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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": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy import linalg"
]
},
{
"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": [
"#given values\n",
"L = .64 #m\n",
"h = .004 #m\n",
"E = 10e9 #Pa\n",
"A = .02*.04 #m^2\n",
"I = .04*.02**3/12 #m^4\n",
"g = 9.81\n",
"\n",
"#d\n",
"#conversion\n",
"c = 10**-3\n",
"d_e = c*.401\n",
"d_b = c*.708\n",
"d_g = c*1.14\n",
"d_d = c*2.333\n",
"d_a = c*4.466\n",
"d_E = c*6.79\n",
"\n",
"#T\n",
"T_e = g*7.28\n",
"T_b = g*7.22\n",
"T_g = g*7.32\n",
"T_d = g*8.41\n",
"T_a = g*9.03\n",
"T_E = g*7.71\n",
"T_tot = T_e + T_b + T_g + T_d + T_a + T_E\n",
"\n",
"M = T_tot*h"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The deflection of the guitars bridge is 1.4155029503999985 mm\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(0,0.64,1000)\n",
"y = lambda x: M*x**2/(2*E*I)\n",
"\n",
"#establishing a matrix\n",
"N = 5\n",
"dx = L/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[N-2,N-1] += 2\n",
"A[N-1,N-2] += 2\n",
"A[N-2,N-2] -= 1\n",
"A[N-1,N-1] -= 5\n",
"\n",
"b=np.zeros(N)\n",
"b[N-2] += -M*dx**2/E/I\n",
"b[N-1] += M*dx**2/E/I\n",
"\n",
"w = np.linalg.solve(A,b)\n",
"num = np.linspace(0,L,N+1)\n",
"\n",
"print('The deflection of the guitars bridge is',w[-1]*1000,'mm')\n",
"\n",
"plt.plot(x,y(x),'-',color='lightpink',label='Analytical Data',lw=3);\n",
"plt.plot(num,np.block([0,w]),'*',color='mediumslateblue',label='Numerical Data');\n",
"plt.title('Deflection of Guitar Bridge');\n",
"plt.xlabel('Position (mm)');\n",
"plt.ylabel('Deflection (mm)');\n",
"plt.legend();\n",
"plt.grid();"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The deflection of the guitars bridge is 1.4155029503993073 mm\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"
}
],
"source": [
"N = 20\n",
"dx = L/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[N-2,N-1] += 2\n",
"A[N-1,N-2] += 2\n",
"A[N-2,N-2] -= 1\n",
"A[N-1,N-1] -= 5\n",
"\n",
"b=np.zeros(N)\n",
"b[N-2] += -M*dx**2/E/I\n",
"b[N-1] += M*dx**2/E/I\n",
"\n",
"w = np.linalg.solve(A,b)\n",
"num = np.linspace(0,L,N+1)\n",
"\n",
"print('The deflection of the guitars bridge is',w[-1]*1000,'mm')\n",
"\n",
"plt.plot(x,y(x),'-',color='lightpink',label='Analytical',lw=3);\n",
"plt.plot(num,np.block([0,w]),'*',color='mediumslateblue',label='Numerical');\n",
"plt.title('Deflection of Guitar Bridge');\n",
"plt.xlabel('Position (mm)');\n",
"plt.ylabel('Deflection (mm)');\n",
"plt.legend();\n",
"plt.grid();"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The deflection of the guitars bridge is 1.4155029504437935 mm\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"
}
],
"source": [
"N = 60\n",
"dx = L/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[N-2,N-1] += 2\n",
"A[N-1,N-2] += 2\n",
"A[N-2,N-2] -= 1\n",
"A[N-1,N-1] -= 5\n",
"\n",
"b=np.zeros(N)\n",
"b[N-2] += -M*dx**2/E/I\n",
"b[N-1] += M*dx**2/E/I\n",
"\n",
"w = np.linalg.solve(A,b)\n",
"num = np.linspace(0,L,N+1)\n",
"\n",
"print('The deflection of the guitars bridge is',w[-1]*1000,'mm')\n",
"\n",
"plt.plot(x,y(x),'-',color='lightpink',label='Analytical',lw=3);\n",
"plt.plot(num,np.block([0,w]),'*',color='mediumslateblue',label='Numerical');\n",
"plt.title('Deflection of Guitar Bridge');\n",
"plt.xlabel('Position (mm)');\n",
"plt.ylabel('Deflection (mm)');\n",
"plt.legend();\n",
"plt.grid();"
]
},
{
"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": 6,
"metadata": {},
"outputs": [],
"source": [
"mu = 1.14e-3\n",
"T = 71.81"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 6-element string (Hz)\n",
"[194.43708661 379.1242858 544.80061022]\n",
"\n",
"\n",
"The longest time period is 5.143 ms \n",
"The shortest time period is 1.174 ms\n",
"\n",
"\n"
]
},
{
"data": {
"image/png": 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nlXUVF7nI7drtxGvxRkdS7IwqrgNkjDaG+dp8GmhgtXU1F+VFoyMpCjX1Vn71YT2VNVb+43Yvbkmy/yuy1MgaVllX0UorC0wLGK2NNjqSYodUcR1AoVooi02L0dFZbV3NGXnG6EiKAztVY+GFD+qpb5Z8e7E36VGOMRxijXXNleEQI8QIoyMpdkoV1wEWKALJNmXjhhtrrWsp18uNjqQ4oNKqdv5vVQOaEDx3hzcxIc5GR+p3x/RjbNA34I03S0xL8BN+RkdS7JgqrgbwET5km7Lxx59P9E84rB82OpLiQHKPt/H7jxoY5il4/k5vQv3t/wj2Qr2QLfoWhjNcDYdQBoQqrgZxF+4sMi0iVISyTd9Gnp6nhk0o/e6zohb+9nEjo4c78f07fPD3tu+pS1JKdlt387n+OZEikgWmBWo4hDIg7P9P1kHMWTgzV5vLVn0r+/R9NIkmpmpTjY6l2CEpJav2NrM+t4W0CGeemOMYwyG26ds4Io+QKBKZqk1VwyGUAaOKq8FMwsQsbRYeugcFsoBmvVkNmlBsyqpL/p7TxM6SNqYnuPLVGR6Y7Pwc1nbZziZ9E6fkKcZp48gQ6hxWZWCpT/FBQAjBJNMkPHQPPtc/xz3ZnVbZqjZfKX3W2i55+ZNGCivaWTjOjcUOcA5rs2xmg3UDNdRwi3YLCVqC0ZEUB6S2kQwiqVoqs7XZNHs3s8a6hibZZHQkZQhrbNH53ZoGiira+eotHmRP8LD7wlov61ltXc0FLjBHm6MKq2IYVVwHmWgtmrBDYTTQ0DFBRg2bUHqhtsHKLz+op6LGwlO3ezEz2f6HQ9TKWlZbV9NCCwtNC4nQIoyOpDgwVVwHIc86TxaZFmHFyhrrGs7Ks0ZHUoaQytqO4RB1Zsm3F3mTMcb+h0NU6VWssa5BIFhsWqyGQyiGU8V1kAoSQWSbsnHBhbXWtVToFUZHUoaAs02e/OrDBgCeu8Ob2JH2PxziuH6c9fp6PPFkiWkJ/sLf6EiKoorrYOYrfFliWsIwhvGx/jEleonRkZRBLO94G5+ejMTXQ/D8nT6EBdj/8YoH9YNs1jdfGQ7hJbyMjqQogCqug17XYRNb9a1q2ITSrZyDLbz0cSP+bs18/04fAhxgOMQe6x526jsZLUazwLQAN2H/+5WVocP+/7S1Ay7ChbnaXHL0HPbp+zALM1O0KeqEeAUpJWv2NbN2fwupo51JcC/Dyy3c6Fj9qutwiHgRz3RtunovKIOOKq5DhEmYyNKy8NA9KJSFNOvNZGlZmIR9dyjKtVl1yT+2mdle3MrUeBcemOnJ9m32vVWjXbazWd/MSXmSTJFJppZp96cXKUOTKq5DiBCCyabJeOge7NZ306K3MEebo4ZNOKA2S8dwiILyduZnurFkgmMMh9ho3ch5zjNdm06ilmh0JEW5JrUtZQhK09LI0rI4I8/wkfUjNWzCwTS16Px2TQOF5e3cP92DOyba/3CIBtnAGusaaqnlNu02VViVQU8V1yEqRothrjaXOupYbV3NJXnJ6EjKALjQYOWXHzZQcc7Ck7d7MSvF/g/iqZW1rLKuwoyZBaYFRGqRRkdSlBtSxXUIC9fCWWxaTDvtHSPf5AWjIyn96HydlRc+aOBSk863FnmT6QDDIc7L81eGQ2SbsgkRIUZHUpQeUcV1iAsSQSwxLUEi2aPvMTqO0k+suuS1zU20WiTfW+JNXKj9D4cA+Nz6OU44kW3KVsMhlCFFFVc74Ct8SdVSOSlPcl6eNzqO0g82Hmjh+FkL99/iQXigYxyHWK1Xc5rTpGvpeAtvo+Moyk1RxdVOJItkXHElV881OopiYxXnLXy0r5nx0S5MjHGcI8NzZS4eeBAv4o2Ooig3zSbFVQgxVwhRKoQ4JoR4vpvbvyqEKLz8b5cQIs0W61X+zUW4kKKlUCErqJE1RsdRbKTd0rE52Ntd8NVbPIyOM2BOy9NUy2rStDSchGN06op96XNxFUKYgL8A84BE4D4hxNXHyZ8AZkgpU4GfAC/3db3KlyWLZFxwUd2rHflgj5nTF608NMsTTzfH2dCUq+fijjsJQl2PVRmabPFunQAck1KWSSnbgBVAdtcFpJS7pLxyYdLdQJgN1qtcxVW4kiJSKJfl1Mpao+MofVRS1c7mglZmJruSPMr+jwzudEaeoUpWkaal4Swc48Atxf6Ivg6BF0LcDcyVUj52+fsHgIlSymXXWP5ZIL5z+W5ufwJ4AiA4ODhzxYoVvcrV2NiIl9fQvEJGX7JbTVbKxpfhccmD0JJQGyfrGUd97m2pzaqx7ngsJk0yP+oITlrP3qeDJX9vNTY2cnHiRVo9W4naH4WmD51ufbA897NmzcqVUo4zOoejs8XOjO5Gw3T7SSCEmAU8Cky71oNJKV/m8mbjcePGyZkzZ/YqVE5ODr29r9H6mt3b6s2BwAOkzkg15PQFR37ubeX1LY20WNv4frYPUcE9P7dzsOTvrQ37N2D2MzNRm8jYW8YaHeemDPXnXrEtW/xZWAl0vQxHGFB99UJCiFTgVSBbSrXNsj+laqk440yenmd0FKUXco+38XlpG/Mz3YgKdqyDeWpH1eKGG0kiyegoitIntiiu+4AYIUSkEMIFuBdY03UBIcQo4APgASnlERusU7kON9Hx4XRcHufilV3dylBwqUnn7a1NjA4ysSDT3eg4A+q8PE+TfxMpWora16oMeX0urlJKC7AM+Bg4DLwnpTwkhHhKCPHU5cX+BwgAXhRC5Ash9vd1vcr1pWqpOOGkutchRErJ8s+aaG2XPHqrF04m+x7Gf7VcPRetXSNZJBsdRVH6zCbbnKSU64H1V/3spS5fPwZ0ewCT0j/chTtJIolCWUimzGSYGGZ0JOUGthe3UnSynXuneRDi51jX6a2RNVTICgKqA3BxgJnJiv0bOofiKTctTUvDhIkD+gGjoyg3cK7Oyns7zSSEOTErxXGmMHXK1XNxwQW/aj+joyiKTajiasfchTuJIpGj8ih1ss7oOMo16Lrk9S1NaJrg4VmeaHZ+bdar1cpaymU5KSIFk9WxOnbFfqniaufStDQ0NNW9DmIbD7Rw/EzHUH5/b8crLnl6Hi50jO9UFHuhiqud8xAeJIgEjsgj1Mt6o+MoVzlZY2HNvmbGjXFhYozj7Wu8IC9QJss6LjwhHG9zuGK/VHF1AGO1sap7HYQ6h/J7uQm+NsMD4WCbg6Gja3XGWXWtit1RxdUBeApP4kU8R+QRGmSD0XGUyz7c00z1BSsPZznWUP5OF+VFjsvjJIkk3ISb0XEUxaYc7x3toMZqHaPkVPc6OJRWtbO5oIWZSY41lL+rPD0PJ5xI1VKNjqIoNqeKq4PwEl7Ei3hKZSmNstHoOA7N3Krz+pYmgnw17p7iONdo7eqSvHSla3UXjjWJSnEMjjW41MGN1cZSYi3hgH6A6abpRsdxWCt2mLnYpPP9O3xwdXa8/azQ0bWaMJGmpRkdxSHk5uYOd3JyehVIRjVVtqIDBy0Wy2OZmZnnrr5RFVcH4i28iRNxlMgSMmQGnsLT6EgOJ6+sYyj/gkw3xoxwzLdfnazjmDxGikhRXesAcXJyenXEiBEJQUFBFzWth9cvVK5L13Vx/vz5xDNnzrwKLL76dvUXjINJ19IByNfzDU7ieOrMOn/PaWJUkImF4xy3qOTpeWhoqmsdWMlBQUH1qrDajqZpMigoqI6OrQFfvn2A8ygG8xbexIgYDsvDNMkmo+M4jC8M5Z/teEP5O9XLeo7KoySKRDyEY+5vNoimCqvtXX5Ou62jqrg6oHQtHR2dAr3A6CgOY/vhVgor2rlzkgcj/R1vClOnA/oB1bUqDkEVVwfkK3yJETEUy2LM0mx0HLt3rs7Kezs6hvJnpTruFKIG2cAReYQEkaD29zugpUuXRvj7+6fFxMQk3WjZtWvXem/atKnfXyRr1671njVrVnR/PLYqrg4qQ8tQ3esA0HXJGw48lL+rznOsVdfqmB555JGaNWvWHO3Jsp9++qn39u3bvfo7U39SxdVB+QpfokU0xbKYZtlsdBy79XF+C8fOWLh/umMO5e/UIBsolaXEi3i8xJD+zFR6ad68eY1BQUGWq3/+05/+dPiYMWOSYmNjExcuXBhVWlrqsnz58qCXXnopOD4+PnHjxo1feMF85zvfGXnnnXdGTJ06NSY0NDTlrbfeGvbUU0+FxcbGJk6fPj2mtbVVAKxevdo7ISEhMTY2NnHp0qURzc3NAmDlypU+kZGRSZmZmXErV668cqHr+vp6benSpRHJyckJCQkJiW+//XafLoLtmOcCKEBH93rUepRCvZCJpolGx7E7J2ssrN7bTOYYZybGOuYUpk6dR6d3TgpTjHP8mbXh5pLzNj2azCM+yDzmDwtP9ea+f/zjH0dUVFQUubu7y5qaGlNgYKD1wQcfPO/l5WX98Y9/fLa7+1RUVLju2rXrSF5enltWVlb8W2+9dfyll16qvO2228a89957vnfddVfdk08+GfnJJ5+Upqamtt5xxx0R//d//xf07LPPnl+2bFnEpk2bSpOSkloXLlwY1fmY//3f/x0ya9as+vfff7+8pqbGNG7cuITFixfX+/j46L35vVTn6sCGiWFEi2gOyoOqe7Wxdovk9StD+T0dcih/p0bZSIksIU7E4S28jY6jDDJxcXHNd9xxR+SLL77o7+zs3KMjmm+99dY6V1dXOWHChGar1SruvvvueoCkpKTmEydOuBQUFLiFhYW1pqamtgI8/PDDtTt27PDOz893CwsLa01JSWnVNI2vfvWrtZ2PmZOT4/O73/0uJD4+PnHatGlxra2t4tixY73+q1h1rg4uQ8vgmPUYRXoRE0wTjI5jN1btbabqgpWnF3jh5YBD+bvq3K/feY61Yqzedpj95bPPPju6YcMG71WrVg371a9+NfLo0aMHb3QfV1dXCWAymXBycpKa1vEe0zQNi8UipLx2jb7WH7pSSlauXHksLS2ttVe/yFUc+12v4Cf8iBJRHJQHaZEtRsexC6VV7WzKb2FGkispox17c3CTbOKwPEysiFVdq/IlVquV48ePuyxatKjhxRdfrGxoaDDV1dWZvL29rQ0NDb0+SGHs2LEtVVVVLgcPHnQFWL58ecD06dMbxo4d21JZWely6NAhV4AVK1b4d95n1qxZ9b/5zW+Cdb1jK/DOnTv7NOlFFVeFDC2Ddtop0ouMjjLkNbdJ3vi0Yyj/Ugcdyt9VgV6Ajq66VoVFixZFTps2Lf7EiROuwcHBqb/73e8CLRaLuP/++yNjY2MTk5OTE5988smzgYGB1rvuuuvSunXrhnV3QFNPeHh4yJdeeql86dKlY2JjYxM1TePZZ5897+HhIf/0pz9VLFy4MDozMzMuPDy8rfM+L7zwQrXFYhHx8fGJMTExST/84Q9D+/L7qs3CCgEigEgRyUF5kFSZiqtw3HMx+2rFjiYuNDr2UP5OZmmmWBYTI2LwET5Gx1EM9tFHH53o7ue5ubmlV/8sNTW19ciRI8XdLf/b3/62uuv3ZrP5QHe3ZWdnN2RnZ3/pMe6+++76u++++9DVP/fy8pLvvPNOxfV/i55TnasCQKaWSRttFEnVvfbWgbI2dpW0MS/DcYfyd9XZtWZoGUZHUZQBp4qrAnR0rxEigiK9iFZpk/35DqXerLM8p4lRgSYWOfBQ/k7NspliWUy0iMZX+BodR1EGnCquyhUZWgZttHFIfmmLiXIdUkqW5zTR0i559FbHHcrfVYFegBWr6loVh6WKq3JFkAhitBhNoV5Im2y78R0UAHYcbqOgvJ27HHwof6dm2cwheYgxYgzDRJ+G3CjKkKWKq/IFmVomrbSq7rWHztdZeXdnE/Ghjj2Uv6tCvRALFtW1Kg5NFVflC4JEEKPEKAr1Qtplu9FxBjVdl7y+pQlNCB7Ocuyh/J1aZMuVrtVP+BkdR1EMo4qr8iUZWgYttKju9QY6h/LfN92DAAceyt9VkV5EO+2qa1W+4NixY84TJ06MjYqKSoqOjk76yU9+MvxmH2PChAlx27Zt69eTx++6666IN954wyZ/FdqkuAoh5gohSoUQx4QQz3dzuxBC/PHy7YVCCPXOG8SCRTBhIowCvUB1r9dw6vJQ/owoZyY5+FD+Tq2ylYxcD/8AACAASURBVIPyIFEiCn/hf+M7KA7D2dmZ3/zmN5VlZWWH9u3bd/i1114bnpub62Z0rv7U5+IqhDABfwHmAYnAfUKIxKsWmwfEXP73BPDXvq5X6V+ZWiYttHBYHjY6yqDTbpW8trkJT1c1lL+rIr2INtpU16p8yejRo9unTZtmBvDz89PHjBnTfPLkSRfo6Ej/4z/+IzQlJSUhIiIiuXMiU2Njo1i4cGFUbGxs4oIFC6JaWlq6faOFhoamLFu2LHTs2LHxycnJCTt27PCYNm1aTHh4ePKvfvWrIABd13nyySfDYmJikmJjYxNfeeUVv86fP/jgg6PGjBmTNHPmzOiamporJ6hv377dY/z48XFJSUkJ06ZNi6moqHC+md/ZFme6TwCOSSnLAIQQK4BsoOtkjGxgueyYprxbCDFMCBEipTxtg/Ur/WCEGEGoCCVfzydBJOAsbup1ZddW7+kYyv+f873wdld7VqCjay2SRUSICAJEgNFxlOt489PG8KoLVptuXg31N5kfzvLq0QUBSktLXYqLiz1mzJjR2Pkzi8UiioqKDr/77ru+P/7xj0fOnTv3yK9//evh7u7u+pEjR4r37NnjPnXq1KubtivCw8Pb8vPzSx599NHwRx55JGLPnj0lzc3NWnJyctJzzz13fvny5cOKiorcDx8+fOj06dNOEyZMSJgzZ05jTk6O57Fjx1xLS0sPVVZWOqekpCQ9/PDDta2treLpp58etW7dumMjR460vPLKK37PPvts6Pvvv1/e0+fEFsU1FOj6pFYCV18ctLtlQoEvFVchxBN0dLcEBweTk5PTq1CNjY29vq/RBkt2zUejObWZtUfX4lfd890QgyV/b9wo+9kmTzZXRBE97AIXygvJKR+waD1i1HNfE15D2+g2ZJ4kp6n367fn144CdXV12p133jnmhRdeOOXv73/lOqlLly69CDBlypSm733vey4AO3bs8Hr66afPAUycOLE5NjbWfK3H/cpXvnIJICUlxdzU1KT5+fnpfn5+uqurq15TU2Pavn2791e+8pULTk5OhIeHWyZOnNi4Y8cOj61bt175eURERPvkyZMbAAoLC12PHj3qnpWVFQsdHW5QUNBN7SOzRXHtrlW/+no/PVmm44dSvgy8DDBu3Dg5c+bMXoXKycmht/c12mDK/pH1Iy5FXWJRzCKcRM9eLoMp/826XvbmNsmP3q0jyAeeWRqNm3PMwIbrASOe+zbZxjvWdxgtRjN3/Nw+PZa9vnYGk552mLbW2toqFixYMGbp0qUXHnrooUtdb3Nzc5MATk5OWK3WK/Wip7tcOu+vaRouLi5XaoumabS3t9/0JeiklCI6Oro5Pz+/pEcBumGLbVqVQHiX78OA6l4sowxCmSITM2ZKZK9fY3bj3ctD+R+91RM3Bx/K39VBeZBWWsnUMo2OogxSuq5z7733jo6NjW353//937M9uc+0adMa3377bX+Affv2uR05cqTXm7JnzJjRsHLlSn+LxUJ1dbXT3r17vaZPn940Y8aMhvfff9/fYrFQUVHhvHv3bm+A1NTUlgsXLjht3rzZEzr+MNi/f/9NHYBli+K6D4gRQkQKIVyAe4E1Vy2zBnjw8lHDk4A6tb91aAgRIYxgBPl6PlZpNTqOYfJPtLGzpI156W6MGaH2P3dqk20U6oWMEqMIEkFGx1EGqU2bNnmtWrUqYMeOHd7x8fGJ8fHxie++++51h04/++yz55qamkyxsbGJP//5z0ekpKQ09Xb9DzzwwKWkpKTmhISEpJkzZ8b+6Ec/qhw1apTlgQceuBQVFdUaFxeX9Oijj46aMGFCA3R0witWrDj+/PPPh8XFxSUmJSUlbt269aYufdfnzcJSSosQYhnwMWACXpdSHhJCPHX59peA9cB84BhgBr7e1/UqA0MIQaaWyTp9HSWyhCSRZHSkAfeFofzj1VD+roplMa20qiOEleu6/fbbG6WUud3dtnfv3iuXnAsJCbFUVVUVQccl4NauXVt2o8fuXB7g6aefrgVqu7vtb3/7WyUdW1Gv0DSN5cuXn+zucadMmdK8f//+L10Or6dscl0sKeV6Ogpo15+91OVrCXzTFutSBl6oCCWYYPL1fOJFPCbhOAMTOofyN7dJvpvtqYbyd9Eu2ynQCwgTYQSLYKPjKMqgos4jUG6os3ttpJFS2es/5IaknSUdQ/nvmOhOqL+6RmtXxbKYFlrUvlZF6YYqrkqPhIkwhjOcA/oBh9n3er7eyoodTcSNdOLWNLseJnPTOrvWUBHKCDHC6DiKMuio4qr0SNfu9ag8anScfqfrkjcuD+X/+mw1lP9qh+VhmmlWXauiXIMqrkqPhYtwgggiT8+z++71k4IWjp62cO80NZT/ahZpoUAvYKQYSYgIMTqOogxKqrgqPSaEIEPLoIEGjsljRsfpN5U1Flbv6RjKPzlODeW/WokswYxZda2Kch2quCo3ZbQYTSCB5Ol56FK/8R2GGKsueHVzEx5qKH+3LNLCAf0AIYQwUow0Oo4yRJjNZpGSkpIQFxeXGB0dnfTtb3+7xy8eDw+P9P7MBh3D/0+fPm3TIxZVcVVuSmf3Wk+9XXavheeDqbpg5aFZnmoofzdKZSlmzOq8VuWmuLm5yR07dpSWlpYWHzp0qHjLli0+W7Zs8bx6ufZ2+7nEpfr0UG5ahIjAH3+7616PVLdTXBvE9ERXUiPU5uCrWaWVA/oBRtBxxSRF6SlN0/D19dUB2trahMViEZ1bhSZMmBC3bNmy0PHjx8f99Kc/DS4pKXHpvHzcM888022HW1pa6hIZGZl0zz33jI6JiUlavHhx5KpVq7wzMjLiR48enfzZZ595AJw9e9Z06623jomNjU1MS0uL37NnjzvAmTNnTFOnTo1JSEhIvP/++0d3nT384osv+qekpCTEx8cn3n///aMtFkuvfmd14p5y0zqPHN6kb6JMlhEtoo2O1GctbZI3Pm3Cy7mNr0xVF/ruTqkspYkmZmgz1ObyISzHmhN+QV6w6SXn/IW/eaZp5nUvCGCxWEhOTk48efKk60MPPXQuKyvryjjDS5cumfbt21cKkJWVFf3YY4+dX7ZsWe0vfvGLa87UPHXqlNu7775blpmZWZGamprwj3/8I2D//v0l77zzzrCf/exnIbNmzTr+3HPPjUxLSzNv3rz5+Jo1a7wfeuihyJKSkuLnn39+5OTJkxt//etfn16xYoXvP//5z0CAvLw8t5UrV/rv37+/xNXVVX7ta18b9dJLLwUsW7as9lo5rkV1rkqvRIpI/PEnV8+1i+713Z1maht0JoeeUkP5u9HZtQ5nOGEizOg4yhDk5ORESUlJ8cmTJwvz8vI89+3bd+Xk8fvuu+9C59d5eXlejz/++AWAJ5988ppFLTQ0tHXChAnNJpOJ2NjY5qysrHpN08jIyDBXVla6Auzdu9f70UcfrQVYvHhxw6VLl5xqa2tNu3fv9n7kkUdqAe699946Hx8fK8DGjRu9Dx486JGWlpYQHx+fuGPHDp+ysjLXXv2+vbmTonTue92sb+aEPMEYMcboSL2Wf6KNHYdbmZfhhn/LNS8Z6dCOyCM00sh0bbrqWoe4G3WY/S0wMNA6bdq0ho8++sh3/PjxLQDe3t5f+Atd07RrXyPusqsvLdd52TmTyXTlsnXdXWpOCHHl8nRXk1KKpUuX1v7lL3+purnf6stU56r0WqSIZBjDyNVzu30RDwWdQ/nDA00sVkP5u9XZtQYRRLgIv/EdFOUq1dXVTjU1NSaAxsZGkZOT45OQkNDS3bIZGRmNr7zyij/AK6+8EtCX9U6aNKnhjTfeCABYu3att5+fn8Xf31+fNGlSw+uvvx4A8N577/nU19ebAObOnVu/du1av6qqKifo2Gd75MiRXh2AoYqr0mua0MjUMrnIRU7IE0bHuWlSSv6+tYnmVsmjs9VQ/ms5Ko/SQAOZWqbqWpVeOXXqlPP06dPjYmNjE9PT0xNnzZpVf99999V1t+yLL7548uWXXx6enJycUFdX16cJLr/85S+r8/LyPGJjYxN/8IMfhL755psnAF544YXqnTt3eiUmJiZ8/PHHviEhIW0AmZmZLT/84Q+rZs+eHRsbG5uYlZUVe+rUqV5dY1JtFlb6JEpEkUsuuXoukSJySH347ippI/9EO0unuBMaoN4K3dGlzgH9AIEEMkqMMjqOMkRNnDix+fDhw8Xd3db1knMA8fHxbfn5+SWd3//85z8/c/V94uLi2o4ePXqo8/t//etf5d3dFhwcbN2yZcvxq+8/YsQI686dO7vOcb2yqfzxxx+/+Pjjj1/s2W92bapzVfpEExrpWjoXuEC5LDc6To/VXB7KH6uG8l/XMXmMeupV16ooN0kVV6XPokU0PviQp+cNiX2vut5x2g3AI2oo/zXpUidPzyOAAEaL0UbHUZQhRRVXpc80oZGhZVBDDRWywug4N7SpoIUj1Rbune6phvJfx3F5nDrqyNAyVNc69Om6rqv/iTZ2+Tnt9lxEVVwVm/hC98rg7V4ray2s2tNMeqQzU9RQ/mvq7Fr98SdSRBodR+m7g+fPn/dVBdZ2dF0X58+f9wUOdne7OopDsQmTMJGupbNV34qL3+AsWu1WyWuXh/I/MFMN5b+eMlnGJS5xq3arep7sgMVieezMmTOvnjlzJhnVVNmKDhy0WCyPdXejKq6KzcSIGHLJpTa8FinloPtQXrO3mcpaK8vme6mh/NchpSRPz8MPP6JElNFxFBvIzMw8Byw2OocjUZ8wis10dq8tPi1Uykqj43zB0dPtfHyghekJrqSpofzXdUKe4CIX1b5WRekDVVwVm4oTcTi1OA2qqU0tbZLXtzQR4KPxlak2nVdud6SU5Oq5DGOY6loVpQ9UcVVsyiRM+Ff6c5azVMk+j+e0ifd2mqmt13lktiduLqoTu55yWc4FLpChZaAJ9fGgKL2l3j2Kzfme9cUTz0HRvRaUt7H9cCu3p7sRE9KrKWYOo7Nr9cV3SF+IQVEGA1VcFZvTpMZYbSxnOMNpedqwHA3NOm991kRYgInFE9RQ/hupkBXUUqu6VkWxAfUOUvpFvIjHAw9yZa4h65dSsjynYyj/Y7d64qyG8l9XZ9fqgw/RItroOIoy5KniqvQLJ+HEWG0s1bKaalk94OvfVdoxlH/JRDWUvydOypPUUEO6lq66VkWxAfUuUvpNgkjAHXfy9LwBXW9NvZUV2zuG8t+mhvLfUOd5rd54EyNijI6jKHZBFVel33R2r1WyijPyS1eN6he6/PdQ/q9neaJpanPwjZySpzjHOdK1dExCzVpWFFvoU3EVQvgLITYJIY5e/q9fN8uECyE+E0IcFkIcEkI805d1KkNLgkjADTdy9YHZ97q5cyj/NE8CfVShuJHOfa1eeBErYo2Ooyh2o6+d6/PAFillDLDl8vdXswDflVImAJOAbwohEvu4XmWIcBbOpGlpVMpKzsqz/bquqloLH+5uZmykM1Pi1RSmnqiSVaprVZR+0Nfimg28dfnrt4AlVy8gpTwtpcy7/HUDcBgI7eN6lSEkSSThhlu/7nu1WCWvbm7C3VXwwAw1lL8nOrtWTzyJE3FGx1EUuyL6cpK/EOKSlHJYl+8vSim/tGm4y+0RwDYgWUpZf41lngCeAAgODs5csWJFr7I1Njbi5eXVq/sabShnh+7z14bVUhNRw6j8Ubg32v6c0/yzIzhUO5wZ4eWEeXf70uoRe3zur6XJt4nKlEqGHx+O3+lrvm0H1FB+/gdL9lmzZuVKKccZncPhSSmv+w/YTMf16q7+lw1cumrZi9d5HC8gF7jzRuvs/JeZmSl767PPPuv1fY02lLNL2X3+Vr1VvtH+htxg2WDz9R2tbpOPv1gr3/y0sc+PZY/P/bWsbl8tl7cvl+16e/8FuklD+fkfLNmB/bKHn7HqX//9u+EJgFLKW691mxDirBAiREp5WggRApy7xnLOwL+Af0gpP+hx5VfshotwIVVLZZ++j/PyPEEiyCaPe2Uov7fGPWoof49Vy2pOc5op2hSchDoPWFFsra/7XNcAD13++iFg9dULiI6dX68Bh6WUv+3j+pQhLEkk4YKLTfe9vrfLTE29ztez1FD+m5Gr5+KBBwkiwegoimKX+lpcXwBuE0IcBW67/D1CiJFCiPWXl5kKPABkCSHyL/+b38f1KkOQq3AlRUuhXJZTK2v7/HgF5W1sL25lTrobsSPVUP6eOi1PUy2rSdPSVNeqKP2kT+8sKWUtMLubn1cD8y9/vQMYsJZCSsnRJ1ZhGtGGnK4jTGpOxmCSIlIooohcPZc5pjm9fpzaBivLLw/lz1ZD+W9Knp6HO+6qax2EpEXn7Ft5NOafJvpPi4yOo/SB3VUea30r7WcacP7bcQ7e/ib1u08ZHUnpwlW4kiySOSFP9Lp7ray18MIH9bRb4VE1lP+mnJFnqJSVpGlpOAvV7Q8mddtOUJj1KuX/9Qlt1fVYze1GR1L6wO6Kq5OvG4lrHqDtmVjaa5ooXvx3jj65itaq3p+eodhWipaCM8692vd6pLqdX33YAMBzd3gTpoby35Q8PQ833EhUc1wGjZYTFyl9aCWH7/4nutlC7Jt3kbDyfkwe6o+focwuP5mEEOhTA0n7djbVf/6c6j/v5uLGI4z8z8mEfGOSetEazE24kSySOSAPcFFexO/LUzO7lXe8jVc2NxLorfGtRd4EeKuJQjfjnDzHKXmKidpE1bUOAtbGVqr+8