN6ctj4Y9RzqmcjZKXHCKyTSnVOOeynTt3HouIiDgP8NyindWjY5PK2PKcAT5uKeMfjjh5s+0OHDjg1LFjx7o5Lx1WqlSp3vHjx3e7urqq8+fP23t5eWU988wzVcuVK5f15ptvnr32GJ988knFrVu3lnVycrK0bds26eLFi/aHDh1yPnbsmHPHjh0Te/TocdHPzy985cqVB+rVq5fepUuXWg0aNEgZPXp0nJ+fX/iqVasOhIaGpnfs2NEvNTXV7rfffjs0YsQI35CQkNQnnngi4fz58/aNGzcO3rVr1153d3fLjZ7Pzp07vSIiImpdu1xfMynF/j73N31W9OGlDS9R0bUiszrM4sO7P8x3kQVQxrEMfYL7sLzLcsa3Go+znSPPrH2G92c0JWPqXbBrIYQ/DEPWweOrodmTUDmk8FqUnN2Moqr3fHjuEDw4GSr6w/oP4KNw+PklSIotnCyaVgKtOr6KXst7ERUfxaiGo1j18CpeiHwh30UWGL9fnqz/JMu6LOPeWvfy5Z4veWDxAyyKXkSWJcsG6TWzBAYGpnbp0qX25MmTPR0dHfPcEtSnT5+E+fPney5cuNCzf//+CdnLd+7c6VKtWrX0evXqpQMMGDAgfsOGDW47duxwqVatWnp4eHi6nZ0dffr0ic/eZ+3ate4TJ06sEhQUFNKiRYvA9PR0OXTo0G2PyNCXDkshpRST/p7EtN3TqORaiXEtxtHRr+N/L+3ZgANCh4Q42h6M4gOndOZ6wN6QO/ig3WS8POvY/Hy3xbU8NOhjPOKi4fcJsGmK0erWsC80fxrK57/41LTSINOSySfbP2Fm1EzqedVjwt0T8CnrUyDn8inrw9st36Z3cG/GbxnPG3++wfIjy/m49cd4OOsRx3mRl5anwvTbb78d/Omnn9yWLFlS/v3336968ODBPXnZr3Xr1inDhw93dXFxsWQXVWD8vbseuc4He6UUixYtOhQREZGe6wa3SLdolTIZlgzGbBzDtN3T6Fq3K8u6LKNznc4FUmRxeA1MvQuWjsCxfHX+98AM3m7xNlFXEujx6xB2nNth+3Pml3cAdJ0KT22FiB5G/7FP6sMPIyDhqNnpNK1Ii0+NZ+iqocyMmkmPwB7M7DCzwIqsnMK8wpjVYRZjm49lZ9xO+v/Un9jLukW6uMnKyuLw4cNOnTp1Spo8eXJMUlKSfWJior2bm1tWUlKS/c32f/PNN2PGjh17Kuey+vXrp506dcppz549zgBz5syp2LJly6T69eunxcTEOEVFRTkDzJ8//+pQ1tatW1+aMGFCZYvFuFK4ceNG1/w8L11olSKXMy4zYvUIlh5eypP1n+T1Zq9TxtGml+YN5/bBvIdhbhdIvwQPz4DBq6BOGzrV6cS8++fh7ODMwJ8H8vW+r2/4icM0nn7QeRKM/BsaDYRd38JnTWHdeMi8YnY6TStydsXtosfyHuyM28lbzd9izB1jCnX+KxHhIf+HmNpuKmdTztJnRR8OJBwotPNrt6ZTp061W7RoEXT06FHnypUr15s4caJXZmam9O7du3ZAQEBIWFhYyNChQ896eXlldevW7eKKFSvKBwUFhfz888/X7Yj3yCOPXOrUqVNSzmVlypRRU6ZMOda9e/c6AQEBIXZ2dowePTquTJkyatKkScc7duzo36hRo8Dq1atf/cX+7rvvns7MzJSgoKCQunXrho4ZMyZfoy10Z/hS4nzqeZ749QmiL0TzWrPX6FK3i+1PkhwHv42D7bPByQ3uGg2RQ4xRgde4dOUSL/3+Euti1tHRryOvNnsVV4d8fWgoWJdOw8//g71LwCsQOn0MNZuZnUrTTKeUYmH0Qt7d/C6VylRi4t0TCa4YbGqm6AvRDP91OCkZKXzc+mMiq0SamsdMN+sMr9mO7gxfih1NPMqjPz7KsUvHmNRmUsEUWXt/gM+awN9zjeJq5N/QfGSuRRaAu5M7n7T5hBH1R7DiyAqeWv0UV7KKcEuRe1V4ZDb0/taYp2tmB1g6ElLzNBeeppVYX+75krF/jaVplaYs6LjA9CILIKBCAF/d/xU+ZX0Y+utQfjr6k9mRtFJMF1ol3I5zO+j7U19SM1OZee9MWlZradsTpCXC4mHwbT9jeoRhG+G+96BsxZvuaid2DI0YyrgW49gUu4kXf3+x6I8YCrgXnvwLmo2Av+fBp02MaSpKUcuwpmX7Lvo7Pt7+MffXvp9P23xapDqg+5T1YVaHWUR4R/D8+ueZHTW7aHZT0Eo8XWiVYNvPbuexlY/h4eTBvPvmEeoVatsTHNsAnzeHXQvgrufhsV+hUtAtH6ZTnU483+R5Vh1fxbhN44r+L0OnsnDvOBjyG3hUh+8Gw/w+unVLK1VWH1/Nm3+9SXPf5rzV/C3s7W7aV7nQeTh7MLX9VO6peQ8fbP2AKTunmB1JK4X09A4l1Mmkk4z6bRRVylZh9n2zbXtvsMx0WDMW/vgUPGvDoJVQvUm+Dtk3pC8JaQlM3z0dTxdPRjQYYaOwBahKhFFc/vU5/Pq6McLykTlQtYHZyTStQG2J3cLz658nrGIYH7b6sHBuKn+bnO2dGd9qPC4bXZi8czI13GvwgN8DZsfSShHdolUCJV1JYsTqEViUhU/bfmrbIuvsXviiNfwxCRoPhGEb8l1kZRvZYCRd63Zl6q6pfLXvK5scs8DZ2cOdI2DQz2CxwJf3wOZp+lKiVmLti9/HU2ueoppbNT5r+1nBjFy2MTux4/Vmr9OociNe3fhq0ZxaRiuxTC20RKSDiBwQkUMi8mIu64NE5E8RSReR0desOyYiu0Vkh4iUzqGEuci0ZPLcuuc4cekEE++eSE33mrY7+P4VML2dccPn3t9Cx4nGZTQbERFeueMV2lRvw7ub32XFkRU2O3aBq9YYhv0OtVvBj6ONy4npSTffT9OKkROXTjDs12G4Obkxtf1UyruUNztSnjnaOzLx7olULluZUb+N4nTyabMjaaWEaYWWiNgDnwH3ASFALxEJuWazBGAk8MF1DtNaKVX/2qGrpdn4LePZeHojY+4YY7shzUoZt6aZ3xu8A2HoeqNTeAFwsHPg/Vbv07hyY8ZsGMOGUxsK5DwFooynUYC2eQWiFhstf2f3mp1K02wiLiWOoauGYlEWprafWigTkdpaBZcKfNr2UzKyMhixZgSXMy6bHalUOnTokGPTpk0D/Pz8Qv39/UPHjh1b6VaPERkZGbh+/fr/NKdGRkYGVqlSJTx7slGAdu3a1SlTpswt9eno1q1brZkzZ1a41Vy5MbNFKxI4pJQ6opS6AswHHsy5gVLqnFJqC5BhRsDiZsH+BXy9/2v6hfSjW0A32xw0IxW+f9zokxX2MAz8Edyr2ObY1+Fs78wnbT7Bv4I/z6x9hqj4qJvvVFTY2Rnzh/X7wRiROa0N7PnO7FSali8pGSkM/3U48WnxTG47GT8PP7Mj3TY/Dz8+uPsDjlw8wgvrXyj6I51LIEdHRyZMmBBz5MiRqC1btuz78ssvK23bti33uYBug5ubW9aqVavKAZw/f97+3LlzpnYiNLPQ8gVy3mMpxrosrxSwUkS2iciQ620kIkNEZKuIbI2Li7vNqEXfH6f/4J3N79CqWiueafSMbQ566QzMvB92L4S2r0K36eBYOJOKujm58Xm7z/Fw9uC5dc+RfCW5UM5rM7XvMi4lVq0PiwYZfdp0vy2tmHp387tEX4jmw7s/JNw73Ow4+XZn1Tt5MfJF1sWsY+K2iWbHKXVq1qyZ0aJFixSAChUqWOrUqZN64sQJJzBapIYPH+4bHh4eXKtWrbDsmeCTk5OlY8eOfgEBASEPPPCAX1paWu43KgS6du2a8NVXX3kCzJs3r3ynTp0uZq+zWCwMHTq0Wt26dUMDAgJCpk2bViF7eb9+/WrUqVMn9O677/Y/f/781cGCv//+e5kmTZoEhoaGBrdo0aLu8ePHb6lwM3PUYW4v0q38JWqulDotIpWAVSKyXym1/j8HVOoL4AswZoa/vahF25HEI4xeOxq/8n68d9d7thlmfWqbMWVB2iXo8RUEd8z/MW+Rl6sX77V8j4G/DGTcpnG80/KdQs+QL24+0HcJLB4CK8dA4im4922j1UvTiomfjv7E4kOLeTz8cVr4tjA7js30DOrJkcQjzN47G7/yfnSt29XsSOZY8mR1zu217YiGSiEpPPRZnm5WfeDAAae9e/eWadWq1dVP05mZmbJ79+59CxYs8HjzzTerdujQIfqDDz6o5OrqaomOjt67adMm1+bNm1/b1eiqe+65J2nYsGE1MzMzWbhwoeeMGTOOT5w4sQrAnDlzyu/evdt13759UWfOnHGIjIwMvueee5LXrl1b9tChQ84HDhyIiomJcQwPDw8dMGBAfHp6uowcObLGihUrDlWtWjVz2rRpFUaPHu27cOHCY3l9Ocz8jR8DVM/xfTUgz70TlVKnrf+eAxZjXIosdZKuJPHU6qdwtHfk0zafUtbRBp3T9y41WrLsHGHwSlOKrGwNKzdkWMQwlh9ZzrLDy0zLcdscXeDhWdB0OGz6HBYNhIw0s1NpWp7EJMXw5p9vEuEdwfD6w82OY3PPN3me5lWbM/bPsWw/u93sOKVOYmKiXdeuXeu8++67Jz09Pa92qurevfsFgDvvvPNyTEyME8CGDRvK9e3bNx6gadOmqQEBASnXO66Dg4OKjIxMnj59umdaWppdYGDg1duO/P77726PPPJIgoODA9WrV89s2rRp8oYNG8qsW7fu6vJatWplNGvWLAlg165dzgcPHnRt06ZNQFBQUMj48eOrnD59uti0aG0B6opIbeAU0BPonZcdRaQsYKeUSrJ+fQ/wZoElLcLe2/weMckxzOowi6rlqub/gDu+hh+eBN/G0OsbKOuV/2Pm05DwIWw6s4m3/nqLet71bDuSsjDY2cF974JHNVj5sjFqs+dX4GqTfpaaViAyLBm88PsLALx313s42hXdubJul4OdA+NbjafH8h68tOElvuv8nW0+rBYneWx5srX09HR54IEH6nTv3j2hf//+F3Ouc3FxUQAODg5kZWVdvfolct2rhf/Rp0+fhF69evk/99xz/2rAudGE2LkdXykl/v7+qTt27Nif55Nfw7QWLaVUJjAC+AXYB3yrlIoSkWEiMgxARHxEJAZ4BhgjIjEi4g5UBjaIyE5gM7BCKfWzOc/EPL+d+I0fDv/A4LDBNKhkg0kyN0+DJcOhVkvot6RIFFkA9nb2vNvyXRzsHHh+/fNkZBXTsRF3joBuX8LJzTCjA1w05febpuXJ5zs+Z1fcLl5r9hq+5W6l+2zx4ubkxrgW4zidfJrxW8abHadUsFgs9OzZs2ZAQEDa66+/fjYv+7Ro0SJ53rx5ngBbtmxxiY6OvuHlznvvvTd55MiRZwYNGpSQc3mrVq2SFi1a5JmZmcnp06cdNm/eXK5ly5aXW7VqlbRw4ULPzMxMjh8/7vjXX3+5AdSrVy8tISHB4ddffy0LRoG4devWW+q4b2pnEaXUj0qpAKVUHaXUOOuyKUqpKZHcLVgAACAASURBVNavY5VS1ZRS7kqp8tavL1lHKkZYH6HZ+5YmCWkJvP7n6wR5BjE8wgZN+hsmGvM/Bd5vTFFgw/mxbMGnrA9v3vkme+P3MunvSWbHuX3hD0Pf7+HSafiyvZ7+QSuSNp/ZzPTd0+latysdancwO06Ba1CpAQPCBvDdwe9YH/Ofrr6aja1atarckiVLKm7YsMEtKCgoJCgoKGTBggU3vFHm6NGjz12+fNk+ICAg5O233/YJDw+/4dwcdnZ2vPnmm2erVKmSmXN53759L4aGhqYGBweH3n333QFvvPFGTI0aNTL79u170c/PLz0wMDB08ODBNSIjI5PAaF2bP3/+4RdffLFaYGBgSGhoaMi6devK3crzlSJ/Xzkbaty4sdq6tfjPbaqU4tl1z/Lbyd9Y0HEBARUC8nMwY+qG3ycY0zd0mQJF+HYab/31FgsOLGBqu6nc6Xun2XFu39komNsVLJnQfxlUvm6/Tk0rVBfSLvDw0ocp41iGBR0XFIuZ323hStYVeizvQWJ6IosfXFykbpCdHyKy7dq5Jnfu3HksIiLivFmZSqqdO3d6RURE1Lp2uR7+VAz9ePRHVh1fxZP1n8xfkWWxwM8vGkVWw/7Q9YsiXWQBjG48Gv/y/ry04SXOpxbj3xOVQ2HACrBzgNmd4Nw+sxNpGkopXt34KhfSLzC+1fhSU2QBONk78XaLt7mQdoFxm0rdRRKtAOlCq5g5e/ks4zaNI8I7goGhA2//QJYsWPoUbJoCzUZAp4+N+/YVcS4OLrx/1/skZyQzZuMYLMpy852KKi9/GLA8R7F1230tNc0mvtn/DWtj1vJs42cJ8gwyO06hC64YzNCIofx09Cd+OfaL2XG0EkIXWsWIUorX/nyNTEsm41qMu/35siwWo8jaMQ9avQj3vAW3MJrDbHUr1OX5Js+z8dRGFkUvMjtO/njVNYotsTOKrbgDZifSSqkTl04wYesE7qp2F72D8jQAvER6LPwxwiqG8dZfbxXvVnOtyNCFVjGy6OAiNp7ayP81+r/bn+JAKfjlf7DjK6PIav2/YlVkZese0J1In0g+2v4R8anxZsfJH6+60H+58T7M6qiLLa3QKaUYt2kcjvaOvNbstVsaRl/SONg5MK7lOFIzU3n9j9dvOB2ApuWFLrSKiZNJJxm/ZTx3VLmDHoE9bv9Av43753Lh3S/aLmAhExFevuNlUjNTmbB1gtlx8s87wOgUD9ZiK9rcPFqp8svxX/jj9B881eApKpW55fv7ljh+Hn6MajiKdTHrWHJoidlxtGJOF1rFgEVZeGXjK9iLPWObj8VObvNt2/gxrB8PDfsVu8uFufHz8GNg6ECWHVnGltgtZsfJP+9Aa7GlYHZHiD9sdiKtFEi+ksz7m98n2DOYnoE9zY5TZPQJ7kPjyo15b8t7nEk+Y3YcrRjThVYxsPzIcrad3cZzTZ7Dp6zP7R1k6wxY9SqEdoWOHxX7IivbkHpD8C3ny9i/xhbfiUxzqhRkXEa0ZMLcLpCUp7n8NO22fbbjM86nnufVZq/a5j6pJYSd2DG2+ViyLFl8sPUDs+OUKCkpKRIeHh4cGBgY4u/vH/p///d/eb6tSZkyZXKdnVtEGj300EO1s7/PyMigQoUKEa1bt/a/lWy+vr7hZ86cseldc3ShVcQlX0lm4raJ1POqx0P+D93eQXYthOXPQEAHYwqHEvTL1MXBhZeavsTRxKPMippldhzbqBQEvRcat+r56mFITzI7kVZC7Y3fy9f7v+aRwEcI8wozO06RU82tGoPDB7Py+Eo2n9lsdpwSw8XFRW3YsOHAgQMH9kZFRe1dvXq1++rVq/8zS3ZGRt4/PLu6uloOHDjgmpycLACLFy92r1y5cpH49K0LrSJu6q6pxKfG87+m/7u9S4b7V8DioVCrBXSfVeTnybodd1W7i3Y12jF111RikmLMjmMb1RrBI3Pg3F5Y8ChkXrn5Ppp2C7IsWbz111uUdy7PyIYjzY5TZA0IHYBvOV/e2fwOmZbMm++g3ZSdnR0eHh4WgCtXrkhmZqZkD8CIjIwMHDFihG+TJk0C33rrrcr79+93ql+/flBYWFjwqFGjbtjy1bZt28SFCxeWB/jmm288u3XrdvX2O2fPnrVv165dnYCAgJCIiIigTZs2uQLExsbaN2/evG5wcHBI7969a+Yc/DB58mTP8PDw4KCgoJDevXvXzMy8vfffzJtKazdxJPEI8/bOo0vdLrf3afPYRlg4AKrWN24Q7ehq84xFxQuRL7BxyUbe2fwOn7b5tGSMmqrbHjp/CkuGGfeg7DrNuEG1ptnAdwe/Y/f53bzd4m3cndzNjlNkuTi48FyT53j6t6dZcGABfYL7mB3Jpl7Z+Er1QxcO2XRmWv8K/iljm4+94c1cMzMzCQsLCzlx4oRz//79z7Vp0+bqLXUuXrxov2XLlgMAbdq08X/sscfiRowYEf/OO+943+iYffv2TXjttdeq9OjR4+K+ffvKDB48OP6PP/4oB/D8889XjYiISPn1118PL1261K1///619+/fv/fFF1+s2qxZs+QPPvjgzPz58z2++eYbL4Dt27e7LFq0yHPr1q37nZ2d1aOPPlpjypQpFUeMGHHLw9z1b+0iSinF+5vfx8XBhZENbuPT5vmDML83VKgFfRaBs5vNMxYlPmV9eLL+k6yPWc+aE2vMjmM79XtBu9dhzyJY9YrZabQS4nzqeT7a/hGRPpF09Otodpwir031NjSr0ozPdnxGQlrCzXfQbsrBwYH9+/fvPXHixK7t27eX3bJly9UbNffq1evqi7x9+/Zyjz/+eALA0KFDb1jkNG3aNDUmJsZ52rRpnu3atUvMuW7z5s1ugwcPjgfo3Llz0sWLFx3i4+Pt//rrL7dBgwbFA/Ts2TPR3d09C+Dnn39227NnT5mIiIjgoKCgkA0bNrgfOXLE+bae6+3spBW8tSfXsvH0Rp5v8jwVXSve2s6Xzxt9e+wcjBtEl/EsmJBFTJ/gPiw9vJR3Nr9Ds6rNSs7tQ5o/DUmx8Oen4OYDdz5ldiKtmJuwdQKpmam8fMfLJaP1t4CJCC9Gvki3pd2Y9PckXmv2mtmRbOZmLU8FzcvLK6tFixZJy5Yt82jSpEkagJub279u+WFnZ5fnycw6dOhw8bXXXqu+cuXKA+fOnbta4+Q2H5qIKOvx/7NOKSXdu3eP/+yzz07l/dnkTrdoFUHpWem8v+V96njUoWfQLQ63zkgzWrKSYqHXfPCsffN9SggHOwdeueMVzqacZfKOyWbHsR0RuPcdCO0CK8fArm/NTqQVY5vPbGb5keUMDB2In4ef2XGKDb/yfvQK7sV30d+xN36v2XGKtdOnTzucP3/eHiA5OVnWrl3rHhwcnJbbtg0bNkyeNm2aJ8C0adNu2uowfPjw888+++zpyMjI1JzL77jjjqSZM2dWBFi+fLlbhQoVMj09PS133HFH0owZMyoCfPvtt+6XLl2yB+jQocOl5cuXVzh16pQDGH28oqOjnW7n+epCqwiaEzWHmOQYXoh8AUe7W+i8brEY/XlOboIuU6F6k4ILWUTVr1SfbnW7MW/fPA5fLEHzUNnZGe9prZZGf62j681OpBVDmZZMxm0ah285X4bUG2J2nGJneMRwKrhU4J1N7+gZ4/Ph5MmTji1btgwMCAgIadCgQUjr1q0v9erVKzG3bSdPnnziiy++qBQWFhacmJh40yHzderUyXjllVfOXbv8vffeO719+/YyAQEBIS+//LLvrFmzjgK8++67pzdu3FguJCQk+JdffvGoUqXKFYBGjRqljRkz5lTbtm0DAgICQtq0aRNw8uTJ2xpNJqXph6Vx48Zq69atZse4odjLsXRe0pnmVZszsfXEW9v51zdgw4fQ7g1o8XTBBCwGLqRd4P7v76dx5cZMajvJ7Di2lZYIX94DyWfh8TXgqVsktLxbGL2QN/98k4/u/oi2NduaHadYWnxwMa/+8Spvt3ibTnU6mR3npkRkm1Kqcc5lO3fuPBYREaFv5GhjO3fu9IqIiKh17XLdolXEfLj1QyzKwugmo29tx22zjSKr0QBoPqpAshUXFVwqMChsEGtj1rLt7Daz49iWi4cxghTg655G4aVpeZCSkcLkHZOp712fNjXamB2n2HrQ/0HCvcKZuG0ilzMu33wHrdTThVYRsjV2Kz8d+4mBYQPxLeeb9x0Pr4Hl/wd12sD9H5SYWd/z49GQR6nkWokPt31Y8pr4Pf2MObYSDsOiwWDJMjuRVgzM3TuX86nneabxM7oDfD7YiR3/i/wfcalxfLHrC7PjaMWAqYWWiHQQkQMickhE/nOHYxEJEpE/RSRdREbfyr7FjUVZeG/Le1QpW4VBYYPyvmNcNHzbH7yDoPvsEjkh6e1wdXDlifpPsCtuF7+e+NXsOLZX+y64fzwcWmXcWknTbiAhLYGZUTNpXb01DSrlegcT7RaEe4fzkP9DzNk7h5OXTB20d7ssFotFV9s2ZH09LbmtM63QEhF74DPgPiAE6CUiIddslgCMBD64jX2LlZ+P/sz+hP2MajgKV4c8TiyalmiMMLR3gt7zwUVPOpjTg/4PUsejDh9v/5gMS5G4E4NtNR4EkUOMaR/+nmd2Gq0Im7pzKmmZaTzdqPT23bS1UQ1H4SAOfLbzM7Oj3I49cXFxHrrYsg2LxSJxcXEewJ7c1ps5j1YkcEgpdQRAROYDDwJXx80qpc4B50TkgVvdtzjJsGTw2Y7PCKgQwH2178vbThYLfD8UEo5Avx+gfI2CDVkMOdg58HSjp3lqzVN8H/09PYJ6mB3J9u59B85Hw7KnwbMO1GxmdiKtiDl56STfRn9Ll7pd9HQONuTl6kWf4D7M2DODQWGDCKgQYHakPMvMzHwsNjZ2emxsbBi6C5EtWIA9mZmZj+W20sxCyxfI2eYaAzS19b4iMgQYAlCjRtEsRpYcWsKJpBN82ubTvN/PcN17EP0TdHgParcs2IDFWKtqrWhYqSGf7/ycTnU6lZxJTLPZOxj3sJzW1rgn4uNroEJNs1NpRcgnf3+Co50jT0Q8YXaUEmdg2EC+PfAtk/6exKQ2xWeEc6NGjc4Bnc3OUVqYWcnm1mSZ117Led5XKfWFUqqxUqqxt/cNb5NkirTMNKbsnEKEdwR3VbsrbzvtXwHr3oWIXtB0aMEGLOZEhGcaP0N8Wjyzo2abHadguFaA3gsgKwO+6QXpyWYn0oqIPef38POxn+kb0hfvMkXv919x5+HswcCwgaw9uZYd53aYHUcroswstGKA6jm+rwacLoR9i5QFBxZwLuUcoxqOyttIoLho45JhlfrQcaIeYZgHEd4RtK/ZnplRMzmfWkKnjvGqC91nwLm9sGwUlLSRltotU0oxcdtEKjhXYGDoQLPjlFh9gvvg6eLJJ39/UvJGOGs2YWahtQWoKyK1RcQJ6AksLYR9i4zkK8lM3z2dO6veSROfPMzinpYI83uBgzP0/Aoc89hpXmNkg5FcybrClJ1TzI5ScPzbQeuXjRtQb55mdhrNZBtObWBz7GaGRgylnFM5s+OUWGUcyzCk3hC2xG7hzzN/mh1HK4JMK7SUUpnACOAXYB/wrVIqSkSGicgwABHxEZEY4BlgjIjEiIj79fY155ncvjl753Ax/SIjG468+cYWC3w/BC4cM+ZQ8qhW4PlKkloetXg44GG+i/6O45eOmx2n4LR8FgI6wC8vwcnNZqfRTJJlyWLi9olUd6vOIwGPmB2nxOse0J2qZavyyXbdqqX9l6mjDZRSPyqlApRSdZRS46zLpiilpli/jlVKVVNKuSulylu/vnS9fYuThLQEZkfNpn3N9oRWDL35DuveheifjVFmtZoXfMASaFjEMBztHfl4+8dmRyk4dnbQZQp4+BrzqyXHmZ1IM8GyI8s4eOEgIxuMxFHPrVfgnOydGF5/OFHxUaw+sdrsOFoRo4d1muTL3V+SlpXGiPojbr5x9EpjlGH9PhD5eMGHK6G8XL0YEDqAVcdXsS9+n9lxCo5rBXhkLqQmwKKBkJVpdiKtEGVkZfD5js8JrRjKPbXuMTtOqdHJrxN+Hn5M+nsSWfpuDVoOutAyQezlWObvn2/8xyx/k3ltEmNg8RCoHAYPTNCd3/Opb0hf3JzcSnZfLYAq9eCBD+HY7/DbW2an0QrR0sNLOX35NE/WfzLv08Vo+WZvZ8+IBiM4kniEZUeWmR1HK0L0/0ITTNk5BQsWnqh/k3ltsjJg4UDj3+6zded3G3BzcqNvSF/WnFzD/oT9ZscpWA36GDcZ3zDRmBJEK/EyLBlM2z2NsIphtPBtYXacUqddjXaEVAzh8x2fcyXritlxtCJCF1qF7FjiMZYcWsIjAY9QtVzVG2+8+g2I2QydPwEv/8IJWAr0Ce6Dm2MpaNUCY0Lbqg1g8TCIP2x2Gq2ALTu8jFPJpxhef7i+cbQJRIRRDUZx+vJpFkYvNDuOVkToQquQTd45GSd7Jx6vd5O+Vvt/hD8mQePBENatcMKVEu5O7vQN6cvqE6s5kHDA7DgFy9HFGKVqZw8L+kJGqtmJtAKSYcngi11fEFoxlJa++m4RZmlWtRlNfJrwxa4vSMlIMTuOVgToQqsQHU08ys9Hf6ZXUC+8XL2uv+GF47BkGFSJgHvfLryApUifkFLUqlW+BnSdDueijGkftBJp+eHlRmtWhG7NMpOI8FSDp0hIS+C7g9+ZHUcrAnShVYim756Os70z/UL6XX+jzCuwcIAxs3f3WUaLhGZz7k7u9Anpw68nfi35rVoAddvBnSNh6wyIWmx2Gs3GsluzQiqG5P1WXlqBaVCpAU18mjBzz0zSs9LNjqOZ7KaFlohUEpEuIvKkiAwSkUgRPZTlVp1MOsmKIyvoHtidiq4Vr7/hqlfg9HZ48DPwvMmIRC1fHg1+lHKO5Zi6a6rZUQpH21fBtzEsHWlMfKuVGCuOrCAmOUa3ZhUhQ+sNJS41jsUH9Qeb0u66BZOItBaRX4AVwH1AFSAEGAPsFpE3RMS9cGIWf1/u/hJ7sWdA6IDrb7T3B9g0BZoOhxB9Y/WC5uHsQZ/gPqw6voroC9Fmxyl49o7w8JeAwKJBxmhWrdjLtGTyxa4vCPYMplW1VmbH0awifSKJ8I5gxp4ZZOj/a6XajVqm7gceV0o1UUoNUUqNUUqNVkp1BiKAv4H2hZKymDuTfIYfDv9Al7pdqFSmUu4bXTgOPzwFvo2g/ZuFG7AU6xvSl7KOZUtHXy2ACrWMUayntsFq/XNWEqw4soKTSScZFjFMt2YVISLC0HpDOXP5jJ5Xq5S7bqGllHpOKXXiOusylVJLlFK6p18ezIyaCQoGhw3OfYOsTPj+cUDBwzPAwalQ85VmOVu1Dl44aHacwhH6EDQeBH98AgdXmZ1Gy4dMSyZTd00lyDOI1tVbmx1Hu0YL3xaEVAxh+u7pZFr0HRpKq7z00SovIiNF5EMR+ST7URjhSoK4lDi+i/6Ozv6dqVKuSu4brX8fTm6CjhONFgetUPUL6Ve6WrXAGM1aKRQWD4VLZ8xOo92mH4/+qFuzijARYUi9IZxMOslPR38yO45mkrx0av8RqAXsBrbleGh5MCtqFpkqk8fCHst9g+N/wPrxENEbwh8u3HAaYLRq9Q7qXbpatRxdoftMY16t7x8HfW+2Yie7b1ZghUDaVG9jdhztOlpXb03dCnWZtnuavgdiKZWXQstFKfWMUmqmUmp29qPAk5UACWkJLIxeyP2176e6e/X/bpB6Ab573GjFuv/9Qs+n/aNfSD9cHVxLzwhEAO9AuH+8cT/E3yeYnUa7RT8d/Ynjl47rkYZFnJ3YMSR8CEcTj/LriV/NjqOZIC+F1lwReVxEqoiIZ/ajwJOVAHP3ziUtM43Hw3OZBV4pY5h9cix0mw7OboUfULuqvEt5egf3ZuWxlRxLPGZ2nMJTvw+EPwJr34WTm81Oo+WRRVmYvns6dSvUpXUN3TerqGtfsz213Gvxxa4vsCiL2XG0QpaXQusKMB74k38uG24tyFAlQWJ6It/s/4b2NdvjVz6X+bC2z4Z9S6HNK8ZIQ810fYL74GTvxKyoWWZHKTwi8MAH4OFrXEJMTzI7kZYHa0+u5UjiER4Leww7Pa1hkWdvZ8/j9R4n+kI0606uMzuOVsjy8j/0GcBfKVVLKVXb+tAzad7E1/u+5nLGZYbUG/LflXEH4KcXwe9uY7ZurUjwcvXiIf+H+OHwD5y9fNbsOIXHxQO6ToOLJ+CnF8xOo92EUoovd3+Jbzlf7ql1j9lxtDy6v/b9VCtXjam7pqKUMjuOVojyUmhFAfrOmLcg+Uoy8/bNo3X11gR6Bv57ZUYaLBoMTmWgy1Sw059Gi5IBoQNQSjF371yzoxSuGndAy9Gw4yvY873ZabQb2Hp2K7vO72Jg6EAc7BzMjqPlkYOdA4+FP0ZUfBR/nP7D7DhaIcrLX/ksYIeITNXTO+TNggMLuHTlEkPrDf3vytVvwNnd8OBkcPMp/HDaDVVzq8a9te5lYfRCEtMTzY5TuFo9b1zGXv40JMaYnUa7ji93f4mniycP+j9odhTtFnWu0xmfsj6la9CNlqdCawkwDvgDG0/vICIdROSAiBwSkRdzWS/Wwu6QiOwSkYY51h0Tkd0iskNEikyfsfSsdObuncudVe8k1Cv03ysPr4G/JkPkEAjsYE5A7aYGhQ0iJTOF+fvnmx2lcNk7GpcQszJh8TA95UMRtC9+HxtPb6RvSF9cHPQN54sbR3tHBoQO4O9zf7P97Haz42iF5KaFVs4pHWw5vYOI2AOfYdxHMQToJSIh12x2H1DX+hgCfH7N+tZKqfpKqcb5zWMrSw8vJT4tnkFhg/69IiUBljwBXoH6FjtFXKBnIHdVu4uv9n1Famaq2XEKV8U6cN97xpQPf0wyO412jRl7ZlDOsRw9AnuYHUW7TV38u1DeuTwz98w0O4pWSG50U+llItJJRBxzWecnIm+KyKDc9s2jSOCQUuqIUuoKMB+4ti38QWCOMvwFlBeR60yvbr4sSxaz9switGIokT6R/6xQClY8A5fjoOsXxmSRWpE2OGwwF9IvsPjgYrOjFL4Gj0JwZ1jzFpzeYXYazerEpROsPL6SRwIfwc1JTwdTXJVxLEPvoN6sjVnLoQuHzI6jFYIbtWg9DrQE9ovIFhH5UUTWiMhRYCqwTSk1Ix/n9gVO5vg+xrosr9soYKWIbBORXIb2GURkiIhsFZGtcXFx+Yh7c2tOruFE0gkGhg389wSCuxdC1GJo/RJUrV+gGTTbaFi5IQ0qNWB21GwyLBlmxylcItDpYyjrDd89Blf0WJiiYFbULBzEgb4hfc2OouVTz6CeuNi7lK6pZEqxG91UOlYp9bxSqg7QHRiLMdVDqFKqvVLqh3yeO7epjK8d83qjbZorpRpiXF58UkTuyu0kSqkvlFKNlVKNvb29bz/tTSilmLF7BjXcatCuRrt/Vlw8CStGQ/U7oPnTBXZ+zfYGhw3m9OXT/Hz0Z7OjFL4yntDlc4g/CCtfNjtNqReXEseSQ0t4yP8hvFy9zI6j5VMFlwp0rduVFUdXEHs51uw4WgHL09wCSqljSqk/lVI7lFK2+ngbA+S8L0014HRet1FKZf97DliMcSnSNFvPbmVP/B76h/bH3s7eWGixwJLhoLKg61TIXq4VCy2rtcS/vD8z9swonbM5+90NzUbA1hlwcJXZaUq1ufvmkqWyGBA6wOwomo30C+2HUop5e+eZHUUrYGZO4rQFqCsitUXECegJLL1mm6VAP+vowzuARKXUGREpKyJuACJSFrgH2FOY4a/15R5jyHXnOp3/Wfjnp0an4vveM+5nqBUrdmLHoLBBHLp4iPUx682OY442r4B3MPwwwhjQoRW6S1cu8e2Bb7m35r253zNVK5Z8y/mW3qlkShnTCi2lVCYwAvgF2Ad8q5SKEpFhIjLMutmPwBHgEDANeMK6vDKwQUR2ApuBFUop067vHEg4wMZTG3k0+NF/hlzH7oE1YyGoo3E/Oa1Y6lC7A1XLVmX67umlczZnRxejNTYl3hjQURpfA5N9e+BbLmdcZlB4fsYeaUVR9lQyC6MXmh1FK0A3LbREZFRelt0OpdSPSqkApVQdpdQ467IpSqkp1q+VUupJ6/pwpdRW6/IjSqkI6yM0e1+zzIyaSRmHMjwS+IixICPNuG+cawXo9InRuVgrlhztHBkQNoCdcTvZfq6UzntTJQLuftEY0LF7kdlpSpW0zDTm7p1Lc9/mBHkGmR1Hs7FAz0CaV23OvL3zSM9KNzuOVkDy0qLVP5dlA2yco9g6nWx0ln444GE8nD2MhWvGwrm98OBnULaiuQG1fHvI/yE8XTyZvnu62VHM0/xpqBYJPz4LiafMTlNq/HDoBxLSEngs7DGzo2gFZFDYIOLT4ll6+NqeM1pJcaN5tHqJyDKgtogszfH4DYgvvIhF25y9cxDknyHXxzbCn59B48FQt7254TSbcHVwpVdQLzac2sDBCwfNjmMOewfoMgWyMuCHJ42BHlqByrJkMXvvbOp51aNR5UZmx9EKSBOfJoRVDGPWnllk6bsxlEg3atH6A5gA7Lf+m/14FtD3jwEupl3k+4Pfc7/f/fiU9YH0JGOUYYVacM9Ys+NpNtQz0Jj3ZnZUvm+KUHxVrAP3vAVHfoMtpbh1r5CsObmGk0knGRA24N/z8mkliogwMGwgJ5JOsPrEarPjaAXgRvNoHVdKrVVKNVNKrcvx2G7tyF7qfXPgG1IzUxkYOtBY8MvLcPGE8cnfqay54TSbKu9Snof8H2LF0RWcSzlndhzzNB4E/u1h1atwvpS27hUCpRSz9syiult12lRvY3YcrYC1rdGWGm41mLlnZukcdFPC5aUzfFcROSgiiSJySUSSRORSYYQrylIzU/lm3ze0qtYK/wr+EL0Sts+G5iOhxh1mx9MKQL+QfliUha/3fW12X1cXvwAAIABJREFUFPOIwIOfGqMRvx9i3IBas7kdcTvYdX4X/UL6/TMvn1Zi2dvZ0z+0P3vi97AldovZcTQby0tn+PeBzkopD6WUu1LKTSnlXtDBirolh5ZwIf2CcfPolARY+hRUCoHWehbtkqq6e3Xa1mh7dbh9qeXmAx0nwunt8PsEs9OUSDP3zKS8c3ke9L/29q9aSfWg/4NUdKnIjKj83NlOK4ryUmidVUrtK/AkxYxvOV+61e1Gw8oN4cfRkHLeuGTo4Gx2NK0ADQgdQFJGEt8f/N7sKOYK7QLh3WH9+/rG0zZ2NPEoa0+upUdgD1wd9A3oSwtne2eGRQyjgXcDffmwhHHIwzZbRWQBsAS4OtGHUqpU/6W5q9pd3FXtLtjzPez5DlqPMeYb0kq0et71aFipIXP3zqVnUE8c7RzNjmSe+96Ho78bA0CGrNUfMmxkzt45ONo50iuol9lRtELWM6in2RG0ApCXFi13IAXjNjedrI+OBRmq2EiKNWbL9m0ELf7P7DRaIRkQOoAzl8+w6lgpv/9fGU/oPMmYM27tO2anKRHiU+NZemgpnf07U9FVz8GnaSXBTVu0lFIDCyNIsaMULB0JGanw0BRjniGtVGhVvRW13GsxK2oW99W+r3QPvQ+4Bxr2g40fQ+D9UN3Ue7sXe/MPzCfDkkG/kH5mR9E0zUbyMuowQERWi8ge6/f1RGRMwUcr4v6eCwd/gXavg3eA2Wm0QmQndvQP7c++hH1sjt1sdhzz3TMO3KvB4mFwJcXsNMVWamYq8/fP5+7qd1Pbo7bZcTRNs5G8XDqcBvwPyABQSu0C9IXkMl5Gh+DIoWYn0f6fvfsOi+La/zj+PjRBEBCwYEEUrNh77LHEHmNJosbYosaYGE1PfrkpJjflpscUNbGn2GLvXbErdlBRREERRTpIZ8/vj1nvNQZ1VXZndzmv59ln3d2Znc+wCF/OnKKDvkF98XH1YW7EXL2j6M/VE574CZLPw9YpeqexWSujVpKam8rIkJF6R1EUpRiZUmiVllLe/me7mjynTi94ci44mPIlVOxNKcdSDK0ztGQvy3Or6h20PzoOTIcLoXqnsTmFhkLmn5pPQ7+GNCnfRO84iqIUI1OqhEQhRBAgAYQQg4B4s6ZSFBtwc/h9iV6W51ZdPwSfIFjxIuSU+DmN74tabkdR7JcphdaLwAygjhAiDpgMvGDWVIpiA9SyPLdxKQ1PTIP0y7BJdeM01c3ldqp4VFHL7SiKHbpnoSWljJZSdgXKAXWklO2klBfNnkxRbMCzdZ/FIA38cfoPvaNYh4BW0OZlbTmqs5v0TmMTjiYc1ZbbCVHL7SiKPTJl1KG3EOJl4GPgEyHEVCHEVPNHUxTrd3NZniVnl5TsZXlu9ej/actRrX4ZslP0TmP15kXMw6uUF/2C1HI7imKPTLl0uA4IBE4Ch2+5KYqCcVmevAyWn1uudxTr4FRKu4R44zqsf0vvNFYtJj2G7Ze283TtpyntXFrvOIqimIEphZarlPJVKeUcKeW8m7fiOLgQoocQIlIIESWEeLuI14WxBS1KCHFCCNHU1H0VxVIaltNGiv1++ncKDGpALgCVGkP71+HEIji9Ru80Vuu3U7/h5OCklttRFDtmSqH1mxBirBDCXwjhc/P2sAcWQjgCPwE9gXrAECFEvds26wnUNN7GAdPuY19FsZgRISOIy4xjS+wWvaNYjw6vQ8WGsGYy3EjSO43VSclJYUXUCvoG9cXPzU/vOIqimIkphVYe8CWwj/9dNgwrhmO3BKKMne3zgIXA7Z0U+gHzpWY/4C2E8DdxX0WxmE5VOhFQJoD5EfORUuodxzo4OkP/6ZCdqq0JqvzNoshF5BbmquV2FMXOmVJovQoESykDpZTVjbcaxXDsysClWx5fNj5nyjam7AuAEGKcECJMCBF2/fr1hw6tKEVxdHDk2XrPcjLxJEcTjuodx3pUCIFH34FTKyB8qd5prEZuYS4LziygXeV2BHkH6R1HURQzMqXQigDMsYBZUbPy3d4UcKdtTNlXe1LKX6SUzaWUzcuVK3efERXFdP2C++Fdylsty3O7NpOgcjNY+xpkXNM7jVVYc34NyTnJarkdRSkBTCm0CoFjQogZN6d2KKbpHS4DVW95XAW4YuI2puyrKBbl5uTGU7WfYselHVxMu6h3HOvh6KSNQszL0vprlfBLqwZpYP6p+dTxqUPLii31jqMoipmZUmitAD4B9lK80zscAmoKIaoLIVzQFqpedds2q4DhxtGHrYE0KWW8ifsqisUNqTMEJwcnfjv1m95RrEu52tDlPYhcB8cX6p1GV7vjdhOdFs2IkBFquR1FKQFMmRl+HrAY2F+c0ztIKQuAl4CNwGlgsZQyQggxXggx3rjZOiAaiAJ+BSbcbd+HzXQ/Dsek8OGqCHLyCy15WMXK+bn50TeoLyvPryQlR03W+TetJ0DV1trcWmlxeqfRzbyIeVQoXYHugd31jqJYmZXH4pi+87zeMZRiZsrM8H2BY8AG4+PGQohiaT2SUq6TUtaSUgZJKT8xPjddSjnd+G8ppXzR+HoDKWXY3fa1pAMXkpi79yIDp+0l+nqmpQ+vWLHh9YaTW5jLoshFekexLg6O8MTPYMiHVRNL5CXEU0mnOHj1IMPqDsPZwVnvOIqVyMor4I0lx5m08BjbzyRQUGjQO5JSjEy5dPgh2nQKqQBSymNAdTNmsgkTOgUzc3hz4lKz6fvDbpYfvax3JMVKBHkH0b5yexacWUBuYa7ecayLbxB0+wjOb4XDc/VOY3HzIubh7uzOwFoD9Y6iWIkzV9N5/Mc9/HXkMhM7B/PHmFY4OZryq1mxFaZ8mgVSyrTbnit5f4oWoWu9Cqx7uT31KnnyyqLjvL7kOFl5amZwRVuWJzknmTXn1azo/9D8OajRCTa+C8kX9E5jMVdvXGXjxY0MrDmQMi5l9I6j6ExKyR8HYuj34x5Ss/L5bXQrXnustiqy7JApn2i4EGIo4CiEqCmE+AGtY7wCVPJ2Y8HY1kzsHMzSI5fp+8NuTsen6x1L0VmLii2o61OX+afmY5DqMsDfODjA4z9qlxJXvgiGkvH1+eP0HwAMqztM5ySK3tKy83npz6O8uzycltV9WD+pPe1qqtUB7JUphdZEIATIBf4E0oDJ5gxla5wcHXjtsdr88Vwr0nMK6PfTHn7fH6NmCC/BhBAMDxlOdFo0u+N26x3H+nhXhR6fQcweODBd7zRml5mXyV9n/+Kxao/h7+GvdxxFR8cupdJ76i42RFzlrR51mDeqJeXKlNJePLVSG5WrfnfYFVNGHWZJKd+VUrYw3v4lpcyxRDhb0ybYj/WT2tO6hi//WhHOhD+OkJadr3csRSfdA7tT0b2imsD0Tho/A7V6wNYpkHhO7zRmtfTcUjLzMxkRMkLvKIpODAbJjJ3nGTRtL1LC4udb80KnIBwcjFN8pMfDqpfh4K+gWsHtiimjDjcLIbxveVxWCLHRvLFsl59HKeaObME7Peuw+dQ1en2/i8Mxaph/SeTs4MywusM4dPUQ4YnhesexPkJA3+/B2Q2Wj4dC++zfmF+Yz/xT82lZsSUhfiF6x1F0kJiZy8i5h/hs/Rm61tX69jar5vO/DaTURuIW5EL/GdpldcVumHLp0E9KmXrzgZQyBShvvki2z8FB8HzHIJaMfwQh4KkZ+/h5RxQGg2oOLmkG1RpEGecyzAmfo3cU61SmIvT+GuLCYO/3eqcxi/UX15OQlaCW2ymh9kQl0vP7XeyPTuLjJ+ozbVhTvErfNrXHkXkQtRm6TQG/YH2CKmZjSqFlEEIE3HwghKiGGnVokiYBZVk3qT09QiryxYZIhs8+SEKGuupakrg7u/Nk7SfZEruFSxmX7r1DSVR/IIT0h+2fwVX7avmTUjI3Yi7B3sG0q9xO7ziKBRUUGvhy4xmGzTqAp6sTK19sy7Otq/1zNYCUi9oI3OodoMVYXbIq5mVKofUusFsI8ZsQ4jcgFHjHvLHsh6erMz8ObcJnAxpw6GIyvb7fRejZ63rHUizombrP4CgcmR8xX+8o1qvX1+BWVruEWJCnd5pis+fKHs6lnGNU/VFquZ0SJC41m6d/2c9P28/zZLMqrJ7Yjrr+nv/c0GCAFRNAOEC/n7URuYrdMaUz/AagKbAIbSmeZlJK1UfrPgghGNIygNUT2+Hj7sLw2Qf5bN1p8gpUh8eSoHzp8vSp0YcVUSvUsjx34u6r9de6dhJ2fq53mmIzJ3wO5UuXp2dgT72jKBay/mQ8Pb8LJfJqBt8PbswXgxpR2sWp6I33/6yNvO3xuTYSV7FLppbPhUAC2tQO9YQQHcwXyX7VqlCGlS+245lWAcwIjebJ6XuJSbqhdyzFAkaGjCSnMIeFZ0r2gsp3VacXNB4Gu7+F2AN6p3loEUkRHLx6kGfrPouzo1pux95l5xXyzrKTvPDHEar7ubP25Xb0a1z5zjsknIGtH0HtXtB4qOWCKhZnyqjDMWiXCzcCU4z3H5o3lv1yc3Hkk/4NmD6sKRcSb9B76m5WHC25C+yWFDW8a9CxSkcWnFlAdkG23nGsV4/PwKsKLH8ecm17DdG54XPxcPZgUK1BekdRzCzyagb9ftrNgoOxjO8YxJLxbajm637nHQrzte/xUh5aS666rGzXTGnRmgS0AGKklI8CTQDVyegh9ajvz/rJHajrX4bJi47x6uJjZOba5/B2RTMyZCQpuSmsiiqWNdntk6snPDFN6yC8+T290zywyxmX2RSziSdrP4mHi4fecRQzkVLy2/4YHv9xN8k38vntuZa83bMOLk73+NUa+hXEH4M+34KHGsRv70wptHJuTlAqhCglpTwD1DZvrJKhsnH5nkldarLiaBx9f9jNycu3Lyup2ItmFZrR0K8h807No9BQqHcc6xXYDh55EcJmw7nNeqd5IPNPzcdBOKjlduxYalYe438/zHsrwmldw5cNk9vTvma5e+945SiEfgkNn4Z6/cwfVNGdKYXWZeOEpSuAzUKIlcAV88YqOZwcHXilWy0WjG1NTn4hA6bt4ZfQ82rOLTskhGBk/ZFcyrjE1titesexbp3fg/L1tLUQs5L1TnNfUnNSWRG1gj41+lC+tGqtsEf7zifR47tdbDuTwL9612XOyBb4eZS69455WbBsHHhUgJ7/MX9QxSqYMuqwv5QyVUr5IfAeMAt4wtzBSppWNXxZP6k9XepU4NN1Zxgx5yAJ6WrOLXvTuWpnAsoEMCd8jloL826cXbUZsrOSYc0rNrX228LIhWQXZKsJSu1QvnFurKEz91PaxZHlE9oypn2N/y2jcy9bPoDEs9B/mjadiVIi3LHQEkL43H4DTgK7AdXpwAy8S7swbVjT/8651eP7XWw9fU3vWEoxcnRwZHi94YQnhRN2LUzvONbNvyE8+g6cWgEn/9I7jUlyCnJYcGYBHap0IMg7SO84SjGKTcriyen7+Gn7eZ5qVpXVE9tRv7KX6W8QtQUO/gKtJ0CNTuaKqVihu7VoHQbCjPe339RvCDO5OefWmontqODpynPzwvhwVQQ5+apPj73oF9wPH1cftdi0KdpMgiotYd1rkGb9o3NXnV9Fck6yas2yM8uPXqbX1F2cv57Jj0Ob8J9BDXEvdYe5sYqSlQwrXoRydaDL++YLqlilOxZaUsrqUsoaxvvbbzUe5qDGFrLNQohzxvsi21CFED2EEJFCiCghxNu3PP+hECJOCHHMeOv1MHmsUXD5Miyf0IbRbaszd+9FnvhpD2evZegdSykGrk6uDK4zmNDLoUSlROkdx7o5OkH/6dqC0ysnaDNpW6lCQyHzIubRwK8BzSs01zuOUgwycvJ5ZdExXll0nDoVy7B+Unv6NKx0f28iJayZDFlJMOBXbRF1pUQxacJSIcQAIcQ3QoivhRDF0T/rbWCrlLImsNX4+PZjOgI/AT2BesAQIUS9Wzb5VkrZ2HhbVwyZrI6rsyPv963HnFEtSMzMpe8Pu5m396Lq22MHhtQegpuTG3Mi1GLT9+QbBN3/DdE74MB0vdPc0ZbYLcRmxDIyZKRabscOHI5JptfUXaw8FsfkrjVZOK41VcqWvv83Or4QTq2Ezu9ql8OVEseUCUt/Bsaj9c8KB8YLIX56yOP2A+YZ/z2PojvXtwSipJTRUso8YKFxvxLn0drlWT+pA48E+fLBqghGzz3E9YxcvWMpD8Hb1ZuBNQeyNnotcZnWf0lMd81GQa2eWmdiK1x4WkrJzJMzCfQMpEtAF73jKA+hoNDAt5vP8uT0fUgJS8Y/wuSutXByfIB1CFNiYN0bENAG2rxc/GEVm2DKd05HoLuUco6Ucg7QC+j0kMetIKWMBzDeFzUGujJw6ZbHl43P3fSSEOKEEGL2nS49AgghxgkhwoQQYdev2+48q+XKlGLOyBZMeTyEPeeT6PFdKNvOqI7ytmxEyAiEEMwJV61a9yQE9PsRXL1h2VjIt64RubvjdnMm+QzPNXgORwdHveMoDyg2KYunZuzj+63neKJxZdZPak+zaj4P9maGQm2RdNAuf6vvixLLlEIrEgi45XFV4MS9dhJCbBFChBdxM7VVqqi295vXzKYBQUBjIB74+k5vIqX8RUrZXErZvFw5EyaTs2JCCEa0CWTNxHaUK1OK0XPDeH9luOoob6MqulekX1A/lp9bTmJ2ot5xrJ+7nzZrfMIp2PKh3mn+ZubJmfi7+9O7Rm+9oygPQErJ0sOX6fl9KOcSMvl+cGO+eboxZVwfYo3KvVMhdi/0+hLKViu+sIrNMaXQ8gVOCyF2CCF2AKeAckKIVUKIO64lIqXsKqWsX8RtJXBNCOEPYLxPKOItLqMVdTdVwThRqpTympSyUEppAH5Fu8xYYtSqUIYVL7bluXbVmb8vhr4/7CbiippR3haNrj+aAlnA/FPz9Y5iG2p2hVbj4cA0OLdF7zQAHL52mCMJRxgZMhJnB7V4tK1Jy8pn4oKjvLbkOCGVvFg/qf3dF4M2RfwJ2PaJNvN7o8HFE1SxWeJeHauFEB3v9rqUcud9H1SIL4EkKeXnxtGEPlLKN2/bxgk4C3QB4oBDwFApZYQQwv/mpUchxCtAKynlPb+bmzdvLsPC7GtmitCz13l9yXFSsvJ47bHajG1fA0dTJ89TrMKboW+y89JONg3ahFep+5iXp6TKz4ZfHtVGcU3Yp7V06Wj85vGcTj7NxoEbcXVy1TWLcn/2RCXy2uLjJGbmMrlrTV7oFPzwPz/zbsAvnSAnXfv+LP2Alx6LiRDisJRSDYPVkSktWmHALmNBFQ94AXullDsfpMgy+hzoJoQ4B3QzPkYIUUkIsQ5ASlkAvARsBE4Di6WUEcb9vxBCnBRCnAAeBV55wBw2r0Otcmyc3IGudSvw+fozDPl1P5dTsvSOpdyH5+o/R1ZBFn+e+VPvKLbB2Q0GzoScVFg1UddZ4yOSIthzZQ/D6w1XRZYNyckv5KPVp3hm5gFKl3Jk2YQ2vNS5ZvH8kbrhHUg8BwN+0b3IUqyDKS1ah4H2QFlgP1rhlSWlfMb88YqXPbZo3SSlZOmROD5cFYEAPnw8hAFNK6th5jZi4taJHL1+lE0DN1Ha+QGGkJdE+36Gje9An2+h+WhdIry641X2X9nPpkGb8HBRC2bYglNX0pm86Chnr2Uy/JFqvNOzLm4uxdRRPWIFLBkB7V6Brh8Wz3s+JNWipT9TWrSElDILGAD8IKXsD4SYN5Zyv4QQDGpWhfWT2lPHvwyvLTnOi38eIeVGnt7RFBOMaTiGtNw0lpxdoncU29FqPNR