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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": 148,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A matrix:\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",
"B matrix:\n",
" [-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00\n",
" -7.86390528e-05 1.57278106e-04]\n"
]
},
{
"data": {
"text/plain": [
"'Converges'"
]
},
"execution_count": 148,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"'''A'''\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy import linalg\n",
"L=0.64 #m\n",
"E=10e9 #Pa\n",
"A=0.02*0.04 #m^2\n",
"I=((0.04*0.02**3)/12) #m^4\n",
"N=6 #steps\n",
"h=L/N\n",
"Mend=(7.28+7.22+7.32+8.41+9.03+7.71)*9.81*0.004\n",
"\n",
"xanal=np.linspace(0,0.64,1000)\n",
"wanal=(Mend/(2*E*I))*x**2\n",
"\n",
"A=np.diag(np.ones(N12)*6)\\\n",
"+np.diag(np.ones(N12-1)*-4,-1)\\\n",
"+np.diag(np.ones(N12-1)*-4,1)\\\n",
"+np.diag(np.ones(N12-2),-2)\\\n",
"+np.diag(np.ones(N12-2),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]=(-Mend*(h**2)/(E*I))\n",
"b[-1]=(2*Mend*(h**2)/(E*I))\n",
"\n",
"wnum=np.linalg.solve(A,b)\n",
"xnum=np.arange(0,L+h,h)\n",
"x=np.linspace(0,L)\n",
"\n",
"print('A matrix:\\n',A,)\n",
"print('\\nB matrix:\\n',b)\n",
"\n",
"plt.plot(xnum, np.block([0,wnum*1000]),'o',label='Numerical Solution')\n",
"plt.plot(x,wanal*1000,label='Analytical solution')\n",
"plt.title('6 Step FDM Beam Deflection')\n",
"plt.ylabel('Deflection (mm)')\n",
"plt.xlabel('Location (m)')\n",
"plt.legend(bbox_to_anchor=(1,0.5), loc='center left');\n",
"'''Converges''' #can be altered by changing N"
]
},
{
"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": 149,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First 3 Natural frequencies of 6-element string (Hz)\n",
"[194.43708661 379.1242858 544.80061022]\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": [
"'''2a'''\n",
"'''G string'''\n",
"from scipy import linalg\n",
"#6 node\n",
"N=6\n",
"L=0.64 #m\n",
"mu=1.14e-3 #g/m\n",
"T=71.81 #N\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",
"e,v=linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e=e.real[isort]\n",
"v=v.real[:,isort]\n",
"print('First 3 Natural frequencies of {}-element string (Hz)'.format(N))\n",
"print(e.real[:3]**0.5/2/np.pi)\n",
"\n",
"x=np.linspace(0,L,N)\n",
"plt.plot(x,v[:,0],label='1')\n",
"plt.plot(x,v[:,1],label='2')\n",
"plt.plot(x,v[:,2],label='3')\n",
"plt.legend(prop={'size':15});"
]
},
{
"cell_type": "code",
"execution_count": 150,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First 3 Natural frequencies of 30-element string (Hz)\n",
"[195.99464595 391.48617646 585.97276757]\n"
]
},
{
"data": {
"image/png": 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p4d+C5yOev80ZJuRnwZL7jW2O3XzhwWVKt0or8WSnJ9UhfczNGH6P/f02Z9gAF1eY8D20HWfct/dLpcOnoNaz7Owy9YPa392fv3Wo4lqnDZEkidd6v0Yjn0YAZBZkMvvgbI1VVQ5bO5mSmNusCo7JNHz3re5NJElyBRYB/sBWWZbX3ub4Jwwh1FHXrmmf9PTXtb/UjGOdpOODgR/g6epZuZOLi+HXJ5SSMQCSC0ycD/WtW203wDOAqe2nqvaXR7+0j7pLLnq470dlLaqE9S/A1ePaaRJoTmZ+Jt8cM/YqeqLjE2oRWHvFx82H/w74r2pvubiFmNQYDRVVDls7mZLVZmvPV3wNDAUSqMSivyzL38qy3EOW5R5BQdoPl7/7yxiuPCpsFK3rta78yVtKhSqP/hDC77SguvJ5pP0jaoXaq1lX+eX0Lza5721x0StTZ8HtFLswF5Y9orR+FtRKfj75M6l5qQA08G7A5DaTNVZUOboEd2Fw48Gq/f2J78s/2E6wtZMxLBBQURZhyWsZFRxTLpIkfQ5MQwmRHirL8tXqXEcrzqScYful7ar9eMfHK39y1I+wxzjHTJ+ZEPGY5cTdBm+9N092elK1vzv+nVomXXPcvGDSAihJYE2JhTUzxfpMLeR6znV+jv5ZtWd2nYm7i7uGiqrG452MnwkbLmzgYrp991SytZOJM3xvVsExJdUe4yo4pkwkSfoYeAa4huJgzt3mFLvDNOlyWLNhtKjTooKjTYjZAutM1m1a3wXDbJ+HOrHVRBr7KMF8aXlp/HTiJ5trKJfAcCU/qISTq2H/N+UfL3BKvjn2DTmGun0t67TkrjDHKg3UKagTfRr0AZQQbM1qB1YSWzuZkpDi9pIklbfIEFHq2EohSdKHKJn/N4BhsiyfrJ5E7YhNi2VT3CbVrvQoJumkeahygy4w4TsllNfG6F30zOo6S7UXnVxEcrYdJfh1vM98dLfpVbgUpZ0egU1JSE9gxdkVqv1s92dt26rCQjzR6Ql1e835NVzJtN8AWps6GVmWE4DDgBswsfTrkiQNQslpuQrsLf16eUiS9F/gBSAVxcEcs4hgG/PD8R/UPuIDGg2gbUDb25+UnVIqVLmRIVTZ24pKK2Zk2Eja1lO05xblMu/YPM20lMmI95ScIYDiAlg+Vfk9CpyeL458oTb7616/OwMaDdBYUfXoEdKDbsHdAKUSwE/RdjRjUAotMv5L0lU/kCSpZclOSZKCga8M5n9lWS42ee19SZJOS5J0S6qrJElvAy8BN1EcTJVGQPbCpYxLrIs1NsAyfVKpkPXPQ5phTtbNBx5YBn4NrKCw8ugkHf/X7f9Ue9W5VVxIu6CholK4uisRdx7+ip2WAKuerBXtAZYvX864ceNo1KgRPj4+dO/enSVLlmgtyyZE34hmQ9wG1X62+7OaFcC0BKafESvPruR6znUN1ZSPzZ2MLMsrgHkoWf3HJUlaK0nSr8A5oB3wG0qhTFMaAK0N31UkSRoHlKTCxgCzJEmaX8aX3beW+/HEjxQZprt6hfSiS3CX2590fAWcMEkBGv81hFi3e19l6dOwD70a9AKgSC4yS3qzC+qGwj1fG+1zm2D3p5rJsRWffPIJPj4+fPrpp6xZs4YhQ4bwwAMP8MUXdvb3sQKfHzKuxw1tOpTOQZ01VFNz+jbsS/sAJTUhvzjfbqs0a1KFWZbl6cCDKFNng4ARKE5iJjBBluXKpoublhDuATxaztdIyyi3DklZSfwW85tqm0aPlEv6ZVj3T6Pd5SFoq0E/l3KQJIlnuz2r2pvjN6utCuyGNqOh7zNG+8934MItZfCcirVr17J48WImTZrEHXfcwezZs5kyZQqffPKJ1tKsyp7Le8xyz57p+sxtzrB/JEky+6z45cwv3My9qaGistGsn4wsy4tlWe4ny7KfLMvesix3l2V5ruk0mcmxU2VZlmRZnlpq/3zD/tt9DbbVz1Ud5kfPp6C4AIDOQZ3pGdKz4hNkGVbPhJI3lH9TpW2yndE+sD0jQkeo9meHPtO2eGZZDH0dmiqROsjFSs+djCRtNVmRwMDAW/Z17drVqasvF8vFfHbIWARzfMvxNK/TXENFlmNIkyFqu42cwhwWnVqksaJbcbw2a07GjZwbZtEuT3R64vbzxAe/h/NbDYYE4+eBh5/1RNaAWV1n4SopxTOjkqLYlbhLY0WlKKkI4GX48M1MUhyN1rXXbMiePXto166d1jKsxqa4TZxKOQWAu4u7XRbBrC46SWe2NrP49GIy8quVYmg1RPtljVl4cqFao6xtvba3j3a5HgObXjPafWZAaH8rKqwZzfyaMaHVBJaeUTpyfnr4U/o27GtfYaN+DZUaZwvHAzLERcK292Doa7c9lTf9rS7v9hrSqn3q1q1bWb16NT/++KMFBdkPBUUFzDkyR7UfbPtg1SqZOwDDmw1nrt9c4tPjycjPYOmZpTzW0XZJ2LdDjGQ0JC0vjV/OGEuvPN7p8YpHMUWFShSUIZGM4HZwRyU+CDXmqc5PqbXXzqWeY/2F9RorKoMWQ2CwSXxI5Gw4t0U7PTYgLi6OBx54gLvvvpupU6dqLccqrDi3goQMpVCsn5ufWadJZ8FF58K0DtNUe0H0ArtqbCacjIYsPr2YrAKlVmhz/+a3L+W/61NINCQO6vRKzxS9h5VV1pxAz0Aebvewan9//Hv7W5sBGPgCNDdporpmJuRWf5Rgz6SkpDBq1CiaNm3KokX2N49vCYqKi5h/Yr5qP9bxMfzd7WDkaQXGtBhDA28l+DY1L9VsCl5rxHSZRmQVZLHopPGf+/FOj6OrqBno5SOww1iBlcEvQ4NOVlRoWaa2n8qik4vILswmNi2WqKQoIkIibn+iLdG5KNNmX/WGrGuQcQW2vAVjKoi8qsFUlVZkZ2czZswY8vPzWbduHd7e2iXuWpNdibu4nHUZgDrudZjSZorGiqyHXqdnWodpvLP/HQB+jv6ZyW0m20VNNjGS0YhlZ5apxSMb+zRmZGgFUdYFOfDrk1CsZCrTuCf0+7/yj7dDfN18GdPcWG6/ZI3G7vAOhFEfGu2oH+DiPu30WJjCwkImTpzIuXPn2LBhA8HBwVpLshqmU9Hjw8fj4Wr/o/6acE/4PQR5KlXkk3OSWR2zWmNFCsLJaEBuYS7zo+er9mMdH1PbF5fJ1rfh+hllW++tJF26ON4gdFLrSer21vitdpuhTPvx0MrE6a95BgrtoDeOBZg+fTrr16/ntddeIyUlhX379qlfeXnO8TMCJGQksDtxNwASklnnVmfF3cWdR9s/qto/HP9BTY3QEuFkNGDluZWk5Cq1sup71Wdci3HlH3xhJ+yba7RHvAMBlazMbGe0rtearsFKzbBCuZCVZ+20YakkwV0fG9sCXD8Dkc6RrLhpk1KA9R//+Ad9+vQx+7pyxX6LLFaV5WeXq3UA+zXqRxPfJrc5wzmY2GoiddzrAHA56zLrY7UPshFOxsYUFBWYlb//W4e/oXfRl31wbhqsMonpDx8O3e23RWxlmNza2Bxq+dnlFJZMAdob/o1h6BtGO/JjKNL+qbCmxMXFIctymV+hoaFay7MIeUV5rDq3SrXvb32/hmpsi5fe65YgmyKNc76Ek7Exa86vISlbySiv51GPCeETyj94w0uQfknZ9qwL475QnrIdmGHNhqndM5Oyk9h5aafGiiogYho0NgQnFBdATopocuYAbIrbxM08pRpGQ++G9G9kv3lk1mBKmyn46pVW0nHpcWyO36ypHuFkbEhhcSHfHze2S53afmr5i5Gn1sIxk+q4Yz4F3xArK7Q+bi5ujG85XrXtNgAAlGizcV8o4eKgrMtk2+k6kkDF9D01sfVE+0r8tQG+br5MaWuMpPv2+LcU31qty2YIJ2NDIi9FcilTGZn4u/ubLYSbkZcB618w2h0nKYvRTsLE1hORUEZkey7vIT49XmNFFRDcFvobC32SfhkK87XTI6iQ0ymn1UKsrjpXswea2sRDbR8yS4COuqpdYz7hZGzIr+d+VbfvC78Pb305+Qk7PlRyNAC8g2H0h2Uf56A08mnEwMYDVXv5meUaqqkEA5+HwFbKtlys9J8R02Z2iekoZniz4QR4BmioRjvqetTl7hZ3q/bKc9oF2QgnYyOSspLYmWhcf7g3/N6yD7x2BvZ9ZbSHv62sxzgZpqO4VTGryC3M1VDNbXB1h7HG+lfkpRsrYAvshoz8DLPGf6ZBJrWRCa2M671b4reQlqdN4rBwMjZizfk16rxoz5CeNPVreutBsqx0uiyJuGraBzo55z9Kv4b9aOTTCID0/HQ2xm3UWNFtaNYH3H2Mdtol499JYBesOb+GHENdv/C64Wq4fG2lTb02tAtQqmvnF+ebOWBbIpyMDSiWi1kVYwypHB9ezjxx9ColLwZAcoHRsx0+mqw8XHQuZglyy84s01BNJfGoYwwCKC5U1mcEdoEsy2bvocmtJjt0a2VLcW9L44zJynMrNakZKJyMDYi6GqVWgvV18+XOpnfeelBeJvzxitHu+YTdtFK2FuPDx6M3fGgfv36c6BvRGiu6DZJOyZ8pIfuGEqQh0JyopChi02IB8HL1YkyLMbc5o3YwqvkoPFyUCNazqWc5eeOkzTUIJ2MDTBfdxjQfU3bY8s4PIcPwZOwdDEP+ZSN12lHPo55Z50yHGM141gEPk0q+NxOgWLvwUIGC6YL/2BZjyw+qqWX4ufkxPHS4amsRACCcjJVJy0tjS7yxL0mZyZfXzsBek9Ixw982/yBzYkwXZ9fHrtdscbJK+DdWpjMBivIg86q2emo517KvsTV+q2rX9gX/0pgGGa2/sN7mvWaEk7Eyv8f+Tn6xklfRPqA9reu1Nj9AlpWcmFqw2F8WnYM607qu8jvJLcplzfk1GiuqBC5uSjfNEjKTlUrZDsCKFSvo27cvAQEBeHh40Lp1a9555x3y8x0392fluZUUysr/T7fgboTXDddYkX3RLbgboX6hgNJiZFP8JpveXzgZKyLLstnwtMyw5ehVcGGHsu3ki/1lIUkSk9sYneqyM8vss6FZabwCjAU0kSE9UVM5leXGjRsMGTKE77//ng0bNvD3v/+dd999l+eee05radWisLjQrEHX/W1qT52yyiJJktlnj2ldN1vgePXiHYjoG9GcSz0HgKerJ6PDRpsfcMti/+NOv9hfFneF3cXHUR+TVZBFXHoc+6/up3eD3lrLqhhJUqbNrp1W7LwMyE0HDz9tdd2GJ5980sweMmQI6enpzJ07ly+++MLhIrJ2XNphVguwzKAaAWNbjGXO4TkUyoUcTj5MbFoszf2b2+TeYiRjRUwz/Ic1G4aPm4/5AaUX+wc7/2J/WXjpvczaHSw9bcf1zEzReyojmhLSLykVARyMgIAAh50uM32vTAifUH5F81pOoGcgg5oMUm1bjmaEk7ES2QXZrL9g7OVwy4J/6cX+Yf9RIpdqKaaLtdsStpGUlaShmirg28AYBFCYB1k3tNVTSYqKisjOzmbXrl3MmTOHp59+2uFGMfHp8ey9shcAnaTjvlb3aazIvjGdMltzfg0FNmpdIabLrMSm+E1kFWQBEOoXap59XNZif+faPZfcok4LetTvQVRSFEVyESvPrWR6l+lay7otHRd101oCxx89XuVzvL291U6YjzzyCB999JGlZVkd05D3gY0G0tCnYQVHC/o17EewVzDJ2cmk5Kaw/dJ2hjUbZvX7ipGMlTCdKpsQPsH8KfHkbyaL/ToY/VGtWuwvD9MAgBVnV9hF61hnZc+ePURGRvLxxx+zevVqZs6cqbWkKpFbmMtvMb+ptul7R1A2LjoXs6rUtsqZEU7GCsTejOVI8hEAXCVXxrYYa3wxLxM2/tto93wCQjraWKF9MrTJUAI9AwG4lnON7QnbtRXkxHTr1o3+/fvz3HPPMWfOHObNm8f58+e1llVpNsZtJD0/HYDGPo3p27Cvxoocg/Hh441tNhL3cDXL+jleYrrMCpiOYoY0HWJebnznRyaL/UG1drG/LPQueu4Nv5dv//oWUBZ1bTGcrwnqVJUsw40YyM9UbHc/CGihnbAq0K2bMuV34cIFWrRwDM2mC/6TWk9CJ4nn5crQyKcRvRv0Zu+VvcjIrIpZxdOdn9IGJdUAACAASURBVL79iTVA/GUsTEFRgVlCoVnTpBvnSy32v12rF/vLYmKrieoHxv6r+7mQdkFjRZVEksCvkdHOS1dCmh2A3bt3AxAWFqaxkspx8sZJTtw4AYCbzo17Wt6jsSLHonTOTFFxkVXvJ5yMhdl+aTupeakA1Peqbz6M3/Km0iseoEnvWr/YXxYh3iFmDc1+j/1dQzVVxM2rVEhzot2FNI8cOZLZs2ezYcMGNm3axBtvvME///lPJk+e7DCjmLXn16rbw0OHU9fD+fotWZM7mt6Bv7tStupK1hX2X9lv1fsJJ2NhTBfTxoePN/YXv7gfTpmUTBnxnljsLwfTjn7rYtdp2p+8yvg2UII5AApz7S6kOSIigvnz5zNx4kQmTZrE2rVref/991m4cKHW0ipFYXGhWWqAaX6VoHK4ubgxtrlxndjaAQDCyViQK5lX2JO4BwAJyTiMl2XY/JrxwPb3QuPuGih0DAY2Hoivmy8AiZmJHE0+qrGiKuCiB58Qo51xBYrsp7nZ22+/zYkTJ8jMzOTmzZscPnyYWbNmodc7RhLjnst7SMlNASDYM5ieIT01VuSYmE6Z/ZnwJ6m5qVa7l3AyFuS3mN+QUepu9WnYR+38yKm1kGAYkur0MPR1jRQ6Bm4ubmYtANbGrq3gaDvEO0gpogkgF4kqzRbEdPp0dPPRxpkCQZUIrxtOp6BOgDI6NJ2CtDTCyViIouIis+6X6pNCUYGyFlNCz8ehnmMssGqJ6XD+j7g/yCvK01BNFdHpzIMAsq5DQa52epyErIIstl3cptpjmovGZDXBtArJr+d+tVphWuFkLMS+K/u4knUFgDrudRjSZIjywqH5kGLIP3D3h4EvaCPQwegS3EUdCWbkZxB5KVJjRVXEw98hqzTbM1vit5BbpDjr8Lrht7bNEFSJEaEj8HT1BOB82nmOXTtmlfsIJ2MhTBfPxrYYi5uLmxLCuv2/xoMG/hO86mmgzvHQSTruan6XaltzOG8VHDik2V4xnTY1HekKqoe33ptRYaNU2zS/z5IIJ2MBUnJT2JZgHMbf29IwVbb7c8i+rmz7N4GeT5ZxtqA8TKdDdibutIuumVWaUnDzMn+oSE9UgkAcEK17/FzNusqBKwcAJajmlrYZgmphGgCwMW6jWm/RkggnYwHWnl9LoaHYZeegzrSs2xLSL5snXt7xGug9NFLomIT5h9EhQOmvU1hcyB9xf2iqR6/Xk5NTxQ6Yvg3NQ5pLHjocjJycHE0j0DZc2KAG1fRs0JP63vU10+JMdArsRMs6LQHIKcxh44WNFr+HcDI1RJblW4phArDtXSg0fCCFdIKOEzVQ5/iMaWEczWg9ZRYcHExiYiLZ2dmVf7J30YOPyQdixlWwcoa1JZFlmezsbBITEwkODtZMh5gqsw6lu2ZaY8pM1C6rIXlFefRt2JcbuTcoKCpQQm+TouHI/4wHDX9biTgSVJmRoSP56OBHFMlFHL12lISMBJr4NtFEi5+f0vXy8uXLFBRUoUK0LENGirG1w5UsJTDAQdDr9dSvX1/9+W3NmZQzaodZDxcP7mwmul9akjHNx/DpoU/xdfOle0h3CosLcdVZzjUIJ1NDPFw9eKnnSzzb/VnOpp7FS+8Fm18Hw9CelsOg+WANFTo2AZ4B9GvUj52XdgJKnoS1C/pVhJ+fX/U+bI8chtUzlG03H3jmKPgEWVack2KaGzOk6RC89d4aqnE+6nrUZf7I+bSt19YqnUXF47WFcHNxo0NgBzi/DWK2KDslHQx7S1thToDp9Mi62HWaL0JXi85TIKiNsp2fCZGztdXjIBQVF7E+1lhGRkyVWYdOQZ2s1rpaOBlLUlxsGMUY6PIA1G+vnR4nYXCTwerTa3x6PMevV70TpOboXMwrPRz8AVLjNJPjKBy4eoDknGQA6nnUo0/DPhorElQV4WQsyfFlcPUvZdvVE4a8oq0eJ8HD1cOsr4xDVWY2pfVoaNJL2S4ugG3vaavHATArIxM22qJrBQLbIJyMpSjIha1vG+0+M8BP9By3FKY5MxsvbHTM1sySBHe+abT/WgZXT2ilxu7JLshmc/xm1RZlZBwT4WQsxf6vIf2Ssu0VCP3+oa0eJyMiJIL6XkoocGpeKrsTd2usqJo06wvhJcU/Zdgq1uzKY1vCNnIMaQBh/mG0C2insSJBdRBOxhJkp0DkJ0Z78MvgoU24p7NSusyMw06ZAdz5Bhj6rHNuE8Q5qMO0MqVzYyTRf8khEU7GEuz8CEpKngS0hO5TNZXjrJhOl2y7uI2M/AwN1dSA+u2h02SjveUNhy03Yy2u51xn7+W9qj26uSgj46gIJ1NTslMg6kejfeebSpa3wOKE1w2nTT0lDDi/OJ8t8Vs0VlQDhvzb2HPm0kE4vU5bPXbGhgsb1I6o3et3N/ZmEjgcwsnUFK968Pg2CB8OTXpDG7E4aU1MRzMO18zMlLrNoMc0o731Pw5VbsbamJYQEgv+jo1wMpagfjt4cDk8tFKJIBJYjdFho9EZCk4evHqQK5lXNFZUAwY+D4Y201w/A8eWaKvHTjh/8zynUk4B4KZzY3jocI0VCWqCcDKWxN3n9scIakSQVxC9G/RW7XUXHHiayTsQ+s4y2tveFx00MQ/qGNRkEH5uIojGkRFORuBwmE6f/H7+d8csM1NCnxngbahhln4JDn6nrR6NKZaLWRdrfHAQU2WOj3AyAodjaNOhZm1jT6ec1lhRDXD3gYEvGu3IjyFX++ZsWnEo6ZDaxtzf3Z8BjQZorEhQU4STETgcXnov7mh6h2o7dAAAKCHvdUOV7ZxUpaNqLcV0qmxk6EirFW0U2A7hZAQOiWk13g0XNqidSR0SVzcY8qrR3vuV0tyslpFXlMemuE2qLabKnAPhZAQOSa8GvQj0DASUxL39V/ZrrKiGdJgAIR2V7cIc2PGBtno0YHvCdjILMgFo4tuEzkGdNVYksATCyQgcEledK6PCRqm2w0+Z6XQw9E2jfehnuHFeMzlaYDpVNqb5GFFGxkkQTkbgsJhOmf158U+1mKLD0nIohBoWuuWiWtUKIC0vjV2Ju1RbTJU5D8LJCByWNvXaEOYfBkBOYQ47EnZorKiGSBIMfcNon1gBVx2wQVs12By/WV1X6xjYkaZ+TTVWJLAUwskIHBZJkhgdZiyc6NCJmSU0iVCam5Xw57vaabEh6y8YWyyb/k0Fjo9mTkaSpAckSYqUJClNkqRMSZKiJEmaIUlStTRZ+noCx8D0A2lX4i7S8pwgx2TIK6itAM5ugIQDmsqxNklZSURdjQKUlg4jQkfc5gyBI6HJB7AkSXOB/wE9gEhgM9AK+BJYIUmSi5bXEzgOTf2a0iGgAwCFxYWOXZm5hJAO0PE+o731P07dCmBj3EZklJ8vIiSCIK8gjRUJLInNnYwkSROA6cBVoJMsy2NkWR4PhAOngPHATK2uJ3A8THuNmE67ODSD/wUlz0ZxkRC7XVM51sT0b3ZX2F0VHClwRLQYyfzL8P0lWZbPleyUZTkJeNpgvlyFaS5LX0/gYIwMHYlkmF46ePUgSVlJGiuyAAEtoNvDRttJRzMX0i5w8sZJAPQ6PUObDdVYkcDS2PSDV5KkxkB3IB9YXvp1WZZ3AIlACNC79OvWvp7AMQnyCqJng54AyMhsjNuosSILMeglcHFXti8fhtMO3HK6HDZc2KBuD2w8UFRcdkJs/XTf1fA9Wpbl8pIaDpY61pbXEzgopgEAph9cDo1fQ+j5uNH+8x2namwmy7LZ38o0uVbgPNjayYQZvsdXcMzFUsfa8noCB2Vo06HodUoxxegb0cSlxWkryFL0fw7cDH2Krp2G47cM2B2WkykniUuPA8DL1YtBjQdpK0hgFWztZEq6emVVcEym4buvra4nSdIThpDnqGvXrlXitgJ7o3RZeKcZzXgHQB+TuJVt70FhvnZ6LMj6WOOC/53N7sTD1UNDNQJrYWsnU1KMyFIrmBa5nizL38qy3EOW5R5BQSJ80lEpHWXm0M3MTOkzAzzrKds34+HIAm31WICi4iI2XjCunYkETOfF1k4mw/C9oj7FJa9lVHCMta4ncGAGNR6El6sXAHHpcWqfeIfHww8GPGe0d3wE+dna6bEAh5MPk5yTDEA9j3r0atBLY0UCa2FrJxNn+N6sgmOalDrWltcTODAerh4MbWoMgTWdjnF4Ih4D3wbKduZVh2/TbNpieXiz4bjqXDVUI7AmtnYyRwzf20uS5FnOMRGljrXl9QQOjumU2YYLGyhylmgsvScMMmnTvOtTh23TnF+Uz+b4zap9V3ORgOnM2NTJyLKcABwG3ICJpV+XJGkQ0Bgle3+vra8ncHx6NehFPQ9l/SI5J5nDyYc1VmRBuj5s3qZ5z5eayqkuuxN3k56fDkAjn0aiOZmTo0UW/PuG7x9IktSyZKckScHAVwbzv7IsF5u89r4kSaclSXqfW6ny9QTOi16nZ1izYaptOi3j8LjoDcUzDeydC5mOFw1pWkZmZOhI0ZzMybG5k5FleQUwDyUL/7gkSWslSfoVOAe0A35DKWxpSgOgteG7Ja5ncZwmkskJMJ1+2Ry/mYKiAg3VWJgO90Fwe2W7IEuZNnMgsguy2Z6wXbVNpzcF2mKtzzBN6nnJsjwdeBBlqmsQMAKIQSlkOUGW5SpNpFv6elUlt6CIqT8dZOOJq9a8jaCSdA7qTEPvhgCk56ez+/JujRVZEJ0O7njVaB/8HtIuaaenivyZ8Ce5RbkAtKzTklZ1W2msSACw6sglnlx4iIIiy0/4aFY0UpblxbIs95Nl2U+WZW9ZlrvLsjy3rGktWZanyrIsybI81RLXsyQFRcXM+N9hdpy9xozFh/n1sOP8wzsrOklnVqLEqaLMAFqPgkY9lO2iPNjxgbZ6qoDp30Is+NsHC/fF8+zSY2w6mcRzy45RVGzZEY2oTFxDUrPzuXBdKThQVCzz3LJjLNwbp6kmgfk0zLaEbWQXOHZeiRmSBENfN9pHFsG1s9rpqSSpuansvWyMvxkZOlJDNQKAedvP89pvJ1T7XFIGGbmWnV4WTqaGBPt6sPTJPrQJMVateW11NF9tj9FQlaBV3Va0rKPEgeQW5bItYZvGiixM80HQfIiyLRfDn//RVk8l2By/mUK5EFCmNBv7NtZYUe1FlmU+3HiaDzaeVvd1aVKHX57oTR0vN4veSzgZCxDk687SJ/rQtWkddd+HG8/wwcbTIiBAQ0xLlThNMzNT7nzTuH1qLVyK0kpJpTCN9BNlZLSjuFjmjTXRfLX9vLqvT/MAFj3Wy+IOBoSTsRj+XnoWTetF3xYB6r5528/z+upoii08xymoHKbrMnsS95Cam6qhGivQsAu0v9dob3nTbhubXcm8ouYsuUguDA8drrGi2klhUTHPrzjGgr3GwvVD2wTz098i8HG3TtUF4WQsiLe7Kz9OjeDOtsHqvoX74nl++TEKrRC1IaiYxr6N1US/QrnQLMvcabjjVSgpyRIXCTFbtdVTDhvijFWxezfoTaBnoIZqaid5hUXMXHyEXw8nqvvGdm7I1w93x0PvYrX7CidjYTz0Lsx7qDvjOjdU9/16JJEZiw+TV+gkJU4cCLMoM2ecMgtoAd0eNdpb3oRi+3ugEc3JtCUnv4jHFxxiY7QxzeL+iCZ8NrkLehfrugHhZKyA3kXHp5O7MKVnE3XfH9FJPPZzFNn5hRoqq32MCB2BTlLe5oeSDnE1ywlzmQa9BHql+jRJx+HESm31lOL8zfOcTlEWmN10bmZFTAXWJz23gEd+3M/Os8bqEI/1D+P9ezviorN+tQXhZKyEi07ivfEdeWJgc3Vf5LnrPPLDAdJynCgD3c4J9Aykd4Pequ00zcxM8a0Pvacb7W3v2FVjM9MR5KAmg/Bxq6gzh8CS3MjM44Hv9nEwzrge+eydrXjlrrbm5XysuJYnnIwVkSSJf41qwz+HGbOao+JTeeC7fdzIzNNQWe3C6aPMAPo9Y2xslhoHh+ZrqUZFlmXzBMwwkYBpK66m5TL5232cSExX9716V1v+cWf4rQ5myRTY8pZVKnsLJ2NlJEli1tBwXh/TTt0XfTmdid/s5fLNHA2V1R6GNh2Km04JzTydcprzN8/f5gwHxMMfBvzTaO/8EPIyyz/eRhy/fpxLmUoVDF+9L/0b99dYUe0g7noW9329h5hk5T0gSfDfezvy2IDmtx4cswXOboBdn8CXERZ/3wgnYyP+3j+MDyd0omQKNPZaFvfNM74JBNbDx82HQU0Gqfaa82s0VGNFIh4DP0OCY9Y1pUqzxpj+roc2G4q7i7uGamoHJy+nc9/Xe7mUqjzEuuok5tzflft7Nr314OIi2GxSPaL1KHC37HSmcDI2ZFJEE758oBt6F8XTXE7LZdI3e/nr0k2NlTk/d7e4W93+/fzvztPMzBS9Bwz5t9HeMweyrmsmJ68oz2x60vRvILAOBy6kMPnbvVw3TMe7u+r49pHujDWJdjXj6GJIPqls671h8L/LPq4GCCdjY0Z3bMCPUyPwclPi0lOy8pny7T72nNfuw6A20LdRX7NmZvuu7NNYkZXofD8EtVW28zNh52zNpGxP2E5GfgagNCfrVr+bZlpqA3+eTuLhH/aTkatEsPp6uLLosV7c0aZ+2SfkZ8G2d412v2eUIBILI5yMBgwID+J/j/WijpcegKz8Iqb+eJA/op0wvNZO0Ov0jGk+RrVXx6zWUI0V0bmYF8+M+gFS48s/3oqY/o7vbnG3GkousDy/HUnk8QWHyCtUcqQCfZRSVxGh9co/ad9XkHFF2fapD31mWkWb+KtrRNemdVn2ZB/q+ylz1PlFxTy96BDLohI0Vua8jGsxTt3eenGr2gLY6Wg9CpoYwraL8mHbezaXcC37Gnsu71HtsS3G2lxDbWH+7gv839Kjaon+xnU9WfFUH9o19Cv/pMxrsOtzoz34XxZfiylBOBkNaVXflxVP9SU0QEmkK5bhxRV/8d3OWI2VOSet67WmbT1lKim/OJ8/4v7QWJGVkCTz4pl/LYWrJ8o72iqsi11HkaFXYI/6PUTFZSsgyzKfbj7Lm2tPqvta1/dl5dN9CQ30rvjkHR+AYSqTwNbQ9WGr6RRORmOa1PNi+VN9adfA+NTx7vpTfCgqOFuFu1saF5+ddsoMoFkfaFXSr0WGrbZrBSDLMqvPm0yVtRQL/pamuFjmzTXRfL71nLqvW9M6LH2yN/X9PCo++XoMHPrJaA97C1ysUxwThJOxC4J83fnlyd70NJk//Wr7ef696oTFu9TVdkaFjcJVUv6hjl07RlxanLaCrMnQ1wFDzPy5PyB+T4WHW4qTKSeJuan0U/J09WRYs2E2uW9toaComGeXHeVnk0rKA1sFVb5U/5Y3oNhQ3qpZf5OHEesgnIyd4OehZ8G0ngxtY6zgvOTARZ5ZckQU1rQg9TzqMbDxQNV22pwZgPrtlWizEja/YZNWAKYjxGHNhuGtv83UjaDS5OQX8cSCKFYfvazuG9OpAd8/0gMvt0qMRi7ug9O/G+3h/1GmV62IcDJ2hIfeha8f7s74ro3UfeuOX+HRHw+QbuGWqLUZ0+mbNefXOGfOTAlD/g0uhqfbSwfglHWdan5RvsiNsRIpWfk88P0+tp0xFrp8sFdTPr+/K26ulfgol2XY9JrR7jABGnW3glJzhJOxM/QuOj6e2Jm/9QtV9+2LTWHS13tJSs/VTpgTMaDRAOq61wUgKTuJA1cPaKzIitRpChGPG+1Nr0GB9d5HOy/tJC1PqX/V0LshPUJ6WO1etYmElGzum7eHIxeNidszh7TknXs6VL6S8snVyoMGKA8epqHuVkQ4GTtEp5N4fUw7XhzZWt13+moG9361h5jkDA2VOQd6Fz13NTcWajRdpHZKBr1gLJ55Mx72z7ParUynysa2GCtyYyxA9OU07p23h9jrWYAyu/XWuPY8P6K1eaHLiijMh61vGe2eT0DdUMuLLQPxDrBTJEli+uCWfDyxM66GJ5XEmznc9/VeDsWnaKzO8THLmYnfSma+E9eQ86xrXm5m58eQkWTx21zPuU5kYqRqm/6OBdVjd8x1Jn+zj2sZSpkYN1cdcx/oxqN9Q6t2oUM/QYohNaJ0MVUrI5yMnTOhe2O+f7SHWobmZnYBD3y3n80nLf8hUZtoU68NreoqLRhyi3LZFL9JY0VWpvvfIKiNsp2fofScsTDrY9eruTHdgrvR1K+MgoyCSrPm2GWm/nSAzDxjmZiFf+/J6I4Nqnah3DQlL6aEAc+DVwWVACyMcDIOwODWwSx5vDcB3soCbl5hMU8ujGLx/osaK3NcJEkyW5R26pwZUPIgRphk/h9eCFf+sugtTCP1RG5Mzfg+MpZnlhyhoEiJBgzx82D5U33o1Tyg6hfb9Rlk31C2/ZsqU2U2RDgZB6FzkzqsfLovTesZqwP8e9VxPt18ViRtVpPRzUfjIikjxMPJh7mY7uROu+VQCB9hMGTY+C+LhTSfTjnNmdQzAHi4eDC82XCLXLe2UVws887vJ3ln3Sl1X3iwD79O70ubkArKxJRH2iWlRlkJQ19TqnXbEOFkHIjQQG9WPt2Xjo381X2fbz3Hv1cdp7CoWENljkmgZyADGg1QbafOmSlh+DugM+RTxO8yz5moAaYjwaHNhooWy9Ugv7CY/1t6lO93XVD3RYTWZflTfWhYx7N6F932HhQaogkbdIYO91lAadUQTsbBCPJ155cnejOwVZC6b8mBBJ5adIicfCfO97AS41oaF6fXnF9DsezkzjqoVamQ5lehsGatwAuKClgXu061xYJ/1cnILeDv8w+y5pgxyXJE+/osnFbJLP6yuHpc6RdTwvB3QGf7j3zhZBwQb3dXfni0B/d2MyZtbjmVzP3f7SM5Q+TSVIVBjQfh766MDK9kXSHqapTGimzAoBeViDOA1DjY/3WNLheZGElqXioA9b3q0yukVw0F1i4u38xh4td72RVj7Cn1cO9mfPVgdzz0LtW7qCwrDxAYpkPDh0PYwApPsRbCyTgoJUmbTw9uoe47lnCT8XP3cDZJ5NJUFjcXN0aHjVZtp8+ZASWyyLQD4o6PIDO52pcznWYc12IcLrpqfjDWQo5fSuOeubs5fdX4P/v88Fb85+72lU+yLIuTqyF2u7It6WCY7QqklkY4GQdGkiReGtmGt+9uT8n7MfFmDhO+2kPkuWsVnyxQMY0y2xy/mayCLA3V2Igef1NKvIMhpPndio8vh9TcVHZc2qHaom9M5dl8MolJ3+wl2ZADo3eRmD2xMzPvCK98kmVZ5GfBHyYPERGPQXDbGqqtPsLJOAEP9wnlh0cj8Dbk0mTkFTL1p4MsOeDk0VIWol1AO1rWaQlATmEOm+M3a6zIBrjoS4U0L1Dm8KvI+gvrKTRU9O0c1Jkw/zBLKXRaZFnmh10XeGJhFDkFyjqqn4crC/7ei/u6W6Dvzs6PID1R2fYKhCGv1PyaNUA4GSdhSJtglj/VlxBDL4miYpl//Xqc9zecoli0C6gQSZLMFqudPmemhPA7oaWhDL9cXK2QZtPflVjwvz2FRcW8vjqat38/qf6qm9bz4tfp/ejToho5MKW5fg72fGm0h/0HPOvU/Lo1QDgZJ6JdQz9+m9GP9iZtV7/ZEcuMxYdF5NltGNN8jFpnKyopiksZlzRWZCNGvAuGXCHiIuHM+oqPN+Fs6llOpSj5HG46N0aGWbcviaOTmVfIYwuiWLjP2Aeme7O6rJrel5bBFgj5lmVY/wIUGyq2N+4JnafU/Lo1RDgZJyPE34NlT/bhzrbGvjQbTlzl/u+M9Y8EtxLkFUTfhn1Ve+35tRqqsSFBrZU5+xL+eKXSIc1rYowL/nc0vQM/t2okC9YSLt/M4b55e9huUqZ/TKcG/O+xXgT4uFvmJqfWQOw2ZVvSwV2zNQlZLo32CgQWx9vdlW8e7mHWLuBYwk3umbtbRJ5VgFlr5vOrnT9npoTBL4OHYUol9QIc+Pa2pxQWF/J7rDGRU5SRKZ+yIshmDmnJnPu7Vj9EuTT5WbDRZLG/xzQl+dIOEE7GSXHRSbwxtj1vjRORZ5VlSJMh+Lr5ApCYmcjhpMMaK7IRXvVg8L+M9o4PIet6+ccDey7v4UauUg8r2DOYPg36WFOhw1I6gsxVJ/HRfZ14fkRrdDUJUS7NztmQbpji9QqEO7Rd7DdFOBkn59G+oXz/aI9bIs/m774gap6Vwt3FnVGho1R7VcwqDdXYmIhpEBCubOelw5Y3Kzx81Tnj7+auFneJ3JhSyLLM3G0xt0aQTevJxB5NLHuz6zGw5wujPewtY7KtHSCcTC3gjjb1b4k8e3PtSV5c8Rd5hSIgwJR7Wt6jbm+4sIHrORU/0TsNpUOajyyEuF1lHpqYmcifCX+q9j0t7inzuNpKdn4hs5Yc4aM/ztwSQda3RaBlbybLsKH0Yv8Dlr1HDRFOppbQrqEfq2f2o3MTYzjj8kOXmPzNPtHW2YQOgR3oGNgRgILiApadWaaxIhvSaji0GWO01zxTZqvmxacWq+tVvRv0pnmd5rZSaPckpGQzYd5efv/rirqvZ1g9y0WQlebUWjhvcPh2tNhvin2pEViV+n4eLH2iNxO6GRO+jibcZOwXuzhyMVVDZfaDJEk83O5h1V56Zil5RbUoKm/0bHA3RImlnIedH5q9nJmfya/nflVt099VbWdf7A3unrubU1fS1X0P925m2QgyU0pn9tvRYr8pwsnUMjz0Lsye2InXxrRTAwKSM/KY/M0+lkclaCvOTriz2Z2EeIcAkJKbYlZh2Onxa6DM6Zew+3O4ekI1V8WsIrNAaVUd5h9G/0b9ba3Q7pBlmQV743jo+/2kZOUDSomY9+/tyNv3dEDvYqWP2ciPIc3wP2tni/2mCCdTC5EkiWn9w1jw9174e+oByC8q5oUVf/HW2uha35tGr9PzQBvjvPbCkwtrV5BEt6nQ1JAzVFwIa2ZBcRFFxUX8Qv5YewAAIABJREFU79T/1MMeavuQmsBaW8krLOLllcd5fXU0hYbKGoE+7ix5vDdTelqx/XTpxf4737SrxX5Tavc7pJbTPzyQNTP70bq+r7rvp91xPPLjAVINT2S1lQmtJuDpqjSKirkZw94rezVWZEN0Ohj7ObgY+phcPgwHvuXPhD9JzFRqYvm7+9f6YpjJ6blM+XYfS01mADo19mftrH70CK1nvRvLMmx4EYoM/6ONI6DLg9a7Xw0RTqaW0yzAm1+n92VE+/rqvj3nbzBu7i6zueXahp+bH+NbjlftBScXaKhGA4JawcAXjPbWt1n41/eqOanVJNUJ10aOJtxk7Je7OHzxprpvfNdGLHuyDw38rfx7Of07nN9qMCRlHc3OFvtNsV9lApvh7e7KvAe78+ydrdR9CSk53PvVHtaadOqrbTzU9iEklIWr3Ym7ib0Zq7EiG9Pv/yBIKRF/XCrgSMpJAFx1rkxpo31NLK1YFpXApG/2kpSuBIToJHhldFs+mdTZchn85ZGfpRQyLSFiGjTsYt171hDhZAQA6HQS/7gznG8e7q4mbuYUFDFryRFe++1ErcynaeLXhMFNBqv2wlMLtROjBa5uMO4LQGKhv3FKdVToKIK8gso/z0nJyS/i+eXHeHHFX+QXKuuWfh6uzP9bTx4f2LxmPWAqy+bXTRb7A+COV61/zxoinIzAjBHtQ1g1ox+hAV7qvoX74pkwbw8Xb2RrqEwbHmn3iLq99vxaUnNrWah3kwiudn+YTd7G98PDYbWvpH9McgZ3z93FikPG6tzhwT6smdmfga1s5HBjtsBB45Qlw9+x28V+U4STEdxCq/q+rJnVn1EdQtR9JxLTueuLSDaeuKqhMtvTvX532tZTpozyivJqV3KmgcXBjSgyPKVH5OTS9uB8bQXZmFVHLjHuy92cTcpU993btRGrZ/YjNNDbNiKyU2D1TKPd+i67KONfGYSTEZSJn4eerx7sxptj26F3UT5gMnILeWrRId5aG61OFzg7pZMzfznzC/lFtSfyLrsgmxXnjSX9H07PgGNLIGZrBWc5B7kFRfzr1794dukxsg39mNxddXwwoSMfT+qMl5ur7cSsfx4yDFUEvIOU6D9bTM9ZAOFkBOUiSRJT+4Wx/Km+NKpjjJj5aXccE7/Zy6XU2jF9NjJ0JMGeSn+e6znX2XBhg8aKbMdvMb+RUaCUqG8quTMoO0d54fdnlUVoJyX2Wibjv9rDkgPG8OTmgd78NqMfkyOa2mb9pYTjK+DESqM9dg74OM6amHAygtvSpUkd1j8zgDvbGsOcjyXc5K45u9h6KklDZbZB76JnSlvj1ERtSc68Jfmy8xPoSvrO3IyHbe+Vc6Zj8/tflxn3pXl5mLGdG7JmVn/aNrBxY7b0y7DuOaPd9SFoM9q2GmqIcDKCSuHvpee7R7rz6l1tcTXUo0nLKWDaz1G8v/4UBU5eJWBiq4l4uChVrM+knuHg1YMaK7I+Oy7t4GLGRQB83Xy5u91DSrvmEvZ9BZePaKTO8uQVFvH66hPMXHyEzLxCANxcdbxzTwfm3N8FH3cbTo+BknS5egbkpil2naYw4n3barAAwskIKo0kSTw2oDlLn+xDQ38Pdf83O2O5/9t9Th195u/ub9b9sTYkZy48aQzZnthqIl56LyWzPGygslMuVkrOFDr+GlVMciYT5u1hwd54dV+zAC9+fbovD/VuZtvpsRIOfm+ssIwE93wNHo7X4lo4GUGV6d6sLuueGcCQ1sZ54UPxqYz6fCe/HLjotFNJD7Y1lu7YcWkHcWlx2omxMidvnCQqKQoAV8kk+VKSYMxn4Gp4yLh6XMndcFCKi2V+2n2Bu+ZEciLROD02umMIa2f1p0Mjf22EXT8Hm14z2n1nQmg/bbTUEOFkBNWirrcbPzwawUsj2+BimD7Lyi/i5V+P8/iCKK5lOF95/DD/MAY1HqTai04t0lCNdTEdxQwPHa5WpQYgoAUMNXEs++dB9G82VGcZrqTl8MiPB3hr7UnyDNGSbi463hjbjrkPdMPPQ6+NsKJCWPUkFBqCLILbwRD7T7osD+FkBNVGp5N4enALVk3vS4sgY77AllPJjPxsJ39EO19OjWk485rza0jLS9NQjXVIykpi44WNqm2akKrSe7qSq1HC6plw47wN1FmG1UcTGfHpTnbFGDuftm3gx5pZ/fhbvzBtpsdK2PUJJB5StnV6uPdb0HtUfI4dI5yMoMZ0alyHdc8MYGrfUHXfjax8nlx4iOeXHyMjt0A7cRamZ0hPWtVVarzlFOaw/OxyjRVZnl/O/EKhrCx8dwvuRvvA9rceJElwz1dQp5li52fAskehIMeGSqvOzex8Zi4+zD9+OUp6rvIzShI8NagFv83oS5sQjdc8Lh+BHR8Y7SH/hpCO2umxAMLJCCyCh96FN8e1Z9G0XoT4GZ+6Vhy6xMjPItkXe0NDdZZDkiSzJ/slp5dQUOw8TrS04yxzFFOCZx2Y9LOxJUDScaUEvZ2y4+w1Rny206w1cpN6nix7sg8vj2qDu6uVi1vejoIc+PUJpYcPQJNe0O8f2mqyAMLJCCxK//BA/vi/gdzdpaG6L/FmDlO+28d76085RaHNUWGjCPAIACA5O5lNcZs0VmQ51p5fq04BNvZpbFYgtEwadoWRJmG1hxfA0SXWE1gNcvKV0ORHfzygVk4GmNyjCRv+MZAIa/Z+qQpb3oLrZ5VtvTeM/xp0Gjs+CyCcjMDi+Hvp+fz+rnwxpavaeVOW4dudsYz7YjfHLzn2Ooabixv3t7lftRecXOAUEXXFcrHZgv+DbR/EpTIfcj2mQYf7jPbvz0LSSSsorDqH4lO4a06kWWhyoI8b3z3Sgw/u62T73JfyiN2uBFCUMOJdqNdcMzmWRBMnI0lSa0mSFkmSdFmSpDxJkuIlSZonSVKDal7rWUmSNkiSFCNJUq4kSWmSJO2VJOn/JElys8bPILg9Yzs35I//G2hWpfZMklLN9s010Q69VjOp9STcXdwBJdx3W8I2jRXVnHWx64hLjwPAR+/D+PDxFZ9QgiQptbQCDf2ICnNg+aOQl1nxeVYkLbuAf/16nAnz9hJ73Vj+Zni7+vzxfwMZ1q5+BWfbmJQLsGKa0Q4fAd2naibH0tjcyUiSNAg4AjwIXAFWAdnAU8AxSZJaVXB6WWwFPgEGm1zvENAF+BTYJ0mSnYyHax8h/h78/LcI3r67PR565e1WLMP8PXEM+2QnG09ccchRQD2PetzT8h7V/u+B/5Jd4LjJqGl5acyOmq3ak1tPxltfhQrD7j4waQHoDS0Brp+Ftf9QhrA2RJZlfjuSyNBPtrPkwEV1v4+7Kx/d14lvHu5OgI+7TTVVSE4qLJ4E2YYoN68AGDfHYYpfVgabOhlJkryBXwBPYJYsy91lWb5fluW2wMdAELBEqlr84BlgGhAky/IAWZanyLJ8B9AWiAa6ojib/2/vzMOjKPI+/qncIbchAUKAhEPAyCHhEpAAcXE5hOUVXtH1VrxAFxFeRXF3EV1YBcRF1kXx1hUUAfEGIwQEBRIRJUAIdw5CAoFc5E69f3RnZhKSkGN6ZjLU53nq6enq6urq38z0t+v6lcJOCCG48/oIvps5nBu6tTbFZ+YV8/CHv/DAewkt0tnmjL4zCPLU1vM4XXialb+ttHOJms7yvcvJKc4BILRVKNN6T2t8JqE9YbzFX23/Wkh4y0olvDzHzxZy51u7mbnmV84WmL0Q3NizDd89MZwp/TvYd2hyTcpL4ZO7zP0wrp4w9WPwa1v/eS0MW9dk7gXaAlullK/VOPYUcBToB4xpaIZSylgp5dtSyoIa8SfQakcA/6uazexPp2Af3r9vIK9O7Utri7fJuENZ/GHpNlbGH21RPtACvQJ5IvoJ0/77Se9z5PwRO5aoafye/Xu1dXKeHvh042oxlvSZCv0sRqR9OxfSf2lmCeunpLyCf8WlcNOy6vNe2gV4sfLOaFbd3b+aF3GHQEr46gk4vs0c96d/Q8dB9iuTQdhaZKraFy6ZKi2lrECr5Vimay5V3vu8gGAr5aloBkIIJvZtT9yTMfx5UEdTfFFZBQu/OcTNy3/kl1MtZ/XJiV0n0i+0HwDlspwXdr3Qopr/KiorWPDzAiRamYe1H8aNHW9sXqZjXjLP7ago1fpnioz5Tn8+do4xr25n6ebDpjWOXATcPyySzbNiuCnKQWsFP74Cey0egyPnQa/JdadvwdhaZK7Tt3W5sN1TI11z6aZvS4EcK+WpsAIB3u68OKkXnz0yhB5tzevHH8rM55bXd/Ls+t/JLXL8gQEuwoV5g+fhJrRRSolnEtlosciXo7M6eTUHcw4C4OnqyTODnml+k5K7N0x5Dzz1iY0XTsGG6Vbtn8kpLGX2p/uY+sbPHMs2d+z3Dg9g44xhPDf+GscZOVaTpPUQN9+83+d2GD7bfuUxGJuJjBDCH6jqgD9ZR7KqnrpIK132aX37pZTS+ZxpOQHRnYL44rFhzB3TA293bbislPDRrlOMWryV93aecPhVOLsFdavmbmZJwpIW4W4m+2I2r+01t1pP6zWNDn4drJN5cBeYuMK8n/wVbG2+m/risgre3HaMkYu3sjYxzRTv6+nG/AlRrH90qP2cWjaE1D2w/mHzfsQNLWqVy6Zgy5qMr8XnupbUq+pX8avjeIMRQtwD3Io2cu2Zy6R9UAiRIIRIyM7Obu6lFY3E3dWFh2K6sHnWcEb1CDXFnyss5W8bkxj9Sjxf/+7Yo9Ae7vOwyYnk+ZLzLPtlmZ1LdHle3vMyBWXaXy7CP4J7r73Xuhe4ZoLm46yK+H/CtpeblFVlpWT93jRil8Tz4tcHq9Vyx/VqR9yTMdw9JMLkrNUhOX8CPp4K5cXafnBXbUSem3N3F4uG/nGFEC8BE5pwjVgpZboQoj1Q9erhLqXuHKn6NboBh4FSKWWTxxkKIWKBrwF34C4pZYPd5fbv318mJCQ09dKKZiKl5Nv9mbzw1UHSL1T3g9W3QyBzx/RgUGfH7F6LOxXHzC0zTfsfjv2QPiF97FiiutmZsZOHNj9k2l81ehWD2hnQ6Vxeqg3RPWYxjyj2b3DDrLrPqcH2lGwWfXOIpIy8avGdglvx95ujGGnxYuKwFF2At0bD2WRt3/sqmBbnNBMuhRCJUsr+tR1rTKNlGNC9Cdev8pedbxHnA9TWnuBbS9pGIYQYBnwOeACPN0ZgFPZHCMGYXu0Y2SOUD346yfIfUkyODH9NvcCtb/zMjT3b8PSY7nQNbXaF16qM6jCKmPAY4tPiAVjw0wJWj1+Nm4tj9Q2UVJTwj13mpZPHRo41RmBAe0uf+l/tDf64Zhfi5oNwgWEz6z01KSOXRd8cYnvK2WrxwT4ePB7bjdsGdsTDrQU4Lako04cq6wLjqtvESQTmcjT4G5JS3iGlFE0IJ/Tz8zB3vneq4zJVDcInmnIzQoghaDUYH+ApKeXypuSjsD9e7q5MG96Zbf83kgeHd8bD1fxT/f7gGUa/so25637jTF6xHUtZHSEEcwfNrbZM88eHHMuPF8Db+9/mZJ7WLern7secAXOMvaBHK7httdb/UMX3f4Odtf89085fZNaaXxm//MdqAuPl7sJjo7qydc4I7h4S0TIERkr4apZZYAEm/hs6XW+/MtkYW39LVUOKB9RxfGCNdA1GCDEY+AatP2eelPKlxhdP4WgEtvLgmbE9iXsyhknXtTfFV0r4eHcqI17eypJNyeRedIyRaO192/NQH3Mz1Gt7X+NM4Rk7lqg6qXmprPptlWn/sX6P0dq7dT1nWAmPVnD7mupCs2ke/GQeHJBTWMrCrw8yakk86/ammwajuQiYOqADW2eP5MnR3fGz12JiTWHHq5rT0CpGPgu9p9ivPHagwX0yVrmYEI8B/wK26LPyLY+5os3e7wKMk1J+3Yh8BwKbAX/g71LK+Zc5pU5Un4xjsz9da0KxnHQH4OPhym0DO3L/DZG0C7DvxLuyijImfzGZY7nHALgp4iYWxyy+zFnGI6XkkbhH2JG+A4Co4Cg+GvtRw5xgWovSQvhoCpzcYYo6P/x5luXHsiYhleKy6iMJY3uE8tSYHlzdxrGaRi+LlNoghy0vmuP63AZ/et0pR5LV1ydj65rMO0AmMFIIMb3GsUVoArMXrUZiQggxUAhxSAhxqGaGQohoYBOawCxojsAoHJ9r2wfw4QODeP++gfRsZ15gqrC0glU/Hmf4S1uY/ek+Us40uVuv2bi7ujNvsHm53O9OfMfO9J12K08Vm09uNgmMQPDc4OdsKzAAHj5w+yfQ0dxcFLTtr7D7jWoC0yc8gNUPDuatewa0PIEpK4Z106oLTKehTj9UuS5sWpMBk4PMb9D8lyUCKUAfNF9jZ4FhUsrkGueMALYASClFjWM5QBBwAa3Dvy5mSynP1nMcUDWZlkRlpeTzfen8e8tRUrIu9fh7Y89QHo7pQn87rRfyzPZn+OLYFwB09OvIuonrTJ6bbU1hWSETNkwg62IWAFO7T+XZwc/avBxSSn46do53t+xn2qk5DHA5bDr2XNk9JIZOZvrIrozt1dax/Iw1lPwzsPp2SLd4hkTGaEOVvQPtVy6Dqa8mY3ORAc09P/BXIBZNIM6gddjPl1KeriX9COoWmYbeQGTVIIT6UCLT8qislGxJzuI/8UfZc+JS9yXRnYJ4OKYLsT1CcbHhPIqzRWeZsGEC+aVareqRPo/waN9HL3OWMby05yXTWjHBXsFsnLQRfw/bLTVcUSn5LimTlfFH2aevJ+RDEe97LCLaJcWUTo5bihhwf13ZODaZ++G/t0KeeZIo/e/T3Oy4tqB+pCbgcCLjyCiRadkknszhP/HH2Hzg0s72bqG+3DcskvG929ms83jNoTW8sOsFANxd3Fk/cT2d/OsaXGkMyTnJ3PrlrVRIbVXShTcsZHzn8Ta5du7FMjbuS+ftHSc4frb6HGwXAZN6+vN8wXP4ZFmM9Rm7GAY80LKalpK/0daEKdPvUbjATQth0EMt6z6aiBKZRqBExjk4kpXPyvhjbPg1nbKK6r9xL3cXxlzbjsnR4VzfOdjQ2k1FZQV3fH0H+8/tB7TRZytiV9AlsIth17TkwLkDzIibQXaR5sliUNtBvDn6TUOboioqJdtTslmbmMamA2cucQvk4ebClOhwpt3QmYjWPlCcCx9MgvREc6KeN8O4peDr4BMtpYSfXoNNz4HuZBQPP5jyDnT7g12LZkuUyDQCJTLORWZuMW/vOM5/d52ioOQSJxO0D/Tmln7tuSU6nE7BTXRvfxkOnDvAn7/6M+W6kwtfd1+WjFjCkLAhhlyvih9O/cDT25+mqFzznODp6sknN39C5wBjJgEezS5gbWIa635J40zepa4C/b3cuOv6CO4eEkGIX42+qaILmtBkWCwL4B0EY17WvBM7Ym2gvFSbA7PXvGQ1gR21gQ2hPe1XLjugRKYRKJFxTnKLylibmManCakcyqx95NnAyKuYHB3OuF7t8LGyB99taduYEz+Hi+Xa4myuwpV5g+cx+Wrru3eXUvLBgQ9YnLDY5MLfz8OPZSOWMbDdwMuc3Tjyisv4ct9p1iam8supC7Wm6R0ewOTocP6nX3j9npFL8rUaQeI71eO7j4PxSx1rMa+LObDmTjj5ozmuw2CY+hH42GDekYOhRKYRKJFxbqSUJGXksTYxjQ2/pnOhlkmcrTxc+eO1bRl9TRuGdm1ttf6b5JxkHo171DTCC+DeqHuZGT0TF2Gd2QTlleUs2r2INclrTHHhvuGsuHGF1WowuRfL2H4km01JZ/guKZOSWrxkt/b1YNJ1Wg2xR9tGDjA4ugU2Pg655uWT8QqEMf+E3rfav1aTuhvWPQjnj5vj+tymDVF2c6ClnW2IEplGoETmyqGkvIIfDmaxNjGNrYezqai89L/g5iKI7hTEiO6hjOwRQvc2fs3qz8i6mMWMuBmmNVwAYjvGsvCGhXi7NW8SaUFpAbPjZ7MjwzzRsW9IX14d9SpXeTV9GHeVMG9NzmJrcjZ7Uy/UaavYnqFMie5ATPcQ3F2bIZwl+fD932HPqurx3W6Cm5eBf1jT824KUmquYbYthhPbqx+L/SsMm2V/8bMjSmQagRKZK5OsvGI2/JrOpwlptc65qaKtvxcjuocwontIk2s5F8su8tT2p9iautUUFxUcxfJRywlpFdKU4pNRkMH0uOkcuWBe/nlM5BgWDF3QpLk5VbWVrcnZxB/OJju/7uWYrmnnz+TocCb2DSPY18pv8se3wecz4ILFElSeAfDHhdD3duMf7JWVcPhb2L64+sAEAPdWMGmltqTBFY4SmUagRObKRkrJ7+m5bEo6w5bkrEvcy1tSVcsZ3DmYqDB/otoHEBbg1aCaTkVlBUsTl/L+AbNfq7Y+bVkRu4Krg65uVJn3n93PjLgZnCs+Z4p7qPdDTO87vUFlkVKSdr6IpIxckjLy+OnouTprK6A913u3DyCmeyg3RbUhKszgRcJKCiDuedi9snp8l1gYOA0ih2ueBKxJRTkc2ADbl0DWgerHhCv0mgLD50Drrta9bgtFiUwjUCKjsCQrr5j4w9ob/baUbPKLLx2hZklQK3eiwgKICvPnmjB/osICiGztU+diWmsOrWHh7oWmOSw+7j4sjlnMsPbDGlS+709+z9ztcymu0LxRu7m4MX/IfCZ0qf3tuqJSciy7gP0ZuSSl55GUkUdSRq5pOYW6CGzlzvBuIYzsEcLwbiHWr7E0hBM74PPp1ftCQHOdHzEMuo3WQnAzhoeXl8C+j+HHZbVcxxOuuwOGPg5BEU2/hhOiRKYRKJFR1EV5RSV7Uy+Y+ibqq+VY0srDlZ7t/One1o+2/l6E+nkS6u9JqJ/2+WDuHp7aPodCfSKfi3BhXOQ4PC/TiVxYVsi3x781jSDz9/BnScwrRPj0Jiu/mOz8ErLyS8jKKyEzr4iDp/M5lJl3iRPKuugTrtVWRnQPoU94oGOsOll6EX5YAD+/jmleSk2CIs2CEzEU3Gv0dUkJJXmaC5iCTH17BvJPw/51kJ9RPb27Dwy4D66f4Vgj3BwIJTKNQImMoqFk5RWz4+hZ9qfnsT89lwOn8y5b06kNFwGBgeeoDH2LCpecy59QC24VIYis+zmfG0hT/tIB3u5ak1+YP9e2D2Bo19a0tkdtpaGc/g32fwYpmyErqe50bt5aLcfdWxeSTCjIgvKius+pwisQBj2szdpvZR//dy0FJTKNQImMoqlIKUnNKdKaovT+jaSMvHo7zS0Rrvl4d3gPV++0yye2oPxiBMVpdyIrGtYv0cbfk2tNTXraNjzIu2U6pATITdPEJmUzHNtqdu3SVHxCYcgMze+YZwvzAG0nlMg0AiUyCmuTlVdMUkYex88Was1XelNWVXNWTmGpRepyXH0P4+LWsKUKKssDqCjoBphd9gf7eBDi50mo3jQX4udJqJ8nnUN8iQrzd+waSnMpL4GTO3XR2QTnUmpP594KfNtowa8N+LbVtkGR0H0suHvZttwtHCUyjUCJjMLWlJZXcrbALDrZ+SWUVzas38Td1YUQX3MfT7CvR/PmpzgbOcfg1M/a4ADfNlqfim8brYbSUmtuDkh9ImNd3xkKhaLReLi5EBboTVigfVf0dEqu6qwFhd1QrzwKhUKhMAwlMgqFQqEwDCUyCoVCoTAMJTIKhUKhMAwlMgqFQqEwDCUyCoVCoTAMJTIKhUKhMAw1GbMGQohs4ORlE9ZOa+CsFYujaDjK9vZD2d5+OIrtO0kpa10MSYmMFRFCJNQ161VhLMr29kPZ3n60BNur5jKFQqFQGIYSGYVCoVAYhhIZ6/KGvQtwBaNsbz+U7e2Hw9te9ckoFAqFwjBUTUahUCgUhqFERqFQKBSGoUSmDoQQtwshtgshcoUQBUKIBCHEdCFEk2xm7fycGWvYSgjhLoSIFUIsEUL8LIQ4LYQoFUKkCyHWCiFGGHgLLRYjf6dCiH8IIaQeZlujvM6EAc8cbyHE/wkh9gghLgghLgohjgshPhVCDLV2+etESqlCjQCsACRQBHwJrAfy9Lh1gKs983PmYC1bATfq50jgtJ7XGuB3i/jn7X2/jhSM/J0CA4ByoFLPb7a979eRggHPnEggRT//DPA58AmwGygF5tns3uxtXEcLwC0WD6ZuFvFtgAP6sb/YKz9nDta0FTAKWAvcUMuxW/UHngRG2vu+HSEY+TsFPIEkIF1/eCqRMdD2gA9wpOpFCnCvcTwYuNpm92dvAztaABL0L+euWo7FWPwYXOyRnzMHW9oKWKXn95a979sRgpG2B/6pn38z8K4SGWNtDyzUz3nP3vcmpRKZml9OuP7llADedaRJ09MMsXV+zhxsbStgup7Xd/a+d3sHI20PDEKrNX6k7yuRMdD2gAeaLzMJ9LT3/UkpVcd/Da7Tt0lSyqI60uypkdaW+TkztrZVN3172gp5tXQMsb0Qwgt4D8gB/tL04jk11rZ9NFpzWKqU8qAQYog+4GKlEGK+EOL65ha4sbjZ+oIOTqS+rc8L86kaaW2ZnzNjM1sJIdoC9+i7nzUnLyfBKNu/CHQHpkopHcFTsCNibdv30rcpQoh3gbtrHP+rEOIz4M56RM2qqJpMdXz1bWE9aQr0rZ8d8nNmbGIrIYQb8CEQAMRJKb9oal5OhNVtL4QYAswENkgp1zSjbM6OtW1/lb4dDtwFLAa6AkHARLTBF7egjWazCUpkqiP0rbV87Vg7P2fGVrb6DxALpAJ3GHytloJVbS+E8AbeQRuC+6g18nRirP27r3qmu6ENapkjpTwqpbwgpdwI/Em/1t1CiM5WumaDCqTQyNe3vvWkqTqWX08ao/JzZgy3lRDiVeB+IBOIlVJmNiUfJ8Tatv8HcDUwS0qp+rzqx6hnDsCbNQ9KKROARLRn/4gG5NdsVJ9MdU7o2071pOlQI60t83NmTuhbQ2wlhFgCPA5kowlMSmPzcGJO6Ftr2X4oW0oWAAACJklEQVQS2qTLu4UQNfsEeujbR4QQ44EjUsoHGlhOZ+SEvrX2MwfgeB1pjgP9gbYNyK/ZKJGpzl59GyWE8K6jY2xAjbS2zM+ZMcxWQoiXgFnAOeAPUsoDTS+mU2KE7V3Q5njURWc9BDYwP2fF2rb/xeJzMNpLVU1a69uCWo5ZHdVcZoGUMhXtS/IAptQ8LoSIQRvXngn8ZOv8nBmjbCWEWATMAc6jCcw+qxTYiTDgdx8hpRS1BbQhzQBz9Li+1ruTlocBtk8Hdum7sbXkFwT003cTmlbqRmLviTqOFoDJmGfYdrWID0VzjXGJiwe0GbaHgIXWyO9KDQbYfoF+znkg2t7358jB2rav5zrvoiZjGmp7NM8KEs1nWV+LeC9gtX4sAX09MaODai6rgZRyrRDideAR4HchxPdAGdpbgT+wAXitxmnt0OYDtLNSflck1rS9EGICME/fPQI8JoSgFg5JKRdZ7SZaKNb+3SsajgHPnC+EEIuB2cAuIcQutKbigUAY2jDm26SuPEajRKYWpJSPCiF+RHM9EgO4or01vA28LqWstGd+zowVbXWVxef+eqiNeOCKFxlQv1N7YsAzZ44QYifwGJqngFZokzqXAouklLX11RiCWn5ZoVAoFIahOv4VCoVCYRhKZBQKhUJhGEpkFAqFQmEYSmQUCoVCYRhKZBQKhUJhGEpkFAqFQmEYSmQUCoVCYRhKZBQKhUJhGEpkFAqFQmEY/w8RWN+0lvCQgQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#30 node\n",