Dmn/7oH4aQR/oOZhDw5Ac3NLj+WHY7dda5dmTycCX/uFsbufJJhc2Ko/NV2Cqb9jdrVxZ3n3ioGSdFScMKpx91rzsEWXvq4kVGBJr5/p48qrL2Qq+fiiqvqWg0mdcn5d4vIn/w3qv+wi4AliYzd/RShz0xRhdWO2HVx7eQa7kvsK3eQuPprOPm6cfTxVRQveZumov6ddatcm7twJ1kkc0we46K8eM3lpJSs3mvmH9vMpIx25juLffByc4iXrU2dl+c5KU+SqqXiItTcZaM05FZxaMFbHP/Pj3AJ9SFp/UNE/3kRLiO8jY6m2JhDfUr5TB5FyuZHiPz1PJqP1FB02+uUPbuB9pomo6M5pFQtFSecOKAf6PZ2qy75+1Yza/e3MDXehW/M88LVWR281Bt5eh6udBxMpgy8trONHPvPjzg07y1aT9Ux5o8LSV7/EN7j1Jh1e+Vw2yCESSP4wXQCshOo/PV2zr6WS+2qYsK+N53gRzLRnNXmxoHiLtxJFIkUySIyZSa+wvfKbW0WycufNFJQ3s6CTDeyJ7irYfy9VCNrKJfljNPGqa51gOktFk6/vJeq3+1CtlsZ+fRkQr81BZOXq9HRlH7mUJ1rV06+bkT85DZScx7DKzOUiv9vM4UzX+XSp2VGR3MoaVoaJkxf2Pfa1KLz2zUNFJa3c/90D5ZM9FCFtQ/y9DxccFFd6wCSUnJhwxEKpr/MqZ/m4Ds9grTtTzDqh7NUYXUQDltcO7nHBhK/4h7i3l4KFp2Se1dQ8rX3aC67YHQ0h+AhOkbwHZVHqZN1XGiw8ssP66k4Z+HJ272YleJmdMQhrVbWckKeIFkk4yrUh/pAMJecp2TpPzny0Eo0Nyfi37uPuOV34xY5OK48pAwMh9ss3B0hBH5zYvCdEcmZV/ZT9dsdFE5/mRFPTCD0O1Nx8lYfSv0pTUuj2FrMzuY8PvtgLK3t8K1F3sSFqtNF+ipPz8MZZ1K1VKOj2L/Gdsr/+xPOvJGLycuViJ/fRvDDmQgnh+9hHJIqrl1ork6MXDaJwKXJnPrFVk6/uJua94oI/+FMgu5JRWhq02R/8BSehJjjOOl2GJNHDN+bNYLwQPXS7KsL8gJlsox0ka661n4kLTpn/34A158e4EyTleAH0wn7/i04B6irNDky9SdVN1yCvRjz+wUkf/x1XCP8KHtmHQdvf4OGvZVGR7NLB8ra+Hh1FEhB1sLjqrDaiOpa+1/djnKKZr9G+fc/Rh/lQcqWR4n81VxVWBVVXK/Ha2wISWsfIPqv2bSfa+LQwuUcfWo1rdVqlKKtbDvUwl8/bmSEuxexxFPhfIQG2WB0rCHvorzIcXmcJJGEm1D7rW2tpeISR77+Lw7f+Q7WpjZiX7+T9v9JwjNpuNHRlEFCtQg3IIQg8K4k/ObGUP2nz6n+y+VRik9PZuR/TERzV/sFe0NKyUf7W/hoXzMpo5x58nYv2p3SOW4tIV/PZ7pputERh7Q8PQ8nnFTXamPWpjaq/7iL6hf3IEwa4f81g5CnJnR8DuScMTqeMoio4tpDJk8Xwp+fQdB9aZz80RYqX9jG+XcKGPX/ZuO/ME6dKnITdF3yj21mthW3MiXehQdmeOJkErjiRZyIo0SWkC7T8RJeRkcdki7JSxyXx0kVqbgLdTk+W5BSUvuvQ5z8yWe0nW4g8K4kRv1PFi4harKS0j21WfgmuY0eRuzrd5Hwwf2YPF04+ugHHL7rHZoOnTM62pDQZpH89eNGthW3Mi/DjYdndRTWTulaOgD5er5REYe8A/oBTJhI09KMjmIXGvNPc2jBco59Yw3OwV4krX2Q6L9mq8KqXJcqrr3kOy3iysEL5uJzFM1+jRPPbaS91mx0tEGrqUXndx81UHCinXuneXDnpC8Ph/AW3sSKWEpkCU1SjaW8WW1ubRyVR0kUiapr7aO2s40cf2YtB+e8QWvFJaL+sIDkjQ/jPSHM6GjKEKA2C/eBcNIIfjjjyijFM6/nUvNhMWHPTSf44Qw1SrGLC406f1jbwLlLVh6f48n46GufGpKupVNqLSVfz2eqaeoAphz6asNr0dBU19oHequFMy/vo+p3O9FbLYQsm0Tot9X57srNUZ2rDTj5uRPxszmkfvYYXmkjqPjBJoqyXuNSzgmjow0K1Res/PKDei40WHl6ofd1CyuAj/AhVsRyWB7GLNWWgJ6ql/XUD68nQSTgIdSpIDdLSsnFj49SeMsrnPzJZ/hMHU3q9icY/T9ZqrAqN00VVxvyiA8i/v37iF1+N3qrlZKv/JPSB1fScuLal1Szd8dOt/PLD+ux6pLv3eFDQljPjq5O19LR0SnQC/o5of04oB9ASMFYbazRUYac5iM1lNz7LqUPvI9w1ohfcS9xf1+Ke5S/0dGUIUptFrYxIQT+c2MZNiuK03/r2LRUMP1lQp6cQOi3HetqGPkn2nj5k0b8vDS+tcibIJ+ebyb3Fb7EiBiKZTFj5Vi1//AGGmQDR+QRfM/44jnK0+g4Q4blUjOVv97Bmdf2Y/J0YfRPbyX46+rqWErfqc61n2iuToQ+PZmxu58i8M4kqv/0OfmTXuL8ikKkLo2O1++2F7fw4sZGQgNMPH+nz00V1k7pWjpWrKp77YHOa+L6V6pOqyekVefsW3nkT36JM6/sY/hXxzJ291OEPDFBFVbFJlRx7WcuwV4dF0be+DCu4b4cf3otB+e/RcP+KqOj9QspJUXnh7M8x0xSuDPfzfbB2713L7NhYhhjxBgOyUM0y2YbJ7UfjbKRUllKvIjHuU0NNbmR+l0VFN36Oie+txH32EBSNj9K1K/n4RyoOn7FdlRxHSBeGSNJWvcQY/68iLaqeg7Nf4tj31xD2xn7GfWn65J3tpspPD+CyXEufHOeF27OfRuukaFlYMFCoV5oo5T2p/OcYLWv9fpaT9Vx5LEPKF7yDyx1LcS8egeJq76GZ0qw0dEUO6T2uQ4goQmCvpKC//w4qv64i9Mv7uHCulJCvz2VkCcnoLkN3f8d7RbJq5sbyStrJzHgHF/Pss3UKj/hd6V7TZNpak7uVZpkE4flYeJEHN5CDTXojrWpjeo/76b6L7sRAsK+fwsjv6FGlyr9S3WuBjB5uTDqv2eStuMJfGdGcupnORRMe5kL60qRcujtjzW36vx+bQN5Ze3cM9WD9OAzNh0HmaFl0E47RXqRzR7TXnR2rZ2TrZR/k1JS88EhCqb+jarf7MB/fixpu54i7LvTVGFV+t3QbZXsgFuEH3Fv3k3dthOU/3+bOfL1f+EzPQKR7Wt0tB67eHk4xJlLVh6/zZMJMa7k5Nh2Hf7CnygRxUF5kFSZqq5Nelln1xorYlXXepXGgtNU/GATDXsr8UwdQfRLS/CZFG50LMWBqOI6CPjeEknqlkc5+1Yep365DZcd5ZwodiL8+7fg5Dd4T0E5fdHK7z9qoKlV5+kF3iSG9183kKFlUGYto0gvYpxpXL+tZygp0AvQ0dW+1i7azjVy6hdbOf9OAc4BHkT9bj5B96YiTGojnTKwVHEdJISTxohHxxFwRyJ7nlnB2TfzqO0cpfhQBsJpcH04HD9j4U/rGtA0+N4SH0YH9e9LKUAEECEiKJJFpMgUh+9ezdLMYXmYGBGDrxg6Wzr6i95m5cyr+6n6zQ705nZCnppI6Hen4uSj9tErxujTJ7YQwl8IsUkIcfTyf/2us6xJCHFACLG2L+u0d87+HlgejSL100fxSB5O+X99QuHs16jbXm50tCsKy9v47Zp6PFwFz9/Z/4W1U6aWSRttHJQHB2R9g1mBXoAVKxlahtFRDHdx8zEKZ7zCyf/dgvekcFK3Pc7oH81WhVUxVF/boeeBLVLKGGDL5e+v5RngcB/X5zA8EoeTsPJ+Yt+4C72pncN3vUPpwytpKTd2lOLOw638ZUMjIX4dwyGG+w7cCfeBIpDRYjRFehFtsm3A1jvYNMtmimUx0SLaobvW5qM1lNz3LqX3vwcC4v55D/H/+Aru0QFGR1OUPhfXbOCty1+/BSzpbiEhRBiwAHi1j+tzKEII/BfEkbbjCcJ/MJO6nBMUTH+Zkz/Pwdo4sMVFSsm63Gbe/KyJ+DAnns32wcdj4DdVZ2qZtNLq0N1roV6IBYvDdq2WuhYq/mczhTNepWFvJaN/NJvUnMfxmz3G6GiKcoXoy6kfQohLUsphXb6/KKX80qZhIcRK4BeAN/CslHLhdR7zCeAJgODg4MwVK1b0hIvh5QAAEe5JREFUKltjYyNeXl69uq/Rrpn9QivO75zEtO080s+Z9q+ORp8WBJrtTnvpji4h98xIjlwMJML3IpNGVmIS137d9PdzX5lYSbN3M2P2j0Gz2rbAD/bXjcXJQtn4MrxqvRh5ZOSXbh/s+W/kuvl1ienTczitqIAGC9asYCz3hoOvy8CGvIbB8tzPmjUrV0qpjvoz2A13lgkhNgMjurnpBz1ZgRBiIXBOSpkrhJh5o+WllC8DLwOMGzdOzpx5w7t0Kycnh97e12jXzX4nNOyrpPyHm2j68zG8Pm8m4me34ZXx5Q9aW2i3Sl7b3MSRi23MSXPjrilRaOL6HUJ/P/fn5Dk+tH6I/1R/mx8pO9hfN3ute5FSMi9kHn4jv3yIw2DPfyPXyl+/+yTlP9iEuegs3hPDiPjZHDxTu/tYMs5Qf+4V27phcZVS3nqt24QQZ4UQIVLK00KIEOBcN4tNBRYLIeYDboCPEOJtKeXXep36BrYdaqHG7IEuJZoNhxkMFt7jw0je8DA17xVx8qefcXDumwTek0LIUxPxSAyy2QAHc6vOixsaKa22sHSKO3PGDo7TgoaL4YSLcAr0Apyx7ek/F0dc5JB+yKaPaUsH5UGiRBR+1z520G5IKTEXnaX6L7up/bAYl1Afol9eQkB2gk2HlChKf+jrYZ5rgIeAFy7/d/XVC0gp/wv4L4DLneuz/VlYW9sl7+4002aJZs/yS6RHupAxxoWYECdM/bz5dCAJTRB0b+r/396dB0dZ53kcf3/7zH00gQAJISRAouFKUAREDIcHiY4741k7q3hUzcxajjO7xe44U7Xu1lhTuzVu1U45luNuWTNbq3/oljKOmyAoAyhyKcohQgKYYIwgSDoJ5Ozrt388vTGyIB3S9NMdvq+qVJHk4cknT5Ln279f/37fxndbBV/823ZO/Pv7nH7lY9Km5ZNfX4GvvoKs6snIJX7PXb1Wc4gTnWEeWZnJwpnJtfXlGsc1vB5+nfci78X3xNPhVOR8jxGTgwMH8x3z7Y5x+UQMZ3Z+jr+xGf+6ZgKfdyNpLorWLGHyY4twZmhnJZUaRltc/wX4bxF5BGgD7gYQkcnAC8aYulGef8S8buHp1Xm8sn4/A95ytjUNsvnAIFlpwtxSNzVlHq6a4sbtHBuF1pnlpeQfljHpRwvwrz+Mv6GZL59/nxPP7sQzKRtffQX59RXkXDcl5r2yX3aG+U3DWXr6I/y4LpuqkuS7oU2QCax2riZMOK7n3b59O4sXL47rOePJhQuPJMdzjPESCYY5s60Nf2MT3j8d4GDXDsTjJLd2GsVrlpB/ywzcvgy7Yyo1IqMqrsaYDmDFeT5+HPh/hdUYswXYMpqvGYsMr4NpuV3U1mYzGDR80hbko5YAH7UE2dYUIM0Nc0o91JR5mFXixjvKV25JBu7xmRTeX03h/dWEugfofOso/oYmTr60ly9f2I1rXDq+VVahzV0yFYf3/D/6lpNWcwgRWPMXOZROSN4+I5ejkYQr6CJD9EZ+uUUGQnRtacHf2EznhiOEuwZwZLiJzMmh4qEl5K2cjis7uWZLlBqJ5L1zxonXLdSUW1PDobDhUHuQPS1B9rQGeP9IALcTqkqsEe3cUjcZ3uTqhHQpXLlpjL97FuPvnkW4N0DXphb8jU10vH6QUy/txZntJf/m6fjqK8hdVoYz0xoJffxZgOc39JCb4eCnt2cndA+rGvvCPYN0bvwUf2MzXRs/JdIbwJmbRv4tM/DVV5BXO413d22joLbK7qhKjdqYL67DuZzC7KkeZk/18P0bMzh6IhQd0QbY2xrE6YDKIjc1ZW7mTfPYso8z3pyZHsbdXsm42yuJDIbo3noMf0MznesPc/q1T3Cku8hbXk7r8nms7cmneJyTx2/LJncMfO/KfqHOfvwbjtDZ2EzXlhbMYBh3QQYFd1bhq68g5/qpODz6IE6NPVdUcR3O6RAqitxUFLm5d0kGx06FrUL7aYAX3wny0rt9zJjkshZElbnxZaf+DcDhdZG/cjr5K6djQqs4s7ONjoZmNh13sutsPpNb2/nOtsMMBqYTvHUG7oJMuyOrFBQ42YN/XTOdjc10b/sMwgZPcQ6FD9bgq68g+9pibaSvxrwrtrgO5xChrNBFWaGLOxem80VHeOg52le29fHKNiid4KSmzHqetjAv9QutuBxkXz+VNxnPrv2DVPtC3PpVB93Np2h56zCsEXIWTbEWRNVV4J2cY3dklcQG2rrobGzG39jM2Q/awUBauY/Jjy3CV19B5tyJun1GXVG0uJ5DRCgucFFc4OI7C+DLrjB7WgLsaQmwdmc/a3f2U+RzUl3mZn6Zh6JxzpS8aQTDhj/8uZcPjgZYOcfL3dfn45BlmCdr6fvklLUVorGJY794m2O/eJus+ZPx1VlbfNLKfHbHV0mg/8hp/A1WQe3d/yUAGbMKKf77pfjqK0ivKEjJvw2l4kGL60VMzHOyqiadVTXp+M+G2dNqrTxu/HCAht0DjM9xWCPacg+lE5wp0bSiP2D43fqzHGoPcdeidG6elzZ0ExQRMmcVkjmrkCk/W0r/0Q7865rxNzTT9tRm2p7aTMbVE/BF99KmXxW/phUquRlj6DtwEn9DE/7GZvoPdwCQdU0RJf+4HF9dBWnTxn5zC6ViocV1BHzZTlbMcbJiThpn+iLsPRZgT0uQjfsH2LB3gLxMoTo6dZysTSu6+6zmEMf9YR5ekcmiim/f7pA+fRxFjy+m6PHFDLZ3DxXa9n/dSvvTW0mblo/vtkpr6q96khbaMcZEDD0ftA81dRhs6waHkHN9CYUPzcdXV4FnUrbdMZVKOlpcL1FOhoOlV6ex9Oo0+gYj7D9mjWi3HRpk88dW04p50cVQlcXJ0bTiZJfVHOJMX4TH6rKYVTKyZgTe4lwm/WABk36wgMCpHjrXH8Hf0MSJ3+3i+G934JlsNa2Qon7MDRFdtJKiIsEwZ7e3DRXU4Kleq6nDjdMo+ttoU4dxuhdYqW+jxTUOMrwOFlZ4WVjhZTBoOBBtWvHhpwHeOzRIukeYPdVta9OK1pMhnmk8C8CaO3KYVji6H71nQhaFD1RT+EA1oa7+aNOKZk6+uBfvQIgPn23Ft2qmtd1iSalut0hykYEQ3e+0DjV1CHX248hwk7ei3NqDurJcX3xcqRHQ4hpnXrcwv9zD/HIPwbChqT3IRy1B9kabVnhcUDXFKrRzEtS04kBbgOfX95CVbjWHmBjn1c6uvHTG3zOb8ffMJtwTYNuzbzCu1cXptQc59eJenDle8m+e8XXTCu0PmxTCPQG6/nzUKqhvR5s65Hi/buqwrAxHuv6slLoUWlwvI/ewphV/dWMGR6JNK/a0BNgTbVpxVbGb6jI380ovT9OKnc2D/OfmXib7nDxen01e5uUt5s4sD5GFBcx4otYaDW09hr+hic71Rzj96gFrNLS8DF99JXk36Wgo0UJd/dZ0/rpmujYPa+rwvavx1VeSs0SbOigVD1pcE8TpECqL3FQWublvSQatJ60tPh+1BHhxS5CXxGpaUVPmYSAYn9HChj39vLqjn8oiF4+uyibdk9jpaEeai/ybppN/03RMKMKZHW3WStN11gsMiMdJ7tJSay/tLdq04nIJnOyh883D+BubObPtM0wogqcoh8LV0aYOC7Spg1LxpsXVBg4Ryie6KJ/o4s5F6bRHm1bsaQny8nt9wFXs6+6musyaXh5pj9+IMby6vZ+39w1wTbmHh1dm2r6gSlwOcm8oJfeGUkr/+RZ6PvxiaI9ky8Z11grUxSXWFh9dgTpqg593D+1VPvt+tKlDmY9Jj15nreyepyu7lbqctLjaTESYUuBiSoGLO6JNK17b2EQXxd9oWlFT5qam3EOR79ubVoTChj9s6uX9IwFWzPZyz5KMpNt7Kw4h+9pisq8tpuSfltN34BT+Rmvv5LGfv8Wxn79F1vyiob20uncyNv1HO3CubefjX/2e3n3Rpg5VEyj+uxusPcmVuidZqUTR4ppkJuY5qSr4itraKjrOhodewadh9wD/s3uACbkOa0RbZjWtGH6zHIg2hzjYHuJ7C9O5tTot6W+mIkLm7EIyZxcy5Ykbra4/6w7jb2ii7ZebaPvlJjKqhjWt0AIxxGrq8PUDk/7m07gBmV9EyZPL8dXN1G5aStlEi2sSG5ftZOVcJyvnRptWtFr9jjfuG2DDngHyMx1Ul7mH+h3/dt1Z2k+HeXB5JtdXpuZrYabPKKDoJwUU/WSxNbW5rhl/QxPtT2+l/ddbSSv3DRXaK3Fq00TMN6bUB9u6hqbUCx+soSmvg4V33mJ3TKWueFpcU0ROhoOlVWksrUqjdyDC/s+svbRbDw6y6eNBBHC74LG6LGZPHVlziGTlnZLLpB8uYNIPF1iLctZbC6FOPLeL48/swF2YhSsvvquNPb297Ms8HNdzxlOoo4/g6T7E7bCaOvzN4m8sBmvassXegEopQItrSspMc7CowsuiYU0rjhwPct1M76ibQyQrT2EWhatrKFxdQ6jTalrR/U4rkcFQXL9Oz1eG9PEFcT1nPDnS3eQtK9NtTEolubF5J76CDG9acaVw5acz/t7ZjL93dtzPfXzLFmbW1sb9vEqpK4tublNKKaXiTIurUkopFWdaXJVSSqk40+KqlFJKxZkWV6WUUirOtLgqpZRScabFVSmllIozLa5KKaVUnIkxxu4MFyQiXwGfXeJ/LwBOxzFOIqVydkjt/KmcHTS/nZIl+1RjzHi7Q1zpkrq4joaI7DbGXGN3jkuRytkhtfOncnbQ/HZK5ewq/nRaWCmllIozLa5KKaVUnI3l4vofdgcYhVTODqmdP5Wzg+a3UypnV3E2Zp9zVUoppewylkeuSimllC20uCqllFJxltLFVURuFZFmETkqIk+c5/MiIs9EP79fRGrsyHkhMeSvFJEdIjIoImvsyPhtYsj//eh13y8i20Vkrh05zyeG7HdEc+8Vkd0issSOnBdysfzDjrtWRMIiclci832bGK59rYh0R6/9XhF50o6cFxLLtY9+D3tF5BMReSfRGVUSMMak5BvgBD4FygAPsA+4+pxj6oA3AQEWArvszj3C/BOAa4FfAWvsznwJ+RcD+dF/r0qW6x9j9iy+XpMwB2iyO/dI8g87bhOwDrjL7twjuPa1QIPdWUeRPw84CJRE359gd259S/xbKo9cFwBHjTEtxpgA8DJwxznH3AH8l7HsBPJEZFKig17ARfMbY04ZYz4AgnYEvIhY8m83xnRG390JFCc444XEkr3HGPN/q/0ygWRa+RfL7z7Aj4HXgFOJDHcRsWZPVrHk/0tgrTGmDay/4wRnVEkglYtrEfD5sPfbox8b6TF2SeZssRhp/kewZhGSQUzZReS7ItIENAIPJyhbLC6aX0SKgO8CzycwVyxi/b1ZJCL7RORNEalKTLSYxJJ/JpAvIltE5EMReSBh6VTScNkdYBTkPB87d3QRyzF2SeZssYg5v4gswyquyfK8ZUzZjTF/BP4oIkuBp4CVlztYjGLJ/xvgZ8aYsMj5DrdNLNk/wuqP2yMidcDrwIzLniw2seR3AfOBFUA6sENEdhpjDl/ucCp5pHJxbQemDHu/GDh+CcfYJZmzxSKm/CIyB3gBWGWM6UhQtosZ0bU3xrwrIuUiUmCMSYbG7LHkvwZ4OVpYC4A6EQkZY15PTMQLumh2Y8yZYf9eJyLPpdi1bwdOG2N6gV4ReReYC2hxvYKk8rTwB8AMEZkmIh7gPuCNc455A3ggump4IdBtjDmR6KAXEEv+ZHbR/CJSAqwF7k+yR+2xZJ8u0coUXWXuAZLlwcFF8xtjphljSo0xpcCrwKNJUFghtms/cdi1X4B1n0qZaw/8CbhBRFwikgFcBxxKcE5ls5QduRpjQiLyGLABawXf740xn4jIj6Kffx5rlWQdcBToAx6yK++5YskvIhOB3UAOEBGRn2KtTDxzwRMnSIzX/0lgHPBc9F4ZMknwqiExZr8T64FZEOgH7h22wMlWMeZPSjFmvwv4axEJYV37+1Lp2htjDonIemA/EAFeMMYcsC+1soO2P1RKKaXiLJWnhZVSSqmkpMVVKaWUijMtrkoppVScaXFVSiml4kyLq1JKKRVnWlyVUkqpONPiqpRSSsXZ/wI37VCa69MMjgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N = 6\n",
"dx = L/(N+1)\n",
"k = T/dx**2/mu\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",
"x=np.linspace(0,L,N)\n",
"\n",
"e,v = linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e = e[isort]\n",
"v = v[:,isort]\n",
"\n",
"w1 = np.sqrt(e[0].real)/2/np.pi\n",
"w2 = np.sqrt(e[1].real)/2/np.pi\n",
"w3 = np.sqrt(e[2].real)/2/np.pi\n",
"\n",
"v1 = v[:,0]/max(v[:,0])\n",
"v2 = v[:,1]/max(v[:,1])\n",
"v3 = v[:,2]/max(v[:,2])\n",
"\n",
"f1=np.sqrt(e.real[0])/2/np.pi\n",
"fn=np.sqrt(e.real[-1])/2/np.pi\n",
"\n",
"print('Natural frequencies of {}-element string (Hz)'.format(N))\n",
"print(e.real[0:3]**0.5/2/np.pi)\n",
"print('\\n')\n",
"print('The longest time period is {:1.3f} ms \\n'\n",
" 'The shortest time period is {:1.3f} ms'.format(1/f1*1000,1/fn*1000))\n",
"print('\\n')\n",
"\n",
"plt.plot(x,v[:,0],'-',color='mediumvioletred',label='1st mode');\n",
"plt.plot(x,v[:,1],'-',color='cornflowerblue',label='2nd mode');\n",
"plt.plot(x,v[:,2],'-',color='palegreen',label='3rd mode');\n",
"plt.grid();\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 30-element string (Hz)\n",
"[195.99464595 391.48617646 585.97276757]\n",
"\n",
"\n",
"The longest time period is 5.1022 ms \n",
"The shortest time period is 0.2588 ms\n",
"\n",
"\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"
}
],
"source": [
"N = 30\n",
"dx = L/(N+1)\n",
"k = T/dx**2/mu\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",
"x=np.linspace(0,L,N)\n",
"\n",
"e,v = linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e = e[isort]\n",
"v = v[:,isort]\n",
"\n",
"w1 = np.sqrt(e[0].real)/2/np.pi\n",
"w2 = np.sqrt(e[1].real)/2/np.pi\n",
"w3 = np.sqrt(e[2].real)/2/np.pi\n",
"\n",
"v1 = v[:,0]/max(v[:,0])\n",
"v2 = v[:,1]/max(v[:,1])\n",
"v3 = v[:,2]/max(v[:,2])\n",
"\n",
"f1=np.sqrt(e.real[0])/2/np.pi\n",
"fn=np.sqrt(e.real[-1])/2/np.pi\n",
"\n",
"print('Natural frequencies of {}-element string (Hz)'.format(N))\n",
"print(e.real[0:3]**0.5/2/np.pi)\n",
"print('\\n')\n",
"print('The longest time period is {:1.4f} ms \\n'\n",
" 'The shortest time period is {:1.4f} ms'.format(1/f1*1000,1/fn*1000))\n",
"print('\\n')\n",
"\n",
"plt.plot(x,v[:,0],'-',color='mediumvioletred',label='1st mode');\n",
"plt.plot(x,-v[:,1],'-',color='cornflowerblue',label='2nd mode');\n",
"plt.plot(x,v[:,2],'-',color='palegreen',label='3rd mode');\n",
"plt.grid();\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 45-element string (Hz)\n",
"[196.04043699 391.85229959 587.20727994]\n",
"\n",
"\n",
"The longest time period is 5.1010 ms \n",
"The shortest time period is 0.1743 ms\n",
"\n",
"\n"
]
},
{
"data": {
"image/png": 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e+cQ2okFKC7WF6Ojs1feOY4RKoFLJdRhaZSv1sp7Z2myvVY7xhRSRQhxxHNIPqVVzgtzeGicfHHFy48xQluT5zwAmALd0c1g/zHQxnUSR6OtwmJcdwpfnmtlR7uSziuGXN4wW0RSJIiplpVqWTrmESq7DcFg/TAghFItiX4cyJkIIrtGuoZtuaqVaBDpYdfTqvPixjYwEA/csDvN1OJeolJXYsA17ndaJsHqBhdxkI6/s7ONM1/Afm8zWZmPEyBFdPXtVvkgl16vokl3Uy3oKRAEhIsTX4YxZukgnhhgO6AfUPL0gJCX89cNePB7JozdGYDT4zwAmGJjXekg/RAIJTBfTfR3OeZoQfH1FOJoQ/Gl737ALTFiEBauwUi2rcZvUSHzl71RyvYqj+lEEgiLN/wtGDMdg67WTTuplva/DUbysoiOW8iY365aG+UUx/otVy2p66WWONsfvRtzHRBp44IYwalvcvHPAMez9Zmoz0dE5O/3sOEanBBqVXK/AIR1UykqyRXZAP2u9WKbIJJpoDuoHVes1iDS3uznUmsisdBPX5fvXc1YYqG52SD9ELLGkilRfhzOkhTmhLMgJYes++7AXWY8W0WSIDDoTO9W8V+U8lVyvoEyW4cbNLG2Wr0PxKk1ozNZm00YbJ+QJX4ejeIHLI/njB32EaB4eXuY/hSIuVCfr6KKLa7Rr/DK+QfdfF0Z0mMaftvfidA3v5nOWNgvdpFMpK8c5OiVQqOR6GW7p5ph+jFSRSoyI8XU4Xpcjcogggv36ftV6DQKbdttpavewaHoTUWH+d1lLKTmoH2QKU/y+ulm4WeNrN4bT2qmz8TPbsPZJEAlYuiwc0Y+okfgKoJLrZdXIGuzYmSlm+jqUcWEQBmZrs2mllZPypK/DUcagotnFtkMOri8IJTnSP9caPS6P00GHXz5rHUpesombZ5kpKXVy5PjwpudMbZ5KDz1qLIMCqOQ6JCklh/XDxBJLskj2dTjjJlfkEkYYB+QBX4eijJLNqfOX7X3ERWusW+J/025g4Ho6oB8giiiyRJavwxm2OxdZSI4x8NeP+ugeRnnEiI4IoonmsH5Y9QYpKrkOpVE20kknM7WZAXGXPVpGYWSWNouT8qRanzJAvfSJjc4+nW/cFEGoyT8/qyfkCdpoY7Y2e1wWQh8vJoPgGzeHY3dKni/pu2rCFAhmajM5wxlaUNfTZBc4n/QJdEQeIYIIMkWmr0MZd/kiHzNmDuuHfR2KMkIH6vrZU93PynkWMvysvOGFDsvDhBOOVVh9HcqIpUwzctciC4ePu9hVdfXu4RyRo64nBVDJ9RJn5BlOypMUa8UBsV7rWJmEiTyRR4NsoFf2+jocZZjs/ZJXdvSRMs3AbXPMvg7nss7Ks5yUJynUCgP2erpplpnMBAOvfWqj13Hl7mGTMFEoCmmQDZyVat7rZKaS60UGSx3miTxfhzJh8rV8JJJyvdzXoSjDtGm3ja4+yUPLwv2uCtOFyvVyNDRyRa6vQxk1TQgeWhaOvV8Oa/RwoVaIAYMqiTjJqeR6gR7ZQ52sI1/kB0Wpw+GKElGkilQqZIVaji4A1J9289FRJ8uKQv1utZsLuaSLSllJhsggTPjnYKvhSplm5OZZZj6t6Key+cqFIizCQq7IpVpWY5PDm8qjBB+VXC9wRD8SVKUOR6JAFGDDRoNs8HUoyhV4dMkLH/cRHS64c6HF1+FcUa2spZ9+CrQCX4fiFSvnWYiN0njx476rrv1arBXjwUOpXjpB0Sn+RiXXc5zSSYWsIEtkESEifB3OhJshZhBBBGWyzNehKFew/YiDE20e7l0aTliof1++5Xo5U5hCEkm+DsUrQk2CB64Po6VTv2rt4SliCukinVJZiluqgv6TkX9fnROoRtbgxk2xFtjLyo2WJjTytXyaZTNdssvX4ShDaOv28OYeO7PSTczJNPk6nCs6I8/QSisFWkFQTWcrmhHCgpwQ3tlvp+XslR+hFItinDipk3UTFJ3iT1RyZWCSe7leTiyxxIk4X4fjM7kiFw2NMl21Xv2NlJKXP7EhgPuuC/P7hFWml2HEGJDTb67mK0vCCDEJXvz4ynNfk0QSUURRoVdMYHSKv1DJFWijjXbaydMmzwjhoYSLcNJFOpWyUnVl+Zn9tS6ONrpYvTCMaZH+PaXFKZ3UyBqyRBahwv9W5xmrqDCNNYstVJ5081nl5ee+CiHI1/I5xSk6ZecERqj4A5VcgQq9AiNGskW2r0PxuQJRoLqy/IzNqbN+Zx8z4gysKPb/ZFUtq3HjplAr9HUo42ZpfijZiUY2fGqjx375ua9WYUVDU63XSWjSJ1eXdFEtq8kUmUF5lz1S08V0oolWXcN+5I1ddrrtkodvCMeg+Xd3sJSSMr2MOOKC+hHL4NxXh0uy4QpzX8NEGDPEDKpklZrmNslM+uRaJ+tw4Zr0XcKDhBAUaAWc5jTtst3X4Ux6x1vdfFzqZEVxKGnx/jundVALLZzlbNBMv7mS6TEGbrnGzOeV/VSdvPzc13yRjx27muY2yXgluQohbhVCVAohaoQQPxzi9TwhxOdCCKcQ4klvnNNbBqcLJJLo61D8hlVYMWBQrVcfk1KyfqeNCItg9YLAKMJQppcRQkhArX4zFl+eYyEmQmP9Thv6ZcY2pYgUwgmnQqqu4clkzMlVCGEAfg/cBhQA9wkhLr5t7QC+A/xyrOfzprPyLKc5TZ6W5/ejLyeSWZjJEllUy2r65fDWslS8b09NP7Utbu5aGIYlxP8/n3Zpp07WYRVWTMK/pwp5S6hJcM9iCyfaPNR1xgy5jSYGyj+ekCfokf653q7ifd5ouS4AaqSUdVLKfmA9sPrCDaSUrVLKvcCV64ZNsAq9Ag0tKKcLjFWBVoCLgefRysRzuiSvf2ZnRpyBJXmBUYqzUlaio0+KLuELzcsOITvJyKHWRGzOoQc3DT52qpSVExma4kPeSK7JwIkLfm469zu/5pEeqmQV6SIdi/DvMnK+EE88scRSppephZ994N2Dds726XxlSRianw9igr8PZEoiialiqq/DmVBCCO5dGobTY+CtfUNXbooUkaSIFCr1SnR59YXXlcDnjRESQ135o/42FkJ8E/gmQEJCAiUlJaM6Tm9v7xX37Y7txpHnoP9oPyWdozvHeLla7BPFkGCgLaeNdw+8i6Vn+Dcg/hL/aPhD7H0uE+/U5JIW1c3JqiOcrBr+vr6Kv29KHz1FPURURFDSNvrz+8P7P1ozwhPYdjie0N5DRIVe+jhFn6bTm9/LO4ffIbwz3AcRKhPJG8m1CUi94OcU4ORoDyalfAZ4BmDevHly2bJlozpOSUkJV9p3q2crETKC22bdhib8a9D01WKfKC7p4gXPC5hnm1lmGH48/hL/aPhD7M+834um9fPt1WlMi8wc0b6+iv99z/uYpZnbC28f07qt/vD+j5b9g5201ifQ4C7mf9wSecnrHunhRc+LmIpNI7qelMDkjayyF8gRQmQIIUKAe4HNXjjuuOmW3TTLZvK0PL9LrP7EJExkiSzqZT0u6VePy4NW1UkXe2v6ueUas99XYhrkkA4aZAM5IidgF0T3BovRzcp5Fo40uDjWeGnL1SAMWIWVBtmglqKbBMacWaSUbuAJ4D2gHHhNSlkqhPiWEOJbAEKIRCFEE/A94EdCiCYhRNRYzz1alXolAhHQCzhPlBwtBxcujsvjvg4l6Om65NWdNqaGa9x6TeCMA6iVtejoWDU1MHDFTDPx0Rqv7rThHmJZujwtDx2dKjmCvn4lIHml2SalfFtKaZVSZkkpf3rud09LKZ8+9+cWKWWKlDJKSjnl3J+7vXHukdKlToWsIFWkTsql5UYqiSQiiVRfBhPg04p+Gts8rLnWQqjJ/wcxDarSq4ghhmlM83UoPmcyCNYtGViW7uNS5yWvTxVTSSSRCr1CDRQMcpOuT/SEPIENG3lCVWQaDiEEOSKHZtlMn+zzdThBy94veWO3jaxEIwuyA2PqDUCn7KSVVqyaVc0VP2dmmomCFCOb99qHrDucr+XTRRenOOWD6JSJMumSa7ksx4KFGWKGr0MJGFbNikSqOa/j6K19dnrsknuX+v9ycheq1qsRCLXoxQWEEKxbGoajX7J5j/2S1zNEBiGEqGL+QW5SJVebtNEoGwfK+03igRcjFS2iSSCBKr1KdWWNgzNdHj444uDavBDSA6B+8CApJVWyimSRTLhQU0sulBxjZFlRKB+XOWnu+OLyjSZhIltkUyfrcMpLu46V4DCpkmutrEUiydXUQKaRsmpWznKWdlQxf2/btMeOQYO7FgZG/eBBpzhFL72qwtllrJxnwWwSvLHr0tarVbPiwUO9rPdBZMpEmFTJtVqvJpbYSVdBxhsyRSYaGlW6GtjkTQ2tbvZU93PTTDNTwgPrcqzSqzBhIl2k+zgS/xRp0bj1GjOHj7suWTUnnniiiFKPWoJYYF3NY9ApOznDGXK0HF+HEpDMwkyaSKNG1qh1Kb1ESsnGz21EmAW3XGP2dTgj4pIu6mQdmSJz0hTpH40bZ5qZEi7Y+LntC49UhBDkaDmclCfVQMEgNWmS6+DAi8myFNZ4sAorduw0ySZfhxIUSk+4qGgeKDwQFhpYl2KDbMCFS3UJX0WoaWC5wPrTHg7UfbH1miMGbvRrZI0vQlPGWWBd0aMk5cBI1+liuhp4MQapIhUzZjXn1Qt0XfL653biojRuKAz1dTgjVikriSCCJJHk61D83rW5IUyPMfC3XV8sLBEtooknnmpddQ0Ho0mRXE9zmh56zt8pKqNjEAayRTYNskGNchyjXVX9NLV7uHOhBaMhcKbeAPTJPpplMzkiJ6CmDfmKpgnuXmShtUtnR/kXr5scLYd22mmXaqBgsJkUybVar8aIkQyR4etQAt7gKMdaWevrUAKWyy15c4+dtDgD8wKoYMSgGlmDRKpyhyMwM82EdbqRLXvtOPr/3nrNElkIBDW66hoONkGfXD3SQ52sI02kESIC74vM38QSyxSmqK6sMfjwqIOOXp01i8PQAqzlJ6WkSq8innimiCm+DidgCCFYsziMHrvkvUN/n5pjERZSRerADYuaQx5Ugj65npAncOBQXcJeIoTAqllpoYUu2eXrcAJOn0Pn7QMOimaYyE8JvFG27bTTQYdqtY5CZoKRuVkhbDvkoMv297KIOSKHXnpVOcQgE/TJtVpWY8ZMikjxdShBY/BGRbVeR+7tAw7sTsmaRYGz6s2FqvQqNDQ16n6U7l5kwa3Dlr1/b72miTRMmNT1FGSCOrn2y34aZANZIkuVO/SiCBFBskimSqpyiCPR3uPhw6MOFuWGkBIbOGUOB+lSp0bWkCbSMIvAmpfrL+KjDVxfEMqOMictZwfmi5uEiQyRQZ2swy3dVzmCEiiCOrnWy3o8eFThiHFgFVZ66KGFFl+HEjDePFfEffWCwGy1Nskm7NjV3NYxWjnPgskIb+z++4Lp2SKbfvpplI0+jEzxpqBOrtWymiiiiCfe16EEnQyRgRGj6soapuZ2N7sq+1lRbGZaZGD2olTLakIJJVWk+jqUgBYVpnHLbAsH6lzUnx5oqSaLZMIIU+UQg0jQJldXiEvNxRtHJmEiTaQN9A6ocohXtWmPHXOI4LY5gdmd6pIujsvjZIpM9YjFC26eZSbCLM63XjUx8By7UTbikA4fR6d4Q9Am1564HgDVJTyOskU2Dhw0y2Zfh+LX6k+7OVTv4kuzzUSYA/OSa5ANuHGrdVu9xBwi+PJcC+VNbsqbBsoi5mg56OjUyTofR6d4Q+CNqhim7rhu4oknWkT7OpSglSpSCSGEGlnDDNTi85fzxu6B4vw3zQzMVisMLNcYRhiJItHXoQSNZYWhbDvkYNNuG3nJUV+YQ16gFXj1XPv37483Go1/BIoI4kbVBNOBY263+xtz585tvfjFoEyuHbIDZ4RTtVrHmUEYvjDK0SiC8uM0JuVNLsqb3KxbEoY5JDAfTzilk0bZSKEoRBPqe9lbTEbByvlmXiixcaTBxaz0EHK0HPbqe+mRPUSKSK+dy2g0/jExMTE/Li7urKZpaoi/F+i6Ls6cOVPQ0tLyR2DVxa8H5ZVSrVeDRM3FmwDZIhsXLjXKcQhSSjbttjE1XGNZAHXzr68AACAASURBVBbnH1Qv69HRydZUl7C3XZsbSny0xqbddnQpz3e7j8PApqK4uLhulVi9R9M0GRcX18VAb8Clr09wPONOSkmNrCH8bDgWEZhTHgLJdDEdCxa1bNYQjjS4qDvtYeV8MyZjYLZaYaBLOIoo4ojzdShBx2gQrFpgoandw76afqJEFIkkUq1Xe3sOuaYSq/ede0+HzKNBl1wHB11MOaXqnk6EC0c59st+X4fjN3Qp2bTbTny0xrW5gdtqtUkbzbJ5oMC8GnU/LuZnh5AcY+DNPXbcHkmRVkSmyERHv/rOit8KuuRqEiYWGhYScTbC16FMGllaFh48HJfHfR2K39hXM7Ck3KoFgbek3IXqZB0SqbqEx5EmBHcuHFiS7vNKJ1laFvMN84NuytPatWvTY2JiZuXk5BRebdutW7dGbtu2bdwX3966dWvk8uXLx+XDHXTJVZl4CSQQQYTqGj7H7RlYUi45xsD8AFxS7kI1eg0xxBAjYnwdSlCblW4iI8HAlr0OXO7g7L39+te/3rZ58+ZhPUz+8MMPI3fs2BHQLSSVXJUxE0KQLbIHyuNJ+9V3CHKfVzpp7dK5a5El4JaUu1CP7OE0p8nS1MDA8SaE4K6FYZzt0/m41Hn1HQLQbbfd1hsXF3dJ8eSf/OQn8VlZWYVWq7Vg5cqVmZWVlSHPP/983NNPP52Ql5dX8O67734hyX7ve9+bfvfdd6cvWbIkJzk5ufi5556b8q1vfSvFarUWXHfddTlOp1MAvPnmm5H5+fkFVqu1YO3atel2u10AbNy4MSojI6Nw7ty5uRs3bjz//LC7u1tbu3ZtelFRUX5+fn7Biy++OKZni2ruhOIV2Vo2hzyHqJf1vg7Fp1xuyZa9DjITDMxMC7wl5S5UK2sBVOGICZKfYiI/xcjbB+wsLQjFbBqfG7Pa725NtVWcCfPmMcPy4mxZv115YjT7/u53v0tsaGg4arFYZFtbmyE2Ntbz8MMPn4mIiPD8+Mc/Pj3UPg0NDaGfffZZ1YEDB8wrVqzIe+6552qffvrppptvvjnrtddei16zZk3X448/nvH+++9Xzpw503nXXXel/8d//Efck08+eeaJJ55I37ZtW2VhYaFz5cqVmYPH/Kd/+qek5cuXd2/YsOF4W1ubYd68efmrVq3qjoqKGtXDb9VyVbwihhimMIUafXJ3DX9c6uRsn85di8ICfgBQjV5DPPFEiShfhzJp3LlwYEH17YcnTwnE3Nxc+1133ZXx1FNPxZhMpmH1id90001doaGhcsGCBXaPxyPuueeeboDCwkJ7fX19yOHDh80pKSnOmTNnOgG++tWvtu/cuTPy0KFD5pSUFGdxcbFT0zQeeOCB9sFjlpSURP3mN79JysvLK1i6dGmu0+kUNTU1o36uo1quilcIIcjWstmn78MSMjmnQDlckrcP2MlPMZKXHNit1rPyLO20s1hb7OtQJpXMBCOzM0y8f9jBzbPNhIzDFK7RtjDHy0cffVT9zjvvRG7atGnKL37xi+nV1dXHrrZPaGioBDAYDBiNRqlpA+1ETdNwu93iStOYLnfTK6Vk48aNNbNmzfJKv7xquSpeM9h92BPb4+NIfOPDIw567JLVC7za4+YTtfpAl7AqxDLx7lkcxg/uihyXxOpvPB4PtbW1IXfccUfPU0891dTT02Po6uoyREZGenp6ekY9XHr27NmO5ubmkGPHjoUCPP/889Ouu+66ntmzZzuamppCSktLQwHWr19/fqTe8uXLu3/1q18l6PpAL/Cnn346plaCSq6K10SLaGKJPb9owmRic+q8d8hBcZqJrMTA7hAaLMQyXUwnXIz7bAjlIglTDCTHBPZnaCh33HFHxtKlS/Pq6+tDExISZv7mN7+Jdbvd4v7778+wWq0FRUVFBY8//vjp2NhYz5o1azrfeuutKUMNaBqOsLAw+fTTTx9fu3ZtltVqLdA0jSeffPJMWFiY/K//+q+GlStXZs+dOzc3NTX1/OT8n//85yfdbrfIy8sryMnJKfzRj36UPJa/b/D9H1R8KlvLZlfkLrpk16RaNOGDww5sThmwC6FfqI02uuhilpjl61CUILJly5YhRzvu37+/8uLfzZw501lVVVU21Pa//vWvT174s81mOzjUa6tXr+5ZvXr1Jce45557uu+5557Si38fEREhX3755YYr/y2GT7VcFa8a7EacTHNeex06HxxxMifTRFpc4N+v1ug1aGhkiAxfh6IoAUslV8WrIkQEli4LNXqNt2uj+q33Dzpw9EtWzQ/8VquUklpZS4pIwSwCd4k8RfE1lVwVr4s8E0knnXTQ4etQxl23TWf7UQfzc0JInhb4rdYWWuijT81tVZQxUslV8brItkgEYlLMeX33oAOXB+6YF/itVhgYJWzESJpI83UoihLQVHJVvM7oNpIskqmVtUHdNdzZp1NyzMHi3BASpwZ+kXVd6tTJOmaIGYSIwK6JrCi+ppKrMi6yRBY99HCGM74OZdy8vd+OLmFlkLRaT8qT2LGrua2K4gUquSrjIkNkoKGdL0YQbNp7PHxS5mRJXihxUYHfaoWBWsImTMwQM3wdihJkampqTAsXLrRmZmYWZmdnF/7bv/1b/EiPsWDBgtxPPvlkXCu0rFmzJv0vf/nLVG8cyyvJVQhxqxCiUghRI4T44RCvCyHE7869fkQIMccb51X8V6gIJVWkBm3X8Fv7HAjg9rnBMaLWIz3Uy3rSRBpGEfgDsxT/YjKZ+NWvftVUV1dXunfv3vI//elP8fv37w+Oi+cyxpxchRAG4PfAbUABcJ8QouCizW4Dcs79+03g/4z1vIr/yxJZ9NFHCy2+DsWrWrs8fFrh5PrCUGIig6PV2iybceJUo4SVcZGWluZaunSpDWDq1Kl6VlaWvbGxMQQGWqTf/va3k4uLi/PT09OLBisy9fb2ipUrV2ZardaC22+/PdPhcAxZDzI5Obn4iSeeSJ49e3ZeUVFR/s6dO8OWLl2ak5qaWvSLX/wiDkDXdR5//PGUnJycQqvVWvDss89OHfz9ww8/PCMrK6tw2bJl2W1tbefvLHfs2BE2f/783MLCwvylS5fmNDQ0jKhguDduURcANVLKOgAhxHpgNXBhZYzVwPNyoAmzSwgxRQiRJKU85YXzK34qTaRhwECtXkuSIcnX4XjNlr12jAa4bU5wPGuFgaIfIYSQIlJ8HYoyzv76YW9qc4fHq92ryTEG21dXRAxrQYDKysqQsrKysBtuuKF38Hdut1scPXq0/NVXX43+8Y9/PP3WW2+t+uUvfxlvsVj0qqqqst27d1uWLFlycaPtvNTU1P5Dhw5VPProo6lf//rX03fv3l1ht9u1oqKiwh/84Adnnn/++SlHjx61lJeXl546dcq4YMGC/C996Uu9JSUl4TU1NaGVlZWlTU1NpuLi4sKvfvWr7U6nU3znO9+Z8dZbb9VMnz7d/eyzz0598sknkzds2HB8uO+JN5JrMnDhm9oELBzGNsnAJclVCPFNBlq3JCQkUFJSMqqgent7R72vrwVy7PDF+C15FiqiKnDtcSHw/0LkV3vvu5yh7K61kjetjUN7j0xcYMM0ms+OLnRqF9YS2RbJjpod4xPYMAXyZz+QY58oXV1d2t13353185///ERMTMz5dVLXrl17FuDaa6/t+/73vx8CsHPnzojvfOc7rQALFy60W61W2+WOu27duk6A4uJiW19fnzZ16lR96tSpemhoqN7W1mbYsWNH5Lp16zqMRiOpqanuhQsX9u7cuTPs448/Pv/79PR01+LFi3sAjhw5ElpdXW1ZsWKFFQZauHFxca6R/F29kVyH+sa8+CHbcLYZ+KWUzwDPAMybN08uW7ZsVEGVlJQw2n19LZBjhy/GX6fXsU3fRs71OaRo/t8qutp7/4f3egkx9fPYqhwiLbkTF9gwjeazU6/XU61Xs3T6UlJSfPv/KJA/+4ES+3BbmN7mdDrF7bffnrV27dqORx55pPPC18xmswQwGo14PJ7z+WK4ayIP7q9pGiEhIedzi6ZpuFyuES9BJ6UU2dnZ9kOHDlUMK4AheGNAUxOQesHPKcDJUWyjBKEZYgYmTNTKwB813NTmZl9tPzfONBNpCZ6B9rWyFjNmpovpvg5FCVK6rnPvvfemWa1Wx7/8y7+cHs4+S5cu7X3xxRdjAPbu3WuuqqoadVf2DTfc0LNx48YYt9vNyZMnjXv27Im47rrr+m644YaeDRs2xLjdbhoaGky7du2KBJg5c6ajo6PD+MEHH4TDwI3Bvn37RjQAyxvfEHuBHCFEhhAiBLgX2HzRNpuBh8+NGl4EdKnnrZODUQxU+6mX9Xikx9fhjMmbe+1YQgRfmhU8gxxd0kWDbCBTZKKJ4LlhUPzLtm3bIjZt2jRt586dkXl5eQV5eXkFr7766hWXzXryySdb+/r6DFarteBnP/tZYnFxcd9oz//QQw91FhYW2vPz8wuXLVtm/dd//demGTNmuB966KHOzMxMZ25ubuGjjz46Y8GCBT0w0BJev3597Q9/+MOU3NzcgsLCwoKPP/54REvfjblbWErpFkI8AbwHGIA/SylLhRDfOvf608DbwJeBGsAGfG2s51UCR5bIokbW0CybA3YO5fFWN4fqXaxeYCHcHDxJqEE24MZNlqYKRyjj55ZbbumVUu4f6rU9e/acX3IuKSnJ3dzcfBQGloDbunVr3dWOPbg9wHe+8512oH2o1/7whz80MdCLep6maTz//PONQx332muvte/bt++S5fCGyysT2qSUbzOQQC/83dMX/FkC/90b5xoOZ3M36ME3tzJQpYpUQgihVtYyg8BMrm/usRMeKrhxZvC0WmGgSziMMBJJ9HUoyjm6y4O7zUZIUqSvQ1HGIHhuwc9xddg4dstfMD1Vg3TrV99BGXcGYSBDZFAv63FLt6/DGbGaUy6ONbq4dY4ZS4j/j3geLqd00igbVZewH9H7PVQ/9gbHVj6Pp9fp63CUMQi6K8oUE0bC1+di+OQM1d9+E90V2M/5gkWWyMKFixPSJwMVx+TNPXYiLYLlRcHVam2QDejoZGuqcIQ/0B1uqr72OmffriLp8fkYIkJ9HZIyBkGXXAFSvrcU14NpdLxZTvVjb6D3qwTra8kiGTPmgBs1XNHsoqLZzZfnWAg1BU+rFQYKR0QQQTwjLvOqeJnH5qLy4Q10bqsh4xe3kvTNBb4OSRmjoEyuAJ5VyaT/7GbOvl1F1ddeR3cEXndkMNGERqbIpEE24JIjmovtM1JK3txtZ0q44IbC4GpFOKSDZtlMlsga9lxCZXx4evupfPA1uj6uJ/O3t5PwVVV6PRgEbXIFSPzGfDJ+eRud22qofGgDHltgfKkHqywtCzduGmSDr0MZltITLmpa3Nw+14LJGFwJqF7Wqy5hP+DucVJx73q6P2sk+/eriL9vlq9DUrwkqJMrQMLD15D5u5V0fVJP5QOv4unt93VIk1YiiYQRFhBdw1JKNu22My1SY2l+cLVaYaBLOJpopjHN16FMWu5OO+VrX6H3wElynrmT2HuKfB3SuLHZbKK4uDg/Nze3IDs7u/Af/uEfhl2xJCws7JrxjA0Giv+fOnXKq8tBBWVyLW9y0e0MOf9z/L0zyX5qNd27TlD+lfW4ux0+jG7yGuwaPiFP4JT+PRLy8HEXDWc8rJxnwWgIrlarTdo4JU+pLmEfcnXYKFvzMrajLeT86W6mrcr3dUjjymw2y507d1ZWVlaWlZaWlm3fvj1q+/bt4Rdv53IFT+9i0CVXm1PnqXd6ONz6xXl7sWsKyXnmTvoOnqR87Su4z9p9FOHklqVl4cHDcXnc16Fcli4lb+6xEx+tsTg35Oo7BJg6WYdEqsIRPtLf2kvZXS9hr2rD+vxaYm6z+jqkcadpGtHR0TpAf3+/cLvdYvDGbsGCBblPPPFE8vz583N/8pOfJFRUVIQMLh/33e9+d8gWbmVlZUhGRkbhV77ylbScnJzCVatWZWzatClyzpw5eWlpaUUfffRRGMDp06cNN910U5bVai2YNWtW3u7duy0ALS0thiVLluTk5+cX3H///WkX1h5+6qmnYoqLi/Pz8vIK7r///jS3e3TjdYJuVeSwUI2bZ5nZsm8KDa1u0uL//lecdkc+WoiRqkf/RtndL5G/4T5MsZfcPCnjKIEEIomkRtaQi/8VvgfYW9NPU7uHb9wcjkELvpZdjV5DDDHEiBhfhzLp9J/qoWzNS/Sf7CHvpXVEX58x4TGUeEpSO2SHV5ecixExtmWGZVecZ+d2uykqKipobGwMfeSRR1pXrFhxvpxhZ2enYe/evZUAK1asyP7GN75x5oknnmj/93//97jLHe/EiRPmV199tW7u3LkNM2fOzH/ppZem7du3r+Lll1+e8tOf/jRp+fLltT/4wQ+mz5o1y/bBBx/Ubt68OfKRRx7JqKioKPvhD384ffHixb2//OUvT61fvz76lVdeiQU4cOCAeePGjTH79u2rCA0NlQ8++OCMp59+etoTTzzRfrk4LifoWq4AN8+2EGJws2nPpa3TqbfkkPviOhx1HZTd+SL9p3uHOIIyXoQQZItsmmUzNnnZFaR8RpeweY+d5BgD87ODr9XaLbs5zWlytBxfhzLpOBo7KV31Aq6WXvLW3+uTxOpLRqORioqKssbGxiMHDhwI37t37/mJ4/fdd1/H4J8PHDgQ8dhjj3UAPP7445dNasnJyc4FCxbYDQYDVqvVvmLFim5N05gzZ46tqakpFGDPnj2Rjz76aDvAqlWrejo7O43t7e2GXbt2RX79619vB7j33nu7oqKiPADvvvtu5LFjx8JmzZqVn5eXV7Bz586ourq6UQ26CLqWK4AlRFA4rZWDjdOpOunCOv2LC8hPWZZB3itfoeKBDZSteoH81+8nNOWKNaQVL8rWsjnoOUidrKNI+NcgjrrOGFq7dJ74cgRaED6PrJE1wEBRD2Xi2Os6KF/zMp7efvI33k/EHN+tQHS1FuZ4i42N9SxdurRny5Yt0fPnz3cAREZGfqGcnqZpV61fe/HScoPLzhkMhvPL1g211JwQ4vzydBeTUoq1a9e2//73v28e2d/qUkHZcgWwxrQzJVzwxm77kG9w1LVp5L92L652G6WrX8RRf9YHUU5OMSKGGGKo1qt9HcoXuNySI2fiyUwwMDPNdPUdAoyUkmq9mkQSiRSqbu1EsVWeoWzVC+gOFwV/e8CnidVXTp48aWxrazMA9Pb2ipKSkqj8/PwhR5bOmTOn99lnn40BePbZZ8c0nH3RokU9f/nLX6YBbN26NXLq1KnumJgYfdGiRT1//vOfpwG89tprUd3d3QaAW2+9tXvr1q1Tm5ubjTDwzLaqqmpUXVhBm1yNmuT2uRZqTrk51jj0CLTI+SkU/O0B9L5+Sle/gL26bYKjnLxytBxaaaVbdvs6lPNKSp3Y3SHctSgsKEfRdtBBJ51qbusE6jt6mrI7XwSgYNODhBcn+Dgi3zhx4oTpuuuuy7VarQXXXHNNwfLly7vvu+++rqG2feqppxqfeeaZ+KKiovyuri7DWM77v//3/z554MCBMKvVWvDP//zPyX/961/rAX7+85+f/PTTTyMKCgry33vvveikpKR+gLlz5zp+9KMfNd94441Wq9VasGLFCuuJEydGdacdlN3Cg5bmh/LeIQebdtspnGEaspsvfGYiBW88QPk9r1C6+kXyN9xPeKEqBzfeskQWu9lNjaxhjvB9RRpHv+Tt/XYSw3vISw7OgT7VejUaA9OhlPHXe+Ak5V9ZjyEihPzX78eSGZyfq+FYuHChvby8vGyo1y5ccg4gLy+v/9ChQxWDP//sZz9ruXif3Nzc/urq6tLBn19//fXjQ72WkJDg2b59+yUT6xMTEz2ffvrphV1n57vKH3vssbOPPfbYmLsyg7blCmA0CFbNt9DY5uFA7eXnT4Xlx1Pw5oNoJgNld75Iz/4xd7crVxEpIkkkkWq9eshu+4n2wREHvQ7JrPhLruOgIKWkVtaSIlKwCIuvwwl6XZ82ULbmZYxTzBS8+eCkTqyTVVAnV4CFOSEkTTXw5h4bnius8WrJnkbB5ocwTjFTfs8rdH0aGCX6Alm2lk0nnXTQcfWNx1GfQ+f9Qw5mZ5iItQTn/OcWWuill2yhuoTH29kPaqi471VCU6Io3PIQ5hlTfB2S4gNBn1w1TXDnQgstnTq7Kq9c+tCcNoXCLQ8RmhJFxX2vcvbS3gTFizJFJhqazwc2vXvQgaNfcueC4G3R1eg1GDGSLtJ9HElwa99STtUjGwmzxlKw6UFCEv1m4Jiu63rwDSTwsXPv6ZALhwd9cgW4JsNEWpyBLfvsuDxX7oIMSYykYNODhFljqXp4A+1byicoysnHIiykiBRqZa3PuoY7+3Q+POpgoTWE5GnBOQTBIz3UylrSRTomEXyjoP2FVtJK9WObiLhmOvl/ux/TNK/WaRirY2fOnIlWCdZ7dF0XZ86ciQaODfV6cH6bXEQIwd2LwvjNlh52lDlZUXzlRa9N08LI/9v9VN7/GtWPbUL/Txdx986coGgnl2yRzYfyQ1poIYmkCT//2/vteHS4Y37wtlqbZBNOnKpLeBy1/GkfIU/VEH19Otbn7sEQ7l8FSNxu9zdaWlr+2NLSUsQkaVRNAB045na7vzHUi5MiuQLkpxjJnW7krX12luSFXnXha2OUmbxX76XqkY3Ufmcrnr5+Eh+dN0HRTh7pIh0jRmr0GpIME5tcz3R7+KTMyZK8UOKjxzTi36/VyBpCCSVFpPg6lKDU/LvPOPGTEjzzYsh9cR2a2f++VufOndsKrPJ1HJPJpLmDEWLg2Wu3XfLBkeGtimMIDyH3xXVMvdXK8f/5Ps3/+alfjGwNJiZhIl2kUytr8UjPhJ578x47QsDKecHbanVJF8flcTJFJgYRvDcQviClpPEnH3HiJyVMu7sQ1/esfplYFd+YNMkVIDvJxKx0E+8ddNBjH/IZ9CU0s5GcP91F7JpCTvzsYxr/9UOVYL0sW2TjxEmTbJqwc55oc7O7qp8bi81MjQjey6BBNuDGrQpHeJn06NR//11O/u5z4h++huzf3wHG4P0cKSM36T4Ndy8Kw+GSvLV/+FMuNJOBrN+vIuHrczn11G7qvvc20jO85KxcXYpIIZTQ83VvJ8Lrn9uxhApum3Pl5++BrlpWE064T55nByu930PNt9+k9fmDTP/utWT8x60Iw6T7KlWuYtJ9IqbHGFiaF0rJMSdnuobfDSk0Qfq/f4nk7y3hzEuHqX7sDXTn6Nb5U77IIAxkikyOy+O45Pgvllze5KL0hIvb55oJNwfvJeCQDppkE9kiOyjLOfqCx+ai6pGNtG8qZ8b/Ws6Mf16m3ltlSMH7zXIFqxZYMGgMuSTdlQghSP3hDaT9+CY6tlZS+eAGPH1XnjurDE+2lo0bNw1yfIt36FKy8XMbMREay4uCu9VaJ+vQ0VWXsJe4uxxUrHuFzg9ryfjVbUz/H4t9HZLixyZlcp0SrnHTTDN7qvtpaB156zPpWwvI/O3tdO04TvnaV3B3BmdVn4mURBLhhFMtx7egxN6afhrPeLhzoQWTMbhbHNV6NVOYwjTGtLCIAvS39lJ210v0HjxJzrN3kfDQNb4OSfFzkzK5AtxyjZkIs2Dj57ZRDVCKv28W1j/dTd+RFspWq0XXx2pwEfUm2YRdjs/Nissj2bTbTso0Awut/jUP0dt6ZA8ttJCj5ahuyzFynuiibNWLOOo6yH1hHdNW5fs6JCUATNrkGhaqsXKehYpmN6UnRvecL+b2XPJeXoejoZPS25/DXufbGrmBLkfLQUenVo5P2cmPjzlp69ZZs9gSlAuhX2iwB0AVjhgbW1krx25/Dle7jfzX7mPKCrWikDI8kza5AtxQGEpclMbrn9vRr1DU/0qir8+gYNODePr6KV35PL2HTnk5ysljmphGLLFU6pVX33iEbE6dt/bbyU8xUpga3CUApZRU6pUkkUSUiPJ1OAGre1cjpateAKBw84NELlBFOJThm9TJ1WgYKCzR1O5hV9XoByZFzE6icOvDGMJMlN31Ep0l9V6McnKxalbaaKNdtnv1uO8dHFhSbk2QLoR+oRZa6KabXC3X16EErI53qihftx5TfDhFbz1CWL5a41kZmUmdXAHmZYeQFmfgzT12XO7RF4ewZE2jcOvDmNOmUPnAq7S9UXr1nZRLZItsNDSvtl7P9up8cMTBgpwQ0uKDv4JOpV6JEaNaFH2UWl86RNXXXiesIJ7CLQ8Tmhrt65CUADTpk6smBGsWh9HRO7A6yliEJEZS8OaDRMxLpuZbb9Lyx71einLysAgLaSKNalnttXKIm/cOFOe/c2HwljkcpGs6dbKOLJGlVsAZISklzb/9jLp/eJvoGzIoeN3vVrZRAsikT64A+SkmimaYePuAgz7H2CovGaPN5K+/d6Ae8T9to/FnJapc4gjlilwcOGiUjWM+1skOD59WOFleFEpcVPDX1u2J7cGFS3UJj5DUJQ0/2saJn5YQu6aQ3BfW+t3KNkpgUcn1nDWLLNidkq37xj4NRLOYsP7pbuIfms3J//yMuu++he6a2KL0gSxVpBJGGJVy7F3DGz6zYTYJvjw3+FutAF0JXUQRRSKJvg4lYOgON9XffIOWZ/eR+PgCsn6/Ci0k+G/ElPGlkus5KbFGrisI5aNjTk6dHXsiFEaNjF/eRsr3r+PM+iNU3v8a7h6nFyINfprQyBE5NMpGbNI26uMcbejnWKOLlfPMRFqC/6PeLbuxR9vJ1XKDftCWt7jP2ilf+zIdmytI+9cbSfvxjQhNvXfK2AX/N84IrF5gIcQoeO3T0X+hX0gIQcr3rxuo5rTz+ECxiZYerxw72OVquUjkqCs2uT2S1z61kTBFY0VxcJc5HFSpV4IEq7D6OpSA4Gjs5NjK5+k9eIqcZ+8k6dsL1U2J4jUquV4gKkxj5Twz9vOk+AAAIABJREFUxxpdHG3wXs3g+PtmkffSV3DUn+XYl5/DVnHGa8cOVlPFVOKJp1KvHNUz64+OOWnp1Fl3bRhGQ/B/YUopqZJVhHWGESEifB2O3+s70kLpl5/D1dpH/ob7mLa6wNchKUFGJdeLrCg2kzBF47VPbbg93huINGVFJoVvPojs91B6xwt0fza+BeqDQa6Wy1nOcoaR3Yz02HW27LVTNMNEcdrkGDHbLJvppZfo02rayNWc3V5L6aoXECEGCrc+RNTiGb4OSQlCY0quQogYIcQ2IUT1uf9Ovcx2fxZCtAohjo3lfBPBaBCsuzaMlk6dj4559xlp+MxECt9+BFN8OOXr1tO2qcyrxw82WSILA4YRz3ndtNuO0yVZd23wF4wYVCkrCSGEiA7Var2S1pcPU/nga5gzYyh6+xHCcuN8HZISpMbacv0hsF1KmQNsP/fzUP4K3DrGc02Y4rSBqTlb9trpsXt3UXTzjCkUbX2YiDnTqfnmJpp/+5maqnMZoSKUDJFBjazBLYe3etGJNjc7yp0sLw4lKWZyjPh0Sif1sn6gAIeuOqOGInVJ489KqPt/3iL6unQKNz9ISGKkr8NSgthYr8TVwHPn/vwccOdQG0kpPwECpqq9EAOt1373wCoq3macaiH/tfuYdnchJ35aMjBVp19N1RlKrsiln36Oy+NX3VZKyas7bYSHCu6YNzmm3gDUylo8eNTc1svQ7S6qv/nG/23vzuOiuu/9j7++ZxaYYVgFAVlFcQFE4x6NRrJoYhaTxizNYhqTh236a2/XdLn9tb2/X2/7y+3tkm5JbvalWZrNmMQY9yUxUdxQQRERQVFQ2WQGGIaZ8/39AUmtERllmDMj3+fjMQ9n4DDnzfHAh3PO9/s5HH/sU4beN4HRr9yByRFhdCzlEif6c9QkhGiRUsad8bpZStnbqeFs4AMpZUEf77kEWAKQnJw86fXXX7+obC6XC4ejf6fIttencqApketzDpIQ2b/uTeckJaa3arG8eRQ9LwbPD0eDwxKQ7EYKZH6JpGpyFdYOKxllGedd9khrDB/XZjMlpZZRCRf3t1w4bvuawhp0k072rmzaXG1hl/9MAd/+LR6s/12OqHThvTcL343DYIAuFYTKvlNUVLRDSjnZ6ByDnpTyvA9gDVB6jscCoOWsZZvP8z7ZQGlf6zvzMWnSJHmx1q9ff9Ff+zlXh09+99km+dulp6Wu6/1+v96cenOv3JL2qNw17QnZfqgxINmNFOj8xd5i+WTXk9KpO3tdxtOlyx+/1Cx/+VqL9Pou/v8q3LZ9k94kn+x6Upb4SqSU4Zf/bIHM37bvhNwx8a9ya9ZvZePy8oC9b29CZdsD2+UF/J5Vj4F59HlaWEp5jZSy4ByPZcAJIUQqQM+/JwNd/I0UFamxYKqNiuNedlZd3D1f/ZG4sICxb92N93QHZde/iNh3esDWFY4+P91ZISt6XWbVbjeNTp07r7BjGkRNACr0CgSCXJFrdJSQ0rLuEGU3vIT0+Mhbdi8J89UpcyW4+nvN9T3g/p7n9wPL+vl+IWdWXgRpCSbe/LQdTz/umtOXmOkZFHz4NcyJdqy/2sep1/cM2LrCTYyIIZXUXue8trTprNjRwWXDLYxNHxxTbwB0qVMhK8gUmdiFajD/ufrndlB+9xtEZMVRsPJrOManGh1JGYT6W1wfBa4VQhwEru15jRBimBDiw88XEkK8BnwGjBZC1AohHuzneoPGpAnummWn0amzYmfgBzedKXJ4PAXLF6GPjeHQv31AzX+sRfoCO1o5XI3RxtBKK8fl8S997o3N7fgk3D5jcBWYI/II7bQzWqijMgC9y8fhH31E9U9WEnfNiO7bxQ1TN4tXjNGvm1tKKRuBq8/x8ePA/DNef7U/6zHamDQL03KtrNjpZurIgZ3iYY6z0fXvYxm2pou6x7fSXn6K3P+5BXPs4Gjh15sckcNnfEapLCWNtC8+vrfGw7ZKDwum2kiKHRxTbz63V+7FgYMskWV0FMN1NbRR8dBSnJ8eIfVb08n82RyESU1LUoyj9j4/3THTToRF8PLGNvRznJoMKLPG8EfnMfx319O6qZrS616go7JxYNcZ4szCzFgxlhpZg1N292fu7JK8sqmd1HiNeZcNrj8+mmQTx+Vx8rQ8NDG4f4zbSk+wd94LuHYeZ+TjN5P1i6tUYVUMp/ZAP8XYNRZebudgnZfN+wPXd/h8khddxth37sZ72k3pvBdoXlMZlPWGqjytu/9rmV4GwPvbOmh06tx7ZRSWQdA/+EyleikmTIwRY4yOYqjG98spu/ElZJeP/GX3krjwvDP9FCVoVHG9ADPHWslNNfPWZ+20tgfnWmjM9EzGrXyAiKw4DtzzBsf/8tk5B/UMBg7hYLgYzn65n6qGDlbvdjNrbASjhg2eQUzQ3ZHpoDxIrsjFJgZPs4wzSV1y9LebOPjgO9jHDmXc6sU4LhtmdCxF+YIqrhdAE4L7royis0sG7LZ0/ojIiCX//ftIuGkMR361nsqH38PXFpyj51BToBXgwcPSw/uIihTcdvngKy7lshwvXgq0wXmU5nV2UrH4bY797hOS7iok7917sCYb37xBUc6kiusFSk0wcf3ESLYe9LDv6MDNfT2bKcpK7tO3kvHTK2lcWkbZ/BfpqAqbjpIBk0IKEe4ETFkV3DHTRlTk4NqFdalTqpeSSipDxBCj4wRde/kpSuc+T/PKg2T96hpy/nQDWkS/xmUqyoAYXL+ZAmT+RBtDYzX+vrFtQOe+nk0IQdr3ZjLmtbvw1LsovfZ5mlb03ljhUtTSJjm0bQS2hFbSRzYYHSfoamQNLlyD8qi1YWkZpde9gK+1k7x37iH161MHzV2PlPCjiutFsJgF914ZxalWneXbB3bu67nEXZVDweoHiMyJp+L+tzjyn+uR3sExH/b1T9poOpSBVUZSJsuMjhN0pbIUBw6yRbbBSYJH9/io/tkqKr++jKiCZMatXazuwaqEPFVcL9LYdAuXj7ayssTNsUb/bocWSJGZceS/v4ih903g+J8/Y/+dr9F1qi3oOYKp5LCHnVVd3HCZg3yte1pOq2w1OlbQfD79Jl/LHzTTbzz1Tvbd+gr1T28n5etTGLv0HnWrOCUsDI6f0AFy+ww7Nqvg5Y3tAz/39Ry0SDM5v59Pzp9uwFlcy95rn8O5/VjQcwSDu0vy2sftpCWYmDshknwtH/jntJzBYLBNv2n9tIa9Vz9He9kJRj51C9m/uhbNMrgahSjhSxXXfoi2adw+w86hei/r9nQalmPoV8dTsPx+hFlj380vc/