4FDb8H1w/a/HDR6dGsyVmC0PqDlFFlg0oNEim7zxPv592k5KVz9xRLfioX/3iK7JSL8Hql6FSU3j03eJ5T8UumFRoCSEeAZ4B1hqfU+NUrVRVn9IsHPcIb/aozeZT1+j+XSg7Iosaa6BYk0blGtGqYivmRcwjr1AVxyZxcNBGITq7wbIxUGDZueVmhc/C1cmVYXWHWfS4yv27lJzF0F/38/n6M3SpU4GNkzvQqXZRswo9IEMhLBun3Q+aBY5qUITyP6YUWpOBd4Dlxo7oNYDt5o2lPAxHB8GETsEsn9AWLzdnRs45xLvLT3Ijt0DvaMpdjGk4huvZ11l5fqXeUWyHp782v1b8cYtO+RCXGcfa6LUMrDmQsq53nMZP0ZmUkkWHYunxXSgRV9L5clBDpg1rio+7S/EeKPQrbSqH3l+Dz0OtUKfYoXsWWsZO749LKf9jfBwtpVRT3NqA+pW9WD2xHWPbV+fPg7H0mrqLsIvJesdS7qBVxVY08GvA7JOzKTCoothkdXpDy+dh/88Qud4ih5wTPkeb1y5khEWOp9y/hIwcxswL462lJ2lQxYsNk9vzZPOqxd9vNXY/7PwcGjylpnJQinTHQksI8Z3xfvXNObNuvVkuovIwXJ0debd3PRaObU2hQfLkjH18tv40uQVqklNrI4RgTIMxXM68zIaLG/SOY1u6fQQVG8CKFyDNvEsaJWYnsvzccvoF9aOie0WzHkt5MOtOxtP921B2RyXyfp96/DnmAdcpvJfsVFg6BrwDtNYsRSmC011e+814/5Ulgijm1aqGLxsmd+CTtaeYsTOanZHX+fqpRoRUUvM2WZNOVTsR7B3MrJOz6FW9Fw7iAdZXK4mcXWHQXJjRQfvFN2I1ON7tx9uDm39qPgWygNH19RnpqNxZWlY+768KZ+WxKzSq4sXXTzUmuLyZBipICWsmQ0Y8jN4Irp7mOY5i8+74U1xKedh4vxNtNvhTN+fOeoj5sxQdeZRy4rMBDZk9sjlJN/J44qc9TN16jvxCg97RFCMH4cCYBmOISo1iW+w2vePYFr9gbaqH2L0Q+oVZDpGak8qiM4voHtidAM+Ae++gWMz2Mwk89t1O1p6I59VutVj6QhvzFVkAR+ZDxHJ49P+gipo9Qbmzu106FEKID4UQicAZ4KwQ4roQ4n3LxVPMoXOdCmya3IGe9f35ZvNZ+v+8h8irGXrHUoy6B3Yn0DOQn479hEGqIvi+NHoaGg2FnV/AhdBif/s5EXPILshmXINxxf7eyoNJy87njSXHGTX3EN5uLiyf0JaXu9TEydGMrcFXw2H9m1CjE7SdbL7jKHbhbt+Jk4G2QAsppa+UsizQCmhrXPZGsWFl3V2YOqQJ055pSnxqDn1/2M1P26MoUK1bunNycOKFRi8QlRrFpphNesexPb2+BN9gWDoWMq8X29smZSex4MwCelbvSXDZ4GJ7X+XB7YhMoPu3oSw9cpkXHw1i1cS2NKhi5u4QOemweDi4esOAmeCgZjtS7u5uhdZwYIiU8sLNJ6SU0cAw42uKHejZwJ9Nr3SgW0gFvtwYycBpezl3TbVu6a17YHeCvIKYdmwahQY1cOG+lPKAJ+dCdorWOd5QPH88zA6fTW5hLuMbjS+W91MeXEZOPm8vPcHIOYco4+rE8glteaN7HUo5mbnokRJWT4KUCzBoNniUM+/xFLtwt0LLWUqZePuTUsrrgJqNzY74epTip6FN+XFoE2KTs+g9dTfTdpxXrVs6cnRwZELjCUSnRbPuwjq949ieivWhx6cQtRn2/fDQb5eQlcCiyEX0qdGH6l7ViyGg8qB2nbtO929DWRx2ifEdg1g9sR2Nqnpb5uBhsyBiGXT+FwS2tcwxFZt3t0LrbtNTq6mr7VCfhpXY9EpHOtcpz382nGHAtL2cuZqud6wSq2u1rtQuW5vpx6erebUeRPPnoO7jsGUKxOx9qLeadXIWhYZC1Zqlo7TsfN786zjPzjqIm4sjS19ow9s96+DqbKFLd1eOagtGB3eDtqr3jGK6uxVajYQQ6UXcMoAGlgqoWFa5MqWYNqwpPw1tSlxKNn1/2M23m8+SV6BatyzNQTjwYuMXic2IZfX51XrHsT1CaLPGlw2EJSMh4+oDvc3VG1dZcnYJ/YL7UbVM1WKNqJhmU8RVun2zk6VH4nihUxBrX25PkwALzsifnap9D7mXg/4ztOWfFMVEd5vewVFK6VnErYyUUl06tGNCCHo39Gfzqx3p3cCf77eeo+8Puzl+KVXvaCVOp6qdCPENYcaJGeQX5usdx/a4esHTv2kdmJeMggf4Gv5y4hckknEN1UhDS0vKzGXigqOM++0wPu4urJjQlrd6WLAVC7R+WStfhLTLMGgOuPta7tiKXVBluXJHPu4ufDe4CbNGNCctO5/+P+/hs3WnyclXnbMtRQjBi41fJC4zjuVRy/WOY5sqhMDjU7X5te5zPcTLGZdZfm45A2sOpJJHJfPkU/5BSsmq41fo9m0oG8K1ebFWvdTO/CMKi3JgOpxZA10/hIBWlj++YvNUoaXcU5e6Fdj0ageeblGVGaHR9PgulL3n/zFOQjGTdpXb0ahcI3458Qt5hap75ANp+BS0GAv7foSIFSbv9suJX3AQDoxtMNaM4ZRbXUnNZuz8MF5ecJSqPqVZM7E9L3epiYuTDr+uLh2ETe9B7V7wyEuWP75iF1ShpZjE09WZzwY05M8xrZDA0F8P8MaS46TcUL/4zU0IwUtNXuJa1jX+OvuX3nFsV/dPoXJz7TLQ9bP33Dw2PZZV51fxVO2nqOBewQIBS7ZCg2TOngt0+2Yne6KSeLdXXZa90IbaFcvoEyg9HhYNA68q8MTPWp8/RXkAqtBS7kubYD82Tu7AC52CWHY0jq7f7GTlsTiklHpHs2utKraiWYVmzDw5k5yCHL3j2CYnF3hqHjiV0n6B5mbedfNpx6fh7ODMcw2es1DAkut0fDoDpu1lyupTNA/0YdMrHRjboQaODjoVNwW5sPhZ7Xtk8J/gZsGO94rdUYWWct9cnR15q0cdVr/Ujipl3Zi08Bij5h7iUnKW3tHslhCClxq/xPXs6yyOXKx3HNvlVUWbaDLpHKyaqHV0LkJ0qjZ/2ZA6Q/Bz87NwyJIjJ7+QLzacoe8Pu7mcnMX3gxszd1QLqvqU1jfYujcgD3qfAAAgAElEQVTg8iF44ieoUE/fLIrN06XQEkL4CCE2CyHOGe+L/HNBCDFbCJEghAh/kP0V86pXyZNlE9ryQd96HLyQzGPfhvJraLRapNpMmldsTmv/1swKn0VWvipqH1iNTtqEkxHLYP+0IjeZdnwaro6ujKo/yqLRSpLd5xLp8V0oP+84z4Cmldn6Wkf6Na6M0PsSXdhsODIP2r0CIf31zaLYBb1atN4GtkopawJbjY+LMhfo8RD7K2bm6CAY1bY6m1/tSJsgXz5Zd5q+P+zmcEyy3tHs0sQmE0nOSWZuxFy9o9i2tq9A7d6w6V9wftvfXjp5/SQbLm5gWL1hlHVVf8MVt4T0HCYuOMqwWQcA+HNsK74Y1Ajv0i46JwNi98O6NyG4K3R+T+80ip0QevStEUJEAp2klPFCCH9gh5Sy9h22DQTWSCnrP8j+t2revLkMCwsrlnNQ/klKycaIa0xZHUF8Wg6DW1TlrR51KOtuBT9A7cgbO99gx6UdrOm/RnXSfhi5GTDrMUiPgzHbwC8YKSUjNowgNj2WtQPW4u7srndKu1FokPy+P4avNkaSW2hgQqcgxncMsuycWHeTHg+/dATn0jBuu930yxJCHJZSNtc7R0mmV4tWBSllPIDxvry59hdCjBNChAkhwq5fv/7AgZV7E0LQo35FtrzakXEdarDk8GW6fLOTxWGXVGf5YjS52WQM0sDUo1P1jmLbSpWBIQvAwQkWPA3ZKWyK2cTRhKNMbDJRFVnF6MTlVJ74aQ8frIqgcYA3Gyd3YHLXWtZTZKnO74oZma1FSwixBahYxEvvAvOklN63bJsipbxTP61A/tmilWrq/rdSLVqWdTo+nX+tCOdwTAotAsvy7yca6DdU2858e/hbZofPZmHvhYT4hegdx7bF7IV5j5NbrQ39PPJwd3ZncZ/FODpYSRFgw9Ky8/lqYyS/H4ihnEcp3u9bj94N/PXvh3UrKWH1y3BkPjw5D0Ke0DtRsVItWvozW4uWlLKrlLJ+EbeVwDXjJT+M9wn3+fYPu79iAXX9PVny/CP8Z2ADziVk0mvqLqasjiAtWy0l87DGNhiLj6sPX4Z9qVoLH1a1NtDnG/5MPkJcZhyvN39dFVkPyWCQLDoUS+evdvDHgRhGPBLI1tc60qdhJesqsgD2/6wVWe1etbsiS7EOel06XAWMMP57BLDSwvsrFuLgIHi6RQDbX+vE4BZVmbv3Il2+3sHisEsYDKpAeFAeLh682PhFDl87zNbYrXrHsXlJdXvzi285OmZl88iVM3rHsWnHLqXS/+c9vLX0JNX93Fk9sR0fPh5CGVcrXCL39GrY+C7U7as6vytmo1dneF9gMRAAxAJPSimThRCVgJlSyl7G7RYAnQA/4BrwgZRy1p32v9dx1aVD/YXHpfH+ynCOxKbSuKo3H/ULoWEV73vvqPxDgaGAJ1c/SW5hLiv6rcDFUQ06eFD/3v9vlp5dylJRhRoX9sLwlRDYTu9YNiUpM5cvNkSyKOwS5cqU4v961eEJa5iu4U7iDsOc3to8WSPWgIvOc3eZibp0qD9dCi29qELLOhgMkuVH4/hs/RmSbuQyuEVVXn+sNr4epfSOZnP2xO1h/JbxvN78dUaEjLj3Dso/RKVEMXD1QAbXHsw7jSbAzK5wIxHGbgOf6nrHs3oFhQZ+3x/DN5vPkpVXyOh21ZnYOdg6W7BuSonRPmdnVxizFTzudzyW7VCFlv5UoaXoJj0nn6lbzjFn70VKuzjycueajGgTqM/isTZs/JbxnEg4wdoBa9W8Tw/ghS0vcPz6cdb1X4e3qzcknYeZXaC0H4zeCO6+eke0WjsiE/hk7WnOJWTSvqYfH/QNIbi8h96x7i47FWZ316ZzeG4TlK+jdyKzUoWW/tRvNEU3nq7O/KtPPTZObk+zamX5ZN1pun27k40RV1UH7/vwRvM3yCrIYtrxomc5V+5sT9wedsft5vmGz2tFFoBvEAxZCGmX4M+nIO+GviGtUFRCBiPnHGTknEPkFxqY8Wwz5o9uaf1FVmE+LBkBSVHw9G92X2Qp1kEVWorugsuXYe6olswd1QJnRwee/+0wQ37dT8SVNL2j2YQg7yAG1RrE4sjFRKdF6x3HZhQYCvgq7CuqlqnKkDpD/v5iQGsYOAuuHIElI7Vf0AopN/L4YGU43b/bxeGYFP7Vuy6bXulI95CK1tsX6yYpYc1kiN4BfadCjY56J1JKCFVoKVajU+3ybJjUno/6hRB5NYM+P+zmrb9OkJCeo3c0q/dCoxdwc3Lj67Cv9Y5iM5adW0ZUahSvNXut6IEEdftA76/h3CZYPfmOC1CXBLkFhczcFU3HL7fz2/4YhrYMYMfrnRjTvobtXOrf/Q0c/R06vAFNntE7jVKCOOkdQFFu5eTowPBHAunXqDI/bDvH3L0XWXX8CmPbV2dcxyA8Sqlv2aL4uvkyruE4vjn8Ddtit9E5oLPekaxaUnYSU49OpVmFZnf/WjUfDRnXYOfnUKYCdHnfciGtgMEgWX3iCl9tiuRScjbta/rxr971bG/i4cNzYetH0OBJePRdvdMoJYzqDK9YtYuJN/hyUyRrT8Tj6+7Cy11qMqRlgO38FW1B+YZ8Bq8ZTGpOKsufWI6ni6fekazWGzvfYGvsVv56/C9qeNW4+8Y3Lzkdngs9v4RW4yySUW97ohL5fP0ZTsalUdffk7d71qFDTT/rv0R4u5N/wdIxENwFBi8Ap5I1DYrqDK8/9dtKsWqBfu78NLQpK19sS80KHnywKoJu3+5kzYkrqsP8bZwdnPmozUck5iTyTdg3esexWttjt7Ph4gaeb/j8vYssACGg19dQuzesfxMiVpg/pI5OXUln+OyDPDPzAMk38vjmqUasndiOjrXK2V6RFbkBlj+vzf7/1G8lrshSrINq0VJshpSSHZHX+Xz9GSKvZdCoqjdvdq9NmyBf2/sFYEZfh33N3Ii5zO4+mxYVW+gdx6pk5GXwxIon8Hb1ZmHvhTg73sdcT/nZML8fXDkKz/xld52pY5Oy+G7LWZYfi8PT1ZmXHg3m2UeqWc/Cz/frQij8PkibkHT4KnAtmS28qkVLf6rQUmxOoXHC0282RXIlLYfWNXx4/bHaNA/00TuaVcguyGbgqoEIBEsfX4qrk6vekazGlH1TWHZuGX/2+vPBFuPOSoY5vSDlIjyzBKq3L/aMlhafls0P26JYfOgSjg6CkW0DmdAxGK/SVjzh6L1cDtOKYq+qMGodlC65PxtUoaU/VWgpNiu3oJAFB2L5cft5EjNz6VS7HK91q02DKl56R9PdwfiDPLfpOUbVH8WrzV7VO45VOHT1EKM3jmZEvRG83uL1B3+jzOswrw+kxmrFlo0u1XM9I5efd0Txx4FYpJQMaRnAi48GU8HTxgvzq+Ewtze4lYXRG6BMRb0T6UoVWvpThZZi87LzCpm/7yLTdp4nNSuf7iEVeLVbbdsbGVXMPtz7IcujlvNn7z8J8X2A1hs7klOQw8BVAzFIA8v6LcPNye3h3jAzAeb20SY1feYvCGxbPEEtIDUrjxmh0czdc5G8QgODmlZhYpdgqpS1g7X+ks7D7B7g4KQVWWWr6Z1Id6rQ0p8qtBS7kZGTz+zdF5m5K5rMvAJ61q/IS4/WpF6lktk3Iz0vnSdWPIGPqw8L+izA2cGGLwU9pG8Of8Oc8DnMfGwmrfxbFc+bZlzTWrbS4mDYX1qHayuWlJnLrN0XmL8vhht5BTzeqBKTutSkRjkrn83dVInntMuFBTkwagOUq6V3IqugCi39qUJLsTupWXnM3HWBeXsvkpFbQNe6FXi5SzANq3jrHc3itsZuZfL2yUxqOokxDcboHUcXp5JOMXTtUPoF92NKmynF++Z/K7aWQrVHivf9i0FCRg6/hkbz+/5YcgoK6dXAn4mdg6lT0Y7+ALl6En7rr/372RVQsb6+eayIKrT0pwotxW6lZeczd89FZu+5QFp2Ph1rlePlLsE0q1ayOsa+uuNVdl7ayV+P/0V1r+p6x7GofEM+Q9cOJSk7iRVPrDDP3GIZV7XLiBnxWrEV0Lr4j/EA4tOymbEzmgUHY8kvNNCvcWVefDSI4PJ2dkn90iH4YyC4eMDwleBXU+9EVkUVWvpThZZi9zJy8vltfwwzd10g+UYebYJ8Gd8xiPa2OPniA0jMTqTfin4EeQcxu/tsnBxKzuz6M47P4MdjP/Jdp+/oUq2L+Q6UcVXrgJ1xVVuQWsfRiNHXM/l11wWWHr6MQUoGNK3MhE7BBPq565bJbC6Ewp+DwaO8VmSpPln/oAot/alCSykxsvIK+PNALL/uiuZaei51/T15vkMNejf0x9nRvufuXRu9lrd3vV2iRiEeiD/AuM3j6F6tO190/ML8B0yP1/oIpVyA/jOg/gDzH/MWR2JTmLHzPJtOXcPZ0YEnm1VhfMcgqvrYQSf3opzdCIuHQ9nqMHxFiR9deCeq0NKfKrSUEie3oJCVx67wa2g05xIyqeztxuh21RncoirudryW4sf7Pmbx2cXmb92xAldvXOXpNU/jVcqLBb0X4O5sodacrGRYOBRi90H3T+GRF816OINBsu1MAjNCz3PoYgpebs4827oaI9oEUq5MKbMeW1cRy7VldSrUh2HLwN1X70RWSxVa+lOFllJiGQyS7ZEJzNgZzcGLyXi5OfNMqwCefaQa/l4POfzfCuUV5jFyw0ii06JZ2HshgV6Bekcyi/zCfEZuHElUShQLei+ghrcJy+wUa4AcWDYWTq+CR16Cbh+DQ/G2mGbnFbLyWBwzd18gyvjHwnPtqvO0nf+xAMDhedrak1VbwdBF4KrmzbsbVWjpT5dCSwjhAywCAoGLwFNSypQitpsN9AESpJT1b3n+Q2AscN341P9JKdfd67iq0FLu5EhsCr/sjGbjqas4CEGP+hUZ1SaQZtXK2lU/rqs3rvLU6qfwdfPlj15/UNrZ/i4rfXrgUxacWcDXHb/mscDH9AlhKISN/wcHpkPIAOg/HZwevoUpLjWb3/bFsPBQLKlZ+dT192R8xxr0amD/l78xFMLm92HfjxDUGZ7+HVzssN9ZMVOFlv70KrS+AJKllJ8LId4Gykop3ypiuw5AJjC/iEIrU0r51f0cVxVayr1cSs7it/0xLDwYS3pOAfUrezKyTXX6NPS33TXfbrPvyj7GbxlPj8AefN7+c7sqJNdEr+GdXe8wvN5w3mjxhr5hpIS9P8Dm9yCwvVYYuN3/FCNSSg5eSGbu3otsjLgKQPeQioxsE0jL6j529fndUU4a/DUaorZAy3HaZdn7WaeyBFOFlv70KrQigU5SynghhD+wQ0pZ+w7bBgJrVKGlWFJWXgHLj8Yxb+9Fzl7LxNfdhcEtqzK4RYBddC7+9cSvTD06lbdbvs0zdZ/RO06xOJtylmfWPkM933rM7D7TeiZoPbEEVrygTTsw+E/wMW2KjYycfFYdv8Lv+2M5HZ+Od2lnhrQMYFjralT2tr9L23eUdB4WDIbkaOj1JTQfrXcim6IKLf3pVWilSim9b3mcIqUse4dtAym60BoJpANhwGtFXXo0bjsOGAcQEBDQLCYmpnhOQikRpJTsO5/EnL0X2Xr6GgYJ7Wv6MaRlAF3rVsDFyTYv1xikgUnbJrE7bjdzesyhcfnGekd6KBl5GQxeM5isgiwW91lMudLl9I70d9E7YfGzIIH+06BO7yI3k1Jy/HIaCw/Gsur4FbLyCqnr78nINtXo17iy3bSqmuz8dlgyEoQDPDXfLhbxtjRVaOnPbIWWEGILUNR423eBeQ9ZaFUAEtF+bH0M+Esp7/lnjmrRUh5GfFo2iw9dZnHYJeJSs/HzcGFgsyoMbhFAdRucoyg9L53BawaTW5DLor6L8HPz0zvSA5FSMnn7ZHZe3sms7rNoVqGZ3pGKlnJRKxquHIU2E6HLB/+9/JWWnc/KY3EsOHiJ0/HpuDk78nijSgxpFUCjKl4l4/LgraSEg7/ChrfBrxYMWWByS6Dyd6rQ0p9NXjq8n9dvpQotpTgUGiSh566z4EAsW88kUGiQtKruw4CmlenZwB9PVyu5ZGWCyORIhq0bRl3fukzvOt3mOsdLKfnh6A/8evJX3mzxJs/We1bvSHdXkKt1kj80E1m1NfubfcWiMwVsiLhKTr6BkEqeDG0VwOONKlHGhr6PilVOOqx/E44vgFo9YcAv4GpHywVZmCq09KdXofUlkHRLZ3gfKeWbd9g2kH+2aPlLKeON/34FaCWlHHyv46pCSylu19Jz+OvwZZYevkx04g1KOTnQrV4FBjStTPua5WxiJNimi5t4I/QNGpdrzLSu02ym2JJS8tOxn5hxYgb9g/szpc0Um2j5OXUlnTNb5tAj+lOypTPviEn4NerBkBYBNKhSwqcquLgHlo+H9MvQ/nXo9DY4lLDLpcVMFVr606vQ8gUWAwFALPCklDJZCFEJmCml7GXcbgHQCfADrgEfSClnCSF+AxqjXTq8CDx/s/C6G1VoKeYipeTYpVSWH41j1fErpGbl4+vuwuONK/F4o0o0rupt1UXAhgsbeHvX2zQq14ifu/5suQk+H9CtLVkDag7gg0c+wEFYb1F7OSWLtSfiWX40jjNXM3B2FAyunsOb6Z/ikR6F6PgWdHi95I6kK8iF7Z/AnqnaMjr9f4GAVnqnsguq0NKfmrBUUYpZXoGBHZEJLD8ax9bTCeQVGqjs7UbP+hXp2cCfJlW9cXCwvqJr48WNvBX6Fg38GjCt6zQ8XDz0jlQkKSVTj05l5smZDKw5kPcfed8qi6xLyVmsD49n7cmrHL+UCkDjqt4MbFqZPg0rUdbdBfJuwNrXtMtkFRpA3++hipX2MTOXaxGwbBxcC4emI7SpG0pZ5/eeLVKFlv5UoaUoZpSWlc+W09dYdzKeXecSySs04O/lSs/6/vRqUJGmAWWtqujaHLOZN3e+ST2/ekzvOp0yLmX0jvQ3Ukq+O/Ids8NnM6jWIN5r/Z5VFVmxSVmsC49n3cl4TlxOA6BBZS96NqhIr/r+d17Y+fRqWPcmZMRDy7HQ+T3775dkMMD+n2DrR9rs7o//CLV76J3K7qhCS3+q0FIUC0nPyWfr6WusPXGV0LPXySs04OfhQqfa5elSpzztavpZRQfoLTFbeGPnG9Tzrcf0btZTbEkp+fbwt8yJmMNTtZ7i3dbv6l5kFRQaOHopla2nE9h25hpnr2UC0KiKFz0b+NOrvj8Bvib2ectJh23/hoO/aAsk9/wC6vYFK77k/MAu7oaN70L8MajdGx6fCu62OerV2qlCS3+q0FIUHWTk5LPtTAJbTyewIzKB9JwCnB0Frar78mgdrfC6Y+uHBWyN3crrO17XRiN2m46ni76tK1JKvg77mnmn5vF07ad5t9W7uvV5S83KY+fZ62w7k8COyOukZefj5CBoVcOHR2uXp3tIxYeb1PbyYVg9Ca6dhNq9tEk6vaoU3wnoKfGctoxO5DrwrAJdP4QGg+yzmLQSqtDSnyq0FEVnBYUGDseksC0ygW2nEziXoLWKVCnrRtsgP9oE+9ImyI9yZR5+rbz7sS12G6/tfI0qHlX4pN0nNCzX0KLHvykpO4l/7/83W2K3MKTOEN5p+Y5Fi6zsvELCYpLZE5XE3vOJhMelYZDg625sjayrtUYW67QehQWw/2fY8Zk2p1SzkdD2ZfCsVHzHsKQbSbDzcwibDU5u0P4VaD0BnEvQDPc6UYWW/lShpShWJjYpi+2RCeyJSmRfdBIZOQUA1K5Q5r9FV7NqZfFxdzF7loPxB3l3z7skZCUwKmQUExpPwMXR/Me9aXPMZj7e9zGZ+Zm81OQlRoWMMnuRlZNfyMm4NPadT2JPVCJHY1PJKzTg5CBoEuBNmyA/OtYuR6Mq3jiau39dSgzs/A8cX6hNc9BkGLSdrI3MswV5N+DQTAj9GvIytYKx0zvgYWUz99sxVWjpTxVaimLFCg2S8Lg09pxPZG9UEocuJpNbYACghp87TauVpWlAWZpVK0vN8h5m6VifkZfBl4e+ZHnUcoK9g/mk3SfU861X7Me5VWpOKp8e/JT1F9ZTz7cen7T9hOCywWY51tW0HA7HpHA4JoUjsSlEXEkjv1D7uVjP35O2wb60CfajZaAP7qWczJLhnlIuwu7v4NgfIA3Q8Glo/xr4BumT516uR8KhWdpoytx0qNkdun0E5evonazEUYWW/lShpSg2JCe/kGOXUjkSm8KRGO0++UYeAGVKOdGoqjchlT2p5+9JSCUvqvu5F1urS+jlUKbsnUJyTjJjG45lbMOxZlm4ecelHUzZN4XU3FTGNxzP6Aaji+U4UkoSMnI5dSWdiCtpnIpP5/ilNOJSswEo5eRAoyreNKnmTdOAsrQI9LFIq+F9SYuDvVPh8FwozIM6faDBk1Czm/6X4Qrz4cxarQXr4i5wdIF6T0CLMWpOLB2pQkt/qtBSFBsmpSQmKeu/rTHHLqVy9lrGf1tkXJ0dqFPRk5BKntTx9yTIz50a5Tyo4FnqgS7BpeWm8fnBz1kTvYa6PnV5pdkrtKzYEsdimL07OjWaWeGzWHV+FbXK1uLTdp9S26fIlbnunTM7n+jrmVxIvEHktQxOXUnn1JV0koxFKUA139LUr+xFM2OLYF1/T9tZJDwzAfb9CEf/gKxEcPHQOs7XHwBBncHJQv35DIUQfxwi18OR+ZB5FbwCoPkoaPKsukRoBVShpT9VaCmKnckrMBCVkMmp+PS/td7c7OsFUNrFkerGoquGnzvVfEtTyduNSl5uVPAqRSmnuxdOW2O38vG+j0nKScLX1Zdu1brRo3oPmpRvcl9TLlxKv8SGixtYf3E951LO4Sgcea7Bc4xvOB7nu8ySbjBIrmfmciU1m/i0HC6nZBF9/YZ2S8wkMfN/BZWzo6BWhTLGVj5P6lXyoo5/GZtak/KOCgvgYiiEL9Pm4spJhVJeULcP1HwM/BtC2erFN6pPSkiOhugd2u1CqHZMBAR31VqvanZTy+ZYEVVo6U8VWopSAkgpiU/L4ULiDaKvZxKd+L+i5HJKNrf/GPDzKEUlb1f8vVwpX8aVsqWdKevuQtnSLsZ7Z0qXMhCecoAdlzex+8oucgtzKV+6PN0Du9M9sDuV3IseIXcj/wY7Lu1g/cX1nEo6BUAjv8Z0qtKNRyp2xsHgSUpWHik38o33eSRn5ZGUmUd8WjZXUnO4lp5DgeHvof08XLTi0c+DGuXc/1tIBviUtp2WqodRkKcVPxHLtEt4uena86U8oWID462hdu9VBZxctZtDEV+bvBvaZcr0y9p92mVIjdHWIkyL1bbxrAI1Omm36h2gTAWLnKZyf1ShpT9VaClKCZeTX/jflqG41GziU3O0giYthyup2SRm5pKWnf+PYuxWwjEXN89InDyPI93OgCi853FFXlUMGY3ISa1PQZ73Xbd1d3HEx8MFfy83Knm54u/tZmyBc8Xfy43KZd3wcrODFqriUpCrLWlz9STEn9Dur4VDftY/t3Vy0/p3ObtphVd2MmSn3LaRAI8KULWFsbh6FHxqqPmvbIAqtPSnCi1FUe6p0CBJy9ZamFKz8kg2tjbdyC0gJ99Adn4hOfmFZOcVkp6XzpW8YxTIIn6pAwIHyjuF4ONaCTdnR+3m4kgpJwdKuzjhXdrZ2HLmjE9pF7xKO9/zUqZiAkOhdtnv6gm4kagVXfk5xvts7VaQDa7e4FUZvKqCZ2Xt32UqgZOVDQxQTKIKLf3pNFZZURRb4ugg8HF3uY9ReG3Mmkd5AA6O4FdTuymKYjEloOOCoiiKoiiKPlShpSiKoiiKYiaq0FIURVEURTETVWgpiqIoiqKYiSq0FEVRFEVRzEQVWoqiKIqiKGaiCi1FURRFURQzUYWWoiiKoiiKmZSomeGFENeBmGJ8Sz8gsRjfz9aU5PNX515yleTzL8nnDrZ5/tWklOX0DlGSlahCq7gJIcJK8tIGJfn81bmXzHOHkn3+JfncQZ2/8mDUpUNFURRFURQzUYWWoiiKoiiKmahC6+H8oncAnZXk81fnXnKV5PMvyecO6vyVB6D6aCmKoiiKopiJatFSFEVRFEUxE1VoKYqiKIqimIkqtEwghOghhIgUQkQJId4u4nUhhJhqfP2EEKKpHjnNwYRzryOE2CeEyBVCvK5HRnMy4fyfMX7mJ4QQe4UQjfTIaQ4mnHs/43kfE0KECSHa6ZHTXO51/rds10IIUSiEGGTJfOZkwmffSQiRZvzsjwkh3tcjpzmY8rkbz/+YECJCCLHT0hkVGyOlVLe73ABH4DxQA3ABjgP1btumF7AeEEBr4IDeuS147uWBFsAnwOt6Z9bh/NsAZY3/7lnCPnsP/tfPsyFwRu/cljz/W7bbBqwDBumd24KffSdgjd5ZdTp3b+AUEGB8XF7v3Opm3TfVonVvLYEoKWW0lDIPWAj0u22bfsB8qdkPeAsh/C0d1Azuee5SygQp5SEgX4+AZmbK+e+VUqYYH+4Hqlg4o7mYcu6ZUsqbo2ncAXsaWWPK/3uAicBSIMGS4czM1HO3R6ac+1BgmZQyFrSfgRbOqNgYVWjdW2Xg0i2PLxufu99tbJG9npep7vf8n0Nr2bQHJp27EKK/EOIMsBYYbaFslnDP8xdCVAb6A9MtmMsSTP2+f0QIcVwIsV4IEWKZaGZnyrnXAsoKIXYIIQ4LIYZbLJ1ik5z0DmADRBHP3f6Xuynb2CJ7PS9TmXz+QohH0Qote+mnZNK5SymXA8uFEB2Aj4Gu5g5mIaac/3fAW1LKQiGK2txmmXLuR9DW0MsUQvQCVgA1zZ7M/Ew5dyegGdAFcAP2CSH2SynPmjucYptUoXVvl4GqtzyuAlx5gG1skb2el6lMOn8hRENgJtBTSplkoWzmdl+fvZQyVAgRJITwk1La2qK7RTHl/JsDC41Flh/QSwhRIKVcYZmIZnPPc5dSpt/y73VCiJ/t5LM39ed9opTyBnBDCPSzyOwAAActSURBVBEKNAJUoaUUSV06vLdDQE0hRHUhhAswGFh12zargOHG0YetgTQpZbylg5qBKeduz+55/kKIAGAZ8Kyd/UVryrkHC2OVYRxp6wLYS6F5z/OXUlaXUgZKKQOBv4AJdlBkgWmffcVbPvuWaL9L7OGzN+Vn3kqgvRDCSQhRGmgFnLZwTsWGqBate5BSFgghXgI2oo1ImS2ljBBCjDe+Ph1txFEvIArIAkbplbc4mXLuQoiKQBjgCRiEEJPRRumk3/GNbYSJn/37gC/ws/H3ToGUsrlemYuLiec+EO0PjHwgG3j6ls7xNs3E87dLJp77IOAFIUQB2mc/2B4+e1POXUp5WgixATgBGICZUspw/VIr1k4twaMoiqIoimIm6tKhoiiKoiiKmahCS1EURVEUxUxUoaUoiqIoimImqtBSFEVRFEUxE1VoKYqiKIqimIkqtBTFzIQQFYQQfwohoo1LduwTQvQ3Yb91Qghv421CMeTYIYSIFEIcE0KcFkKMu8u2M4UQ9Yp4fqQQ4seHzWJ8r4tCCL/ieK8i3nuycY6jm4/XCSG8i/G9TV52RQjhIoQIFUKo6XQUpQRShZaimJFxUscVQKiUsoaUshnaJIj3XHxaStlLSpkKeAP3VWgZJ88t6v/3M1LKxkBb4D/GSRlv39dRSjlGSnnqfo5pZSYD/y20bvlaPhRjsTQa+NPUfYyLE28Fnn7Y4yuKYntUoaUo5tUZyLt1gkspZYyU8gf4ZwuREGKNEKKT8d83W3w+B4KMLVFfCiE8hBBbhRBHhBAnhRD9jNsHGluqfkZbi+7WpURu5wHcAAqN+2YKIT4SQhxAWyx4hxCiufG1UUKIs0KInWgF2s2sQUKI/UKIQ8Z9M2957Q3j8yeEEFNM/WIJIXyEECuM++0X2vJGGM95jvF8TwghBhqfnyaECBNCRNw8jhDiZaASsF0Isf22ryVCiFeFEOHG2+Tbvna/Gt9rkxDCrYiInYEjUsoC4347hBDfGlusTgshWgghlgkhzgkh/n3LfiuAZ0z9OiiKYj9UoaUo5hWCVvQ8jLeB81LKxlLKN4AcoL+UsinwKPC1seUMoDYwX0rZREoZU8R7/SGEOAFEAh9LKQuNz7sD4VLKVlLK3Tc3FkL4A1PQCqxuwK2XE78HvpdStuCW9eCEEI+hLTDcEmgMNBPaotOmmAIclVI2BP4PmG98/j20pa0aGF/bZnz+XeNM/A2BjkKIhv/f3v2EWFnFYRz/PkUkVkgMJSGlQUFhi2SQKfpDAxG0yhaFYVAELcIWQWK1M4iiVRANVAQJ1aIiDaKGJCQK0Uodq5GKyD+rAadQyWlSm3lavOfWO7fbzL3GW+k8H7hwOP/ew1kMv/mdc+9r+/mynkHbg/XJJfVTvblhALgOeFDSitJ8JTBkezlwhOqX79vdAOxqqzth+2bgRarXs6wFrgHul9RX+owCK7vcg4g4gyTQivgXSRqS9KWkL/7JNMDTJWD6CFgCLC5tB23vmGXsmhKoXAask7S01E8B73ToPwB8bHu8HIG9WWu7Hni7lOtHabeVzwhVkHkVVRDTjRuB1wBsbwX6JC0CbgWGWp1sHy7FuyXtLs9azsxA8O/m32x7wvYxqvdU3lTa9tveU8q7gGUdxl8CjLfVtd6F9zWw1/aY7ePAPkpWsQS0JyRdMMf6IuIMk8uZEc3aSy0zYnttOcLaWap+Y+Y/PAu6mHMNcBHQb/ukpAO1cRPdLMr2eAlQBoCDwK+17NZfunczZ42AZ2y/1OO41thOz1f7OiRdDqwDVto+LGkjc+9fp/lbjtfKU0Cno8PJDs9ojZtum2OamX9jz6XKRkbEPJKMVkSztgILJD1Uq1tYKx8ArpV0lqRLqY7b2v0M1DMhi4BDJcgaBJZ2GDOr8o28FcAPc3T9DLhFUp+kc4C7am07+DOIXF2r/xB4QNL55VlLJF3c5dI+odxlKnfVfiwvKN8CPFxb/4VULzKfAI5KWgzcXpunfc/q86+StFDSecCdwKddrg3gG+CKHvq31tsHjNs+2evYiDi9JaMV0SDblrQKeE7SeqpjpwngsdJlG7Cf6thplA73uWz/JGmbpFFgGHgWeE/STmAP8G0PS3pD0iRVdmWj7fb7Ru3PHpO0AdgOjJX1nV2aHwFel/Qo8D5wtIzZIulqYHu5OnYMuBc41OERX0maLuW3gA3Aq+VY9BfgvtL2FDBU9mAKeNL2JkkjVFnDfVR72fIyMCxprH5Py/bukvn6vFS9YntE0rLZ9qFmmHK02aNB4INTGBcRpznZvZ4KRET8kRWbLMHkauAe23f81+tqmqTNwHrb3/cwZhPwhO3vmltZRPwfJaMVEaeqH3ihfOPxCNXvS80Hj1Ndiu8q0FL1W2XvJsiKmJ+S0YqIiIhoSC7DR0RERDQkgVZEREREQxJoRURERDQkgVZEREREQxJoRURERDTkdz1ryRA23siHAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 576x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#60 node plot\n",
"plt.figure(figsize = (8,4))\n",
"plt.plot(x, v[:,0], label = \"1st Mode\")\n",
"plt.plot(x, v[:,1], label = \"2nd Mode\")\n",
"plt.plot(x, v[:,2], label = \"3rd Mode\")\n",
"\n",
"plt.xlabel('Guitar Bridge Location (m)')\n",
"plt.ylabel('Displacement (m)')\n",
"plt.title('First Three modes of G-string (60 steps)')\n",
"plt.legend(bbox_to_anchor=(1,1));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1A) The solution converges by 45 nodes. I determined this based on visual judgement where there was a large difference in the modes of n=6 and n=30, a slight difference between n=30 and n=45, and virtually no difference between n=45 and n=60, indicating the solution must have converged around n=45"
]
},
{
"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": 139,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"e string Natural Frequencies\n",
"--------------------------------\n",
"1st natural frequency: 329.635 Hz\n",
"2nd natural frequency: 658.886 Hz\n",
"3rd natural frequency: 987.369 Hz\n"
]
}
],
"source": [
"#Constants\n",
"L = 0.64\n",
"N = 45\n",
"dx = L/(N+1)\n",
"\n",
"#e-string\n",
"ke = te/(de*dx**2)\n",
"Ae = ke*(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(Ae)\n",
"isort = np.argsort(e.real)\n",
"e = e[isort]\n",
"v = v[:,isort]\n",
"\n",
"freq1 = e.real[0]**0.5/2/np.pi\n",
"freq2 = e.real[1]**0.5/2/np.pi\n",
"freq3 = e.real[2]**0.5/2/np.pi\n",
"\n",
"print('e string Natural Frequencies\\n--------------------------------')\n",