yvW5D6pTVd583N7TS7dO690o7ZJIgSUQwXwymX5XTJ4A0sM4pbur+YfhMpLu2GGdKnU/u7j9n3lVcxxUZQsPJrJN6SZ3QsRbkgqrj20+WjrYzPtvD2lnZDTg9/LqowhXFrFhM/L5cj/3cd5Xf/45I5Tby72sOmfZ3MnRDJyNR/zmkdp43Dg4eD8qCB6YJj0Ey/afKwf+Gr1P72YxJvzWPcqgewj04yOpWiXDBVXPtJCMGiOVHYrIJn1rTR5TPuiNEcZyP3ua+Q/eg8WjfXsOeqZzn9cbVheQKhtV3nxfVtpA8xsWDav85pTSaZRBIp1Usv6cYautQp08su+ek3zWsqiXikBNeuOkb8+UZGPH4zJkeE0bEU5aKo4hoAMXaN+4uiqG308e7W4I8ePpMQgpTFkyhY8TVM0Vb2L3yVo49uDMvRxFJKXtrQRodH8tA1X25xKISgQCugmWaOyUvzWjNc+tNvdI+Pml+u5cDdbyATrIxb/QBJdxWqaTZKWFPFNUDGZ1uZnRfB6hI35ceMvwYYVZDMuNWLSbqzkGN/2My+r7xC57HwGln78b5Odld3cdt0O2lDzt0oYIQYQSSX9rScS3n6jbu6mbKbXqLuia0kL56E59eF2HITjY6lKP2mimsA3THTTlKsxvNr22jvNP5I0RRl7T699rebadt7gj1znqHhnfAoQidafPxjcztj081cVdj7qUGzMJMn8qiW1TTL5iAmDI6T8uQlOf1GSsnJV0rYU/Qs7qpmRj33FYY/Og+sl873qAxuak8OoAiL4KFrHLS06byyKXi9h/uSdHsBhWsXY8sdQuU3lnFwyVK8zcaevj4fr0/y7BoXZpPga1c50Po4PVigFWDBwnZ9e5ASBs82fRuRRJInLp3Rsp6TLioWvUXV9z7EcVkqhesfJOHGwTG9SBk8VHENsOHJZm6aYqP4oIetB42bnnO2yJwE8t+7j4yfzaFp+QF2z36alnWHjI51Th/u6ODwSR/3XmknwdH3LmoTNsaJcVTJKhrkpdMS8bg8Tq2sZYI2AauwGh0nIJqWH2DPlU/TsqGKrF9dw9i37iYiPdboWIoScKq4DoDrJ0aSk2zilY3tNDp9Rsf5gjBrpH1nBgUfPYA5PpLyu/5B1SMrQuoOO4fqvSzf4Wb6KCtTRvo/UrRQKySCCLbp2wYwXfBIKdnm24YdO/ki3+g4/eZtdVP57fepeOBtItJiGbdmcXdvYE0NWlIuTaq4DgCTJnjwGge6Lnl+bRt6iDV0iBqXzLhVi0l9eBonX9rF3quexbn1qNGxcHd1nw6Oi9L46iz7BX1thIhggjaBI/II9bJ+gBIGz1F5lHrqmahNxCzC+64vpz+u7r7e/1Ypad+fSf6H96u5q8olTxXXATI01sRds6I4cNzLu8Whd31TizST9X+uJm/pPehenbKbX+bwT1ficxlzKluXkufXumhw6iy+Ogp7xIXvmvkiHxs2in3FYT3vVUrJNn0b0USHdatDb0sHh763nP23vYpmNZP/wSIyfnIlmlW1MFQufaq4DqCZY6zMyotgxU4320Lo+uuZYmZkMX7jQ6Q8OJkTz+1g96ynaV5dGfQcH+5ws7Oqi4WX2xidZun7C87BIixM1CZSR11Yz3s9LA/TQAOTtEmYRPgVIiklje+Xs/uKpzj1+h5SvzWdwvUPEj0pzehoihI0qrgOICEEd8+yMzLFzAvr2zjSYFx7xPMxOSLI/s1c8j9YhMlh5cA9b3DwG+8GrX1iyWEPy4o7mD7KyrXj+9c3d6wYiwMHxXp4Hr3qUmebvo044sgVuUbHuWCeOicVX3ubgw++gyXZwbiVD5D1i6vQbBf3B5OihCtVXAeY2SR4+DoHUREaf/vQhbPD+PmvvYmeks64NYtJf2QWTZ8fefxj74AWqWNNXp5Z4yIrycR9c6L63ZXHJExM0iZxilPUyJoApQyeSllJCy1M1iaH1bxWqUtOvLiT3Vc8Rcv6KjJ/XsS4lQ8QVZhidDRFMUT4/PSGsRi7xjevd+Ds0HlypQuvgf2H+6JFmEl/ZBbj1j5IZE4Ch779Pvtve5X28lMBX1ebW+dvH7qIMAu+eX00VnNgRo6OEqOIJZZt+rawOnr1SR879B0kkkiOyDE6jt/a9tZTdtPLHH7kI6IKkync8BDDvn05wqx+vSiDl9r7gyR7qJlFRVFUHPfyxubQaTDRG/uYJPI/uI/sR+d1d3cqeobqn6/G2+oOyPv7dMlTq1w0uXQevs7h13xWf2lCY7I2mSaaOCRDcy7vuRyQB2illSnalLDoq9vV1E7VIyvYe81zuA83kfPYDYx95x5sOQlGR1MUw4X3GP8wM31UBEcbfKwqcZOeaGJ2Xmjfl1OYNFIWT2LIgrEc/c0G6p/aRuPbZWT8vIikOwv7NUfxnc862FfrZdEc+7/cRi5QRogR7GIX2/RtDBfDQ35gkFd62anvJJlkMkSG0XHOS/p0Try0i9pHN+FtdZPy0GTSfzQbc2xo78+KEkzqyDXIbptuIy/DzKub2qmsM77Bvz8sQ+zk/H4+BaseICI7nqrvLKfshhdxldRd1PttOdDJqt1uigoimDVAf2AIIZiiTaGVVipkxYCsI5D2yX200cZUbWpIH7U6tx5l77XPU/3jldjzkihc+yDZv56rCquinEUV1yDTNMGSax0MidZ4/CMX9c2h08GpL47xqeR/sIgRf7mJziOnKZ33PJXfep/Oo6f9fo8Dx7p4cUMbo4aZuWPmhTWKuFBZIouhDGWHvgOPDJ0uVGdzSze79F2kiTSGacOMjnNO7qomDi5ZStlNL+Ntaif36VsY+8492POGGh1NUUKSKq4GiIrU+Nb8aAB+/14rJ0+HT4EVmiDpznGM/+zrpH5zOo3L9lFy+ZNU/3w1XY3nv5ZccbyLvyx3khSj8Y15DsymgT1CE0IwwzSDdtrZrG8e0HVdLCklm/RNePBwuXa50XG+xHPCxeEffcTuK56ieVUlad+fyfjNX2fIgryQPsJWFKOp4mqQ1HgTP7g5Gq8PfveuM6wKLIA5JpKsX17FhC0Pk7iwgPqnt1My5XFqf/8JuL/8vVTWdfHn5U7iHRo/WBBDtC04u16ySOYycRkVsoIqvSoo67wQFbKCw/IwU7QpDBFDjI7zBW+rm6P/bwMl057g5N9LGHrfBCZsfZiMn1yJKerSuImAogwkVVwNlDbEzA9ujsbjlfx+mZNTreFVYAEi0mIY8dgNFG58iJhZ2dT+1yYivr2T+me3o3d2N804VO/lTx84ibV3F9ZYe3B3u4naRBJJ5GP9Y9pkcBpj+MMpnWzWN5NKKoWi0Og4AOhuL3VPbKVk6hMc++OnxM8dyfhPljD8v67DmuwwOp6ihA1VXA2Wnmjm+zdH4+7qLrChdBedC2EfncToFxeSv3wRcpiN6p+uomTaE2z/n9089n4r0TaNHy6IIS4q+LucSZi4ynQVXrxs1DeGxNxXXeqs860DoMhUZHjDCJ+rk+N/3cKuSX+j5pdriSpMoWD1A+Q+dSuRamqNolwwNRUnBGQmmfn+TdH84X0nv1vm5Irk8G0VFz0lHc9/5DNBZrHzub287RpKhMfJvbZ6ovXxgDGjSuNFPNO0aWzWN7NP7jP8Nm575B7qqadIKyJaRBuWo6upnfpntlP/zHZ8LW5iZ2cz7KlbiJ2ZZVgmRbkUqOIaIrKGmvnujdH88X0na6pzmOHSiQ9gY4WgEoLWcZksK4onSvq47eOttK7Yx66/fkLKg5NIWTIVy5CBHSl8LvkinxpRwxZ9C2kijTgRF/QMAA2y4Yv5t0b1D/accFH3xFZOvLATvb2L+OtGkfbdGTgmhuZoZUUJN2H62/vSNDzZzHdvisbtM/Pf77ZyrDE0G/33pb4tij8scxJpETxyRzzTXryFcWsWEzs7m2OPfcquSX+j6gcf0lZ2Mqi5hBDM0eZgwsQ63zp8Mvin4L3SyzrfOiKJZLY2O+gjbl276zj0nQ/YNflv1D1ZTPx1oyjc8BCjX1qoCquiBJA6cg0xOclmrs6sYsvJUfzm7VYWzYli2qgIo2P5RZeSlbvcrKvJISVe8O350STFdHdGiipMYdRzt9FR0cDxx7dy6s1STr5cQvT0DJIXTyLhhtFoloHvohQlopitzWa1vppd+i4mmyYP+DrPVKwX00wz87X5RIrgnCLXO700LtvPied34NpxHM1uIemuQoY9PE1dT1WUAaKKawhKtHfwv2+P5alVLp5Z08ahE17umGEf8Hmh/dHeqfPc2jZ2V3eRFXOaHy4cTqTly3ltoxIZ8dgNZP6iiFOv7eHECzupXPIulmQHQ++bQPKiy7CmDOw1yBwth1yZy065kwyZQbJIHtD1fa5Wr2Wv3Eu+yCdDG/gWh521pznx4i5OvlKCt6GdyBEJZP36WpLuHIc5RnVUUpSBpIpriIqL0vj+zdG8vaWdNbs7OXLSx5J5gW1wHyi1DV6eWOmi0alz50w7pqY9RFrOf1cXS4KdYf9rOqkPT6Nl3SFOPLuDY7//hGN/3ExcUQ6JCwuIv24UJvvADO6aqc2kzlfHGt8abjDdMODXXxtlI+v19cQRxzRt2sCtqMPHqX/speGtUk5/XA1A/NxckhdPInZ2dr/6QSuK4j9VXEOY2SS4c2YUOclmXlzXxn++eZolcx2MSQud0cRbDnTy8sY2bFbBDxZEk5tqYcMG/79eaIL4a0YSf81I3IebOfn3EhreKaPyG8vQoqwkzB9F4sICYmdlB/QWZhEigrmmuazwrWCZbxnzTPNIEQNz79FavZbV+mosWJhrmotFBPb/T+/ycXrDYRreKiVieTmHPDoRmXGkfXcGQ++ZQERGbEDXpyhK3/pVXIUQCcA/gGygGrhDStl81jIZwEtACqADT0kp/9Sf9Q42U0ZGkJ5g5vGPnPzhPSc3T7Exd0JkwO5/ejHa3DpLt3awsayTUcPMLJnr6HdziMjh8WT+vIiMn83BueUIDW+V0fjefhreLMUyNIoht+QRf10u0dMyAnJ9NkkkscC0gBW+FXzg+4Crtav7/Z5nO6gfZIO+gVhimW+aj0MEphGD3uml9bOjNH9UQeOyfXgbOzDH2/DNSWL8v83DMSVNtSdUFAP198j1J8BaKeWjQoif9Lz+8VnLeIEfSCl3CiGigR1CiNVSyn39XPegkppg4mcLY3lpQxvLijvYWObmpsk2ZoyJCOq1WHeXZO1uNytL3Lg9krnjI7l1ui2gGYQmiJmRRcyMLLJ/M5eWNZWcequUEy/spP6pbZiiI4gtGk78tbnEXZ2DJTHqotcVK2JZYFrAR76PWKWvYmhqYBrRSykpkSUU68UME8OYq80lQvRvYJrnhIuWtYdoXnWQ0xur0ds8iEgz8fNySVpYQGxRDps+/ZjoqekB+R4URbl4/S2uC4A5Pc9fBDZwVnGVUtYBdT3PnUKI/UAaoIrrBYq0CpbMdXBlfhdLt3Tw8sZ2Vpa4WTDVxuSRVrQBPFLp8kk2lXWyfEcHzg7J+GwLt0yzkT5kYK8saJFmEm4cQ8KNY/C5PJzedJjm1ZW0rK6k6b1yEOCYmEbc1TlEX56J47JhF3yd1iZs3Gi6kbX6WmpG1LDVt7Vft37Tpf5Fs4oRYgRFWtFF3U/W5/Lg2nmM1s+O0rL2EG09t/izpkaTeFs+8XNHEnNF9oBdl1YU5eKJ/rSCE0K0SCnjznjdLKWMP8/y2cAmoEBK2drLMkuAJQDJycmTXn/99YvK5nK5cDjCsxeqP9mlhGOuaHafTKGl00Z8RAfjh9YzzOEkkDVWl1B9Op49p5Jp67KSbHcxfmg9Sfbe74ATlG2vS0R1G9qOZkw7m9EOuQCQJoHMjkIfHY0+JgZ9TDTE+ddoXiI5lnmMtsw2ok9Gk3IwBU1e2KluXdOpG12Ha4iL+Np4kqqTEPj5H9LUiVbuRCtvRTvgRNS0IXSQAmRuNL6J8egT45FZdnr7Tw7n/R7CO3+oZC8qKtohpQzuHDPlS/osrkKINXRfLz3bz4AX/S2uQggHsBH4tZTyHX/CTZ48WW7fvt2fRb9kw4YNzJkz56K+1mgXkl2XkuKDHt4r7uBUq05agon8TAtj083kplqIOMd0mL60uXUOHPOyv7aLvUe6aHTqZCWZuHWanbwMc59HdEZse29zB87tx3AW1+IsPoprVx3S3d2Ew5oRi310IrbRSdhGJ3Y/z03E5Phy0V2/YT1xs+Mo1ouJI44ckUOWlkUSSb1+37rUOclJavQaqmQVrbQyU5tJgVZw7qzOTjoqGug40P1oP3CKjvJTeI47AdDsFhwThxE9NZ3oqek4JqX5fTPycN7vIbzzh0p2IYQqriGgz3N6UsprevucEOKEECJVSlknhEgFztlyRwhhAd4GXvG3sCr+0YRg+qgIJo+w8ml5J8WVHtbtcbOqBMwajEgxMzbdwtgMC8mx2jkPeKSEo40+9h/tYn9tF9WnfEgJERYYNczC7TPsTMyxhPQAGXO8jfhrRxJ/7UgAdI+Ptj31OItradtdR8eBBk5vqkZ6/tmVyZoRi214PJbUaKzJDqwpDkwNjYy052LLnkF5bCW7tF3slDuxYydTZJIpMkkX6UgktbKWGlnDEXkEN26EFKToyUxuLiSlJobGE/vxnHDRVe/CU+/EU+/CXdWE59g/T9qISDO2kUOInp6J47JUoqemYy9IDkpDDUVRBk5/L5i9B9wPPNrz77KzFxDdv5GfBfZLKf/Qz/UpvTCbBLPzI5mdH0lnl6SyrvvIc39tF+8Wd/BucUef72HSulsw3jjZRl66meyh5pBuXHE+mtVE9OQ0oienffEx6dVx1zTTUd5AR0X3EaO7uoWOT2roOuFCenWsQNkfKoDu0zWJCQLnVVZa53VRMXs/5dHliE4JGkiLwHRaErPBy9CVnUSv92A+3UAjZTSekUVYNCzJDqzJDmKmZ2Abk4RtVPcRdERWHMIUenOXFUXpn/4W10eBN4QQDwJHgNsBhBDDgGeklPOBmcB9wF4hREnP1/27lPLDfq5b6UWERZCfaSE/s3ugi7NDp/xYF6fber8EkBSrMXqYhUhreBZTfwizhm3EEGwjhsANo//lc1KXeJva+fSDDYzPHIOn3oW3xY3u7kJ2etF3ePFu7aIptZ1To9oROiRV2Imvt2O2WtGGm9DGWhARZswJNqxDu4+ELckOzAm2kD7qVxQl8PpVXKWUjcCXJgdKKY8D83uefwL+juhQBkK0TWPKyPDoT2wUoQksiVHI7Cji5ozodbl/+cz1Ax5LUZQwpc5HKYqiKEqAqeKqKIqiKAGmiquiKIqiBJgqroqiKIoSYKq4KoqiKEqAqeKqKIqiKAGmiquiKIqiBJgqroqiKIoSYP26K85AE0KcAmou8ssTgYYAxgmmcM4O4Z0/nLODym+kUMmeJaVMMjrEYBfSxbU/hBDbw/XOEOGcHcI7fzhnB5XfSOGcXQk8dVpYURRFUQJMFVdFURRFCbBLubg+ZXSAfgjn7BDe+cM5O6j8Rgrn7EqAXbLXXBVFURTFKJfykauiKIqiGEIVV0VRFEUJsLAurkKI64QQB4QQlUKIn5zj80II8eeez+8RQkw0Imdv/Mg/RgjxmRCiUwjxQyMyno8f+e/p2e57hBCfCiHGG5HzXPzIvqBiMIpTAAADh0lEQVQnd4kQYrsQ4gojcvamr/xnLDdFCOETQiwMZr7z8WPbzxFCnO7Z9iVCiF8YkbM3/mz7nu+hRAhRJoTYGOyMSgiQUoblAzABh4AcwArsBvLOWmY+sAIQwHRgq9G5LzD/UGAK8Gvgh0Znvoj8M4D4nufXh8r29zO7g3+OSSgEyo3OfSH5z1huHfAhsNDo3Bew7ecAHxidtR/544B9QGbP66FG51aP4D/C+ch1KlAppaySUnqA14EFZy2zAHhJdtsCxAkhUoMdtBd95pdSnpRSbgO6jAjYB3/yfyqlbO55uQVID3LG3viT3SWl/Hy0XxQQSiP//Nn3Ab4NvA2cDGa4PvibPVT5k/9u4B0p5RHo/jkOckYlBIRzcU0Djp7xurbnYxe6jFFCOZs/LjT/g3SfRQgFfmUXQtwqhCgHlgOLg5TNH33mF0KkAbcCTwYxlz/83W8uF0LsFkKsEELkByeaX/zJPwqIF0JsEELsEEIsClo6JWSYjQ7QD+IcHzv76MKfZYwSytn84Xd+IUQR3cU1VK5b+pVdSrkUWCqEmA38CrhmoIP5yZ/8jwE/llL6hDjX4obxJ/tOuvvjuoQQ84F3gdwBT+Yff/KbgUnA1YAN+EwIsUVKWTHQ4ZTQEc7FtRbIOON1OnD8IpYxSihn84df+YUQhcAzwPVSysYgZevLBW17KeUmIcQIIUSilDIUGrP7k38y8HpPYU0E5gshvFLKd4MTsVd9ZpdStp7x/EMhxONhtu1rgQYpZRvQJoTYBIwHVHEdRML5tPA2IFcIMVwIYQXuAt47a5n3gEU9o4anA6ellHXBDtoLf/KHsj7zCyEygXeA+0Lsr3Z/so8UPZWpZ5S5FQiVPw76zC+lHC6lzJZSZgNvAd8MgcIK/m37lDO2/VS6f0+FzbYHlgGzhBBmIYQdmAbsD3JOxWBhe+QqpfQKIb4FrKR7BN9zUsoyIcQ3ej7/JN2jJOcDlUA78IBRec/mT34hRAqwHYgBdCHEd+kemdja6xsHiZ/b/xfAEODxnt+VXhkCdw3xM/ttdP9h1gV0AHeeMcDJUH7mD0l+Zl8IPCyE8NK97e8Kp20vpdwvhPgI2APowDNSylLjUitGUO0PFUVRFCXAwvm0sKIoiqKEJFVcFUVRFCXAVHFVFEVRlABTxVVRFEVRAkwVV0VRFEUJMFVcFUVRFCXAVHFVFEVRlAD7/8ZE2FY7MLv/AAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N = 45\n",
"dx = L/(N+1)\n",
"k = T/dx**2/mu\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",
"x=np.linspace(0,L,N)\n",
"\n",
"e,v = linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e = e[isort]\n",
"v = v[:,isort]\n",
"\n",
"w1 = np.sqrt(e[0].real)/2/np.pi\n",
"w2 = np.sqrt(e[1].real)/2/np.pi\n",
"w3 = np.sqrt(e[2].real)/2/np.pi\n",
"\n",
"v1 = v[:,0]/max(v[:,0])\n",
"v2 = v[:,1]/max(v[:,1])\n",
"v3 = v[:,2]/max(v[:,2])\n",
"\n",
"f1=np.sqrt(e.real[0])/2/np.pi\n",
"fn=np.sqrt(e.real[-1])/2/np.pi\n",
"\n",
"print('Natural frequencies of {}-element string (Hz)'.format(N))\n",
"print(e.real[0:3]**0.5/2/np.pi)\n",
"print('\\n')\n",
"print('The longest time period is {:1.4f} ms \\n'\n",
" 'The shortest time period is {:1.4f} ms'.format(1/f1*1000,1/fn*1000))\n",
"print('\\n')\n",
"\n",
"plt.plot(x,-v[:,0],'-',color='mediumvioletred',label='1st mode');\n",
"plt.plot(x,v[:,1],'-',color='cornflowerblue',label='2nd mode');\n",
"plt.plot(x,-v[:,2],'-',color='palegreen',label='3rd mode');\n",
"plt.grid();\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 60-element string (Hz)\n",
"[196.05687232 391.9837462 587.65070938]\n",
"\n",
"\n",
"The longest time period is 5.1006 ms \n",
"The shortest time period is 0.1314 ms\n",
"\n",
"\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
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"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N = 60\n",
"dx = L/(N+1)\n",
"k = T/dx**2/mu\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",
"x=np.linspace(0,L,N)\n",
"\n",
"e,v = linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e = e[isort]\n",
"v = v[:,isort]\n",
"\n",
"w1 = np.sqrt(e[0].real)/2/np.pi\n",
"w2 = np.sqrt(e[1].real)/2/np.pi\n",
"w3 = np.sqrt(e[2].real)/2/np.pi\n",
"\n",
"v1 = v[:,0]/max(v[:,0])\n",
"v2 = v[:,1]/max(v[:,1])\n",
"v3 = v[:,2]/max(v[:,2])\n",
"\n",
"f1=np.sqrt(e.real[0])/2/np.pi\n",
"fn=np.sqrt(e.real[-1])/2/np.pi\n",
"\n",
"print('Natural frequencies of {}-element string (Hz)'.format(N))\n",
"print(e.real[0:3]**0.5/2/np.pi)\n",
"print('\\n')\n",
"print('The longest time period is {:1.4f} ms \\n'\n",
" 'The shortest time period is {:1.4f} ms'.format(1/f1*1000,1/fn*1000))\n",
"print('\\n')\n",
"\n",
"plt.plot(x,v[:,0],'-',color='mediumvioletred',label='1st mode');\n",
"plt.plot(x,-v[:,1],'-',color='cornflowerblue',label='2nd mode');\n",
"plt.plot(x,v[:,2],'-',color='palegreen',label='3rd mode');\n",
"plt.grid();\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**DISCUSSION**\n",
"_The number of nodes needed to converge for the first three modes is about N=30._"
]
},
{
"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": 11,
"metadata": {},
"outputs": [],
"source": [
"N = 30\n",
"L = .64\n",
"T = np.array([T_e,T_b,T_g,T_d,T_a,T_E])\n",
"mu = np.array([d_e,d_b,d_g,d_d,d_a,d_E])\n",
"dx=L/(N+1)\n",
"\n",
"x = np.linspace(0,L,N+2) "
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"------NATURAL FREQUENCIES (30 ELEMENT)------\n",
"\n",
"\n",
"e string:\n",
"1st natural frequency = 329.5582417096115 Hz\n",
"2nd natural frequency = 658.2705121393168 Hz\n",
"3nd natural frequency = 985.2930116053443 Hz\n",
"\n",
"\n",
"b string:\n",
"1st natural frequency = 246.99641153429778 Hz\n",
"2nd natural frequency = 493.35878682265803 Hz\n",
"3nd natural frequency = 738.4547171810427 Hz\n",
"\n",
"\n",
"g string:\n",
"1st natural frequency = 195.99355421041057 Hz\n",
"2nd natural frequency = 391.4839957781058 Hz\n",
"3nd natural frequency = 585.969503543348 Hz\n",
"\n",
"\n",
"d string:\n",
"1st natural frequency = 146.85180950460807 Hz\n",
"2nd natural frequency = 293.32665252038413 Hz\n",
"3nd natural frequency = 439.048530226062 Hz\n",
"\n",
"\n",
"a string:\n",
"1st natural frequency = 109.98239925642098 Hz\n",
"2nd natural frequency = 219.6824752713306 Hz\n",
"3nd natural frequency = 328.8186295229268 Hz\n",
"\n",
"\n",
"E string:\n",
"1st natural frequency = 82.41968979777636 Hz\n",
"2nd natural frequency = 164.6278094339143 Hz\n",
"3nd natural frequency = 246.41333184434473 Hz\n"
]
}
],
"source": [
"k_e = T[0]/dx**2/mu[0]\n",
"lilE = 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",
"e_e,v_e = linalg.eig(lilE)\n",
"isort_e = np.argsort(e_e.real)\n",
"e_e = e_e[isort_e]\n",
"v_e = v_e[:,isort_e]\n",
"\n",
"k_b = T[1]/dx**2/mu[1]\n",
"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",
"e_b,v_b = linalg.eig(B)\n",
"isort_b = np.argsort(e_b.real)\n",
"e_b = e_b[isort_b]\n",
"v_b = v_b[:,isort_b]\n",
"\n",
"k_g = T[2]/dx**2/mu[2]\n",
"G = k_g*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"e_g,v_g = linalg.eig(G)\n",
"isort_g = np.argsort(e_g.real)\n",
"e_g = e_g[isort_g]\n",
"v_g = v_g[:,isort_g]\n",
"\n",
"\n",
"k_d = T[3]/dx**2/mu[3]\n",
"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",
"e_d,v_d = linalg.eig(D)\n",
"isort_d = np.argsort(e_d.real)\n",
"e_d = e_d[isort_d]\n",
"v_d = v_d[:,isort_d]\n",
"\n",
"k_a = T[4]/dx**2/mu[4]\n",
"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",
"e_a,v_a = linalg.eig(A)\n",
"isort_a = np.argsort(e_a.real)\n",
"e_a = e_a[isort_a]\n",
"v_a = v_a[:,isort_a]\n",
"\n",
"k_E = T[5]/dx**2/mu[5]\n",
"bigE = 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",
"e_E,v_E = linalg.eig(bigE)\n",
"isort_E = np.argsort(e_E.real)\n",
"e_E = e_E[isort_E]\n",
"v_E = v_E[:,isort_E]\n",
"\n",
"T_e,T_b,T_g,T_d,T_a,T_E\n",
"w_lilE = e_e.real**0.5/2/np.pi\n",
"w_b = e_b.real**0.5/2/np.pi\n",
"w_g = e_g.real**0.5/2/np.pi\n",
"w_d = e_d.real**0.5/2/np.pi\n",
"w_a = e_a.real**0.5/2/np.pi\n",
"w_bigE = e_E.real**0.5/2/np.pi\n",
"\n",
"print('------NATURAL FREQUENCIES (30 ELEMENT)------')\n",
"print('\\n')\n",
"print('e string:')\n",
"print('1st natural frequency =',w_lilE[0],'Hz'\n",
" '\\n2nd natural frequency =',w_lilE[1],'Hz'\n",
" '\\n3nd natural frequency =', w_lilE[2],'Hz')\n",
"print('\\n')\n",
"print('b string:')\n",
"print('1st natural frequency =',w_b[0],'Hz'\n",
" '\\n2nd natural frequency =',w_b[1],'Hz'\n",
" '\\n3nd natural frequency =', w_b[2],'Hz')\n",
"print('\\n')\n",
"print('g string:')\n",
"print('1st natural frequency =',w_g[0],'Hz'\n",
" '\\n2nd natural frequency =',w_g[1],'Hz'\n",
" '\\n3nd natural frequency =', w_g[2],'Hz')\n",
"print('\\n')\n",
"print('d string:')\n",
"print('1st natural frequency =',w_d[0],'Hz'\n",
" '\\n2nd natural frequency =',w_d[1],'Hz'\n",
" '\\n3nd natural frequency =', w_d[2],'Hz')\n",
"print('\\n')\n",
"print('a string:')\n",
"print('1st natural frequency =',w_a[0],'Hz'\n",
" '\\n2nd natural frequency =',w_a[1],'Hz'\n",
" '\\n3nd natural frequency =', w_a[2],'Hz')\n",
"print('\\n')\n",
"print('E string:')\n",
"print('1st natural frequency =',w_bigE[0],'Hz'\n",
" '\\n2nd natural frequency =',w_bigE[1],'Hz'\n",
" '\\n3nd natural frequency =', w_bigE[2],'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": 13,
"metadata": {},
"outputs": [
{
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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": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Audio\n",
"\n",
"samplerate = 20000\n",
"t=np.arange(0,3,1/samplerate)*100\n",
"\n",
"e_audio = (np.sin(t*w_lilE[0]**0.5)+np.sin(t*w_lilE[1]**0.5)+np.sin(t*w_lilE[2]**0.5))\n",
"b_audio = (np.sin(t*w_b[0]**0.5)+np.sin(t*w_b[1]**0.5)+np.sin(t*w_b[2]**0.5))\n",
"g_audio = (np.sin(t*w_g[0]**0.5)+np.sin(t*w_g[1]**0.5)+np.sin(t*w_g[2]**0.5))\n",
"d_audio = (np.sin(t*w_d[0]**0.5)+np.sin(t*w_d[1]**0.5)+np.sin(t*w_d[2]**0.5))\n",
"a_audio = (np.sin(t*w_a[0]**0.5)+np.sin(t*w_a[1]**0.5)+np.sin(t*w_a[2]**0.5))\n",
"E_audio = (np.sin(t*w_bigE[0]**0.5)+np.sin(t*w_bigE[1]**0.5)+np.sin(t*w_bigE[2]**0.5))\n",
"\n",
"Audio(data=e_audio+b_audio+g_audio+d_audio+a_audio+E_audio,rate=samplerate)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
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