"print('1st natural frequency:', freq1.round(3), 'Hz')\n",
"print('2nd natural frequency:', freq2.round(3), 'Hz')\n",
"print('3rd natural frequency:', freq3.round(3), 'Hz')"
]
},
{
"cell_type": "code",
"execution_count": 140,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"B string Natural Frequencies\n",
"--------------------------------\n",
"1st natural frequency: 247.054 Hz\n",
"2nd natural frequency: 493.82 Hz\n",
"3rd natural frequency: 740.01 Hz\n"
]
}
],
"source": [
"#B-string\n",
"kB = tB/(dB*dx**2)\n",
"AB = kB*(np.diag(np.ones(N)*2)\\\n",
"-np.diag(np.ones(N-1),-1)\\\n",
"-np.diag(np.ones(N-1),1))\n",
"\n",
"eB,vB = linalg.eig(AB)\n",
"isort = np.argsort(eB.real)\n",
"eB = eB[isort]\n",
"vB = vB[:,isort]\n",
"\n",
"freq1 = eB.real[0]**0.5/2/np.pi\n",
"freq2 = eB.real[1]**0.5/2/np.pi\n",
"freq3 = eB.real[2]**0.5/2/np.pi\n",
"\n",
"print('B string Natural Frequencies\\n--------------------------------')\n",
"print('1st natural frequency:', freq1.round(3), 'Hz')\n",
"print('2nd natural frequency:', freq2.round(3), 'Hz')\n",
"print('3rd natural frequency:', freq3.round(3), 'Hz')"
]
},
{
"cell_type": "code",
"execution_count": 141,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"G string Natural Frequencies\n",
"--------------------------------\n",
"1st natural frequency: 196.04 Hz\n",
"2nd natural frequency: 391.852 Hz\n",
"3rd natural frequency: 587.207 Hz\n"
]
}
],
"source": [
"#G-string\n",
"kG = tG/(dG*dx**2)\n",
"AG = kG*(np.diag(np.ones(N)*2)\\\n",
"-np.diag(np.ones(N-1),-1)\\\n",
"-np.diag(np.ones(N-1),1))\n",
"\n",
"eG,vG = linalg.eig(AG)\n",
"isort = np.argsort(eG.real)\n",
"eG = eG[isort]\n",
"vG = vG[:,isort]\n",
"\n",
"freq1 = eG.real[0]**0.5/2/np.pi\n",
"freq2 = eG.real[1]**0.5/2/np.pi\n",
"freq3 = eG.real[2]**0.5/2/np.pi\n",
"\n",
"print('G string Natural Frequencies\\n--------------------------------')\n",
"print('1st natural frequency:', freq1.round(3), 'Hz')\n",
"print('2nd natural frequency:', freq2.round(3), 'Hz')\n",
"print('3rd natural frequency:', freq3.round(3), 'Hz')"
]
},
{
"cell_type": "code",
"execution_count": 142,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"D string Natural Frequencies\n",
"--------------------------------\n",
"1st natural frequency: 146.886 Hz\n",
"2nd natural frequency: 293.601 Hz\n",
"3rd natural frequency: 439.974 Hz\n"
]
}
],
"source": [
"#D-string\n",
"kD = tD/(dD*dx**2)\n",
"AD = kD*(np.diag(np.ones(N)*2)\\\n",
"-np.diag(np.ones(N-1),-1)\\\n",
"-np.diag(np.ones(N-1),1))\n",
"\n",
"eD,vD = linalg.eig(AD)\n",
"isort = np.argsort(eD.real)\n",
"eD = eD[isort]\n",
"vD = vD[:,isort]\n",
"\n",
"freq1 = eD.real[0]**0.5/2/np.pi\n",
"freq2 = eD.real[1]**0.5/2/np.pi\n",
"freq3 = eD.real[2]**0.5/2/np.pi\n",
"\n",
"print('D string Natural Frequencies\\n--------------------------------')\n",
"print('1st natural frequency:', freq1.round(3), 'Hz')\n",
"print('2nd natural frequency:', freq2.round(3), 'Hz')\n",
"print('3rd natural frequency:', freq3.round(3), 'Hz')"
]
},
{
"cell_type": "code",
"execution_count": 143,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A string Natural Frequencies\n",
"--------------------------------\n",
"1st natural frequency: 110.008 Hz\n",
"2nd natural frequency: 219.888 Hz\n",
"3rd natural frequency: 329.511 Hz\n"
]
}
],
"source": [
"#A-string\n",
"kA = tA/(dA*dx**2)\n",
"AA = kA*(np.diag(np.ones(N)*2)\\\n",
"-np.diag(np.ones(N-1),-1)\\\n",
"-np.diag(np.ones(N-1),1))\n",
"\n",
"eA,vA = linalg.eig(AA)\n",
"isort = np.argsort(eA.real)\n",
"eA = eA[isort]\n",
"vA = vA[:,isort]\n",
"\n",
"freq1 = eA.real[0]**0.5/2/np.pi\n",
"freq2 = eA.real[1]**0.5/2/np.pi\n",
"freq3 = eA.real[2]**0.5/2/np.pi\n",
"\n",
"print('A string Natural Frequencies\\n--------------------------------')\n",
"print('1st natural frequency:', freq1.round(3), 'Hz')\n",
"print('2nd natural frequency:', freq2.round(3), 'Hz')\n",
"print('3rd natural frequency:', freq3.round(3), 'Hz')"
]
},
{
"cell_type": "code",
"execution_count": 144,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"E string Natural Frequencies\n",
"--------------------------------\n",
"1st natural frequency: 82.439 Hz\n",
"2nd natural frequency: 164.782 Hz\n",
"3rd natural frequency: 246.932 Hz\n"
]
}
],
"source": [
"#E-string\n",
"kE = tE/(dE*dx**2)\n",
"AE = kE*(np.diag(np.ones(N)*2)\\\n",
"-np.diag(np.ones(N-1),-1)\\\n",
"-np.diag(np.ones(N-1),1))\n",
"\n",
"eE,vE = linalg.eig(AE)\n",
"isort = np.argsort(eE.real)\n",
"eE = eE[isort]\n",
"vE = vE[:,isort]\n",
"\n",
"freq1 = eE.real[0]**0.5/2/np.pi\n",
"freq2 = eE.real[1]**0.5/2/np.pi\n",
"freq3 = eE.real[2]**0.5/2/np.pi\n",
"\n",
"print('E string Natural Frequencies\\n--------------------------------')\n",
"print('1st natural frequency:', freq1.round(3), 'Hz')\n",
"print('2nd natural frequency:', freq2.round(3), 'Hz')\n",
"print('3rd natural frequency:', freq3.round(3), 'Hz')"
]
},
{
"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": 145,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" <audio controls=\"controls\" >\n",
" <source 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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": 145,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Audio\n",
"r=20000\n",
"t=np.arange(0,3,1/r)*100\n",
"e_sound = np.sin(t*e.real[0]**2)+np.sin(t*e.real[1]**2)+np.sin(t*e.real[2]**2)\n",
"G_sound = np.sin(t*eG.real[0]**2)+np.sin(t*eG.real[1]**2)+np.sin(t*eG.real[2]**2)\n",
"B_sound = np.sin(t*eB.real[0]**2)+np.sin(t*eB.real[1]**2)+np.sin(t*eB.real[2]**2)\n",
"D_sound = np.sin(t*eD.real[0]**2)+np.sin(t*eD.real[1]**2)+np.sin(t*eD.real[2]**2)\n",
"A_sound = np.sin(t*eA.real[0]**2)+np.sin(t*eA.real[1]**2)+np.sin(t*eA.real[2]**2)\n",
"E_sound = np.sin(t*eE.real[0]**2)+np.sin(t*eE.real[1]**2)+np.sin(t*eE.real[2]**2)\n",
"Audio(data=e_sound+G_sound+B_sound+D_sound+A_sound+E_sound, rate=r)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This would make good music for a horror film XD"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
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