"N=30\n",
"L=0.64 #m\n",
"mu=1.14e-3 #g/m\n",
"T=71.81 #N\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",
"e,v=linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e=e.real[isort]\n",
"v=v.real[:,isort]\n",
"print('First 3 Natural frequencies of {}-element string (Hz)'.format(N))\n",
"print(e.real[:3]**0.5/2/np.pi)\n",
"\n",
"x=np.linspace(0,L,N)\n",
"plt.plot(x,v[:,0],label='1')\n",
"plt.plot(x,v[:,1],label='2')\n",
"plt.plot(x,v[:,2],label='3')\n",
"plt.legend(prop={'size':15});"
]
},
{
"cell_type": "code",
"execution_count": 151,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First 3 Natural frequencies of 45-element string (Hz)\n",
"[196.04043699 391.85229959 587.20727994]\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": [
"#45 node\n",
"N=45\n",
"L=0.64 #m\n",
"mu=1.14e-3 #g/m\n",
"T=71.81 #N\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",
"e,v=linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e=e.real[isort]\n",
"v=v.real[:,isort]\n",
"print('First 3 Natural frequencies of {}-element string (Hz)'.format(N))\n",
"print(e.real[:3]**0.5/2/np.pi)\n",
"\n",
"x=np.linspace(0,L,N)\n",
"plt.plot(x,v[:,0],label='1')\n",
"plt.plot(x,v[:,1],label='2')\n",
"plt.plot(x,v[:,2],label='3')\n",
"plt.legend(prop={'size':15});"
]
},
{
"cell_type": "code",
"execution_count": 178,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First 3 Natural frequencies of 60-element string (Hz)\n",
"[196.05687232 391.9837462 587.65070938]\n"
]
},
{
"data": {
"image/png": 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WGlPJdDXs9XJny4ail1Z/uapyF3L0N6B2+E/rNa1tb5TBMXDFf8GRSMnhNbD2uWYPaQ2X9XPOZjpbcymTltl5cidHy44CEGgNZFrPaQZLBBf1uUjpLZNTnkN6frrBErliKpmuRslxufglyJFUYX1A1W558eLFXHrppSQkJBAUFERycjKLFnmmw7A5autrXTL8m3X4N8U5M+Dc+5zj1U9B9roOyXVRn4uULoY7i3Zy8PTBDp3PxLNQm8pmJ87Gz9vPQGlk/Lz9XMobrcxeaaA0Z2Mqma5E1akz/DA9wdvXZZfnn3+eoKAgXnjhBb7++mtmzJjB/PnzefnlztMECeQQ0tM1cpvouMA4JsZNbN+Jpj0AvSfLy8IOS26E8vbXggr1DWV6r+nKeOlBczbTVbDZbS4mUKNNZWouSLpAWf7xyI8eFUJvKpmugq0WTh9zjv3DGy0Z88033/DJJ58wb948Zs6cybPPPstvfvMbnn/+eTcK23Ea2h8DzOk/By+LV/tO5OUNV77j9FmV58HSOzpUsVntG/r2oJkz01XYdGITRdVy1YxI/0jGx3pO2+3R0aOJ9o8G5M6Zm/I2GSyRE1PJdAWEgNNHnPkwXj7yLKYRIiPP9luMHj26U1VfLq4uVm4iCanjiXAhcXCFqoLy/pWw7eOm92+BSfGTiPCLAOSSH2kn0jomn4lHsOyw0+F/YdKF7X+x0QGLZOH8pPOVsSeZzEwl0xUoL3B0uHTQo7ccQdVKUlNTGTJkiA6C6cPPR39WeqmPih5FbGBsx0/abzaMv805/u5B2b/VDrwt3lzS15kzYwYAdH6qbdUu9cHU/7+ewpkmszq7ZxTNNNsvd5S/hRotASxY41wOimlTPsyqVatYunQp7777rg6C6cMPR39QlmcnztbuxLMeg/3fyx1Da0ph6Z3wuy/bFZl3ab9L+WD3BwD8dPQnSmpKlAggk87H6uOrlSrfvUN6MyTC817KRkSNIDYwlryKPEprS9l4YiNTEqa0fKDOmDOZLkFDuHIABLf+rT47O5v58+dz2WWXcf311+sjmsY03DwNzO6toZLxCYDLX3eW3Tn0M2x5r12nGhA2QEmSq7XX8uORH7WS0sQAlh9yRpVd3Odit5X0bwsWycL5vZ0ms+8Of2egNE5MJdNVkCwQ1rvVdcmKi4u56KKLSExM5KOPPtJZOO1Yc2yN4kgfGjGU+CCNq0knjoeJdzrHKx9x5B21HbVJ5adjP3VQMBOjKKkpYW3OWmXsSVFlZ6LubfTT0Z88os+MaS7rKH8zqHRIXRUUZqHMYoLjoJUx+5WVlVxyySXU1taybNkyAgMD9ZNTY344ojKVaTmLUTPjYdi3Ek5mQV0FfHUH/P4bl3yj1jAzcSbPpD8DQFpuGhV1FQRaO8+/tYnM90e+V15shkUMo3dIb4MlapphkcNICEogpzyHsroyUnNTmdbL2IRRcybTGRHCEa6sMpM1lEhpAZvNxty5c9m/fz8rVqwgOjpaPzk1prKu0qW6sab+GDVWP5jzurMtwJF1sOmtNp+mZ3BPBoQNAGST2fqc9VpKaeImXExlfS82UJKWkSTJ46LMDFMykiTNlyRprSRJJZIklUuSlC5J0h2S1LY69JIkDZQk6R5Jkj6SJGmvJEl2SZKEJEntSAHvJFQUym/YAEjQI7HVzunbb7+d5cuX8+ijj1JcXExaWpryV1NTo5/MGrA2Zy019bKM/Xr0Iyk0Sb+LJSTDlD86x6v+DqePtvk0MxNnKss/H/tZC8lM3EhhZaFSpsUiWbiwz4UtHGE86iizn479pNwzRmGIkpEk6VXgYyAFWAv8AAwAXgGWSJLUlgD024AXgWuBgSjFqLoothq5s2MDQTFyfbJW8v333wNwzz33MHHiRJe/EydOtHC0said5+o+Grox7S8Q7YgiqquE5fe3OUlzRq8ZyvKa42s8JqzUpHWsOe6M3EyJSTG04nJrGRI+hF7BvQCoqKswfAbtdiUjSdKVwO1AHjBCCHGJEGIO0B/YA8wB7mzmFGeyE3gGuBroB6xpfvdOTEOPGEeOCN5+cqHHNpCdnY0QotG/pKQk7WXWiJr6Gn45/osy1s0fo8bbFy550Tnet0JudNYGBocPVvJ4ymrL2JK/RUsJTXRmzTHn48QTimG2BkmSXGYzRpvMjJjJPOj4/IsQYn/DSiFEPvKsBOCB1prNhBBvCyHuF0L8TwjRtasRVhVDTZlz3COxS3W5bI7UnFQqbZWAnKfQv0d/91w4cTwkX+8cL7/f9f+gBSRJYmYvlcnsqGky6yxU26pdqjWoa9J5Ouoos9XHVlNtqzZMFrc+oSRJ6gkkA7XA4jO3CyHWADlALDDBnbJ5PPU21x4xgVHg030ilX486jSVzU6c7d48hdl/cwZWlOXCz0+26XC1X+anYz8hOlAXzcR9bDyxkep6+eHcJ7QPiSGJBkvUegaEDSApJAmASlsl63ONM5m5+zV4tONzlxCiqol9Np+xrwnIfhh1bbLgOGPlcSN19XUuTnO3+GPU+IfBBSrFsvENyN3W6sPHxIwh2CcYgLyKPPYW79VaQhMdWH18tbI8ved0w+RoD5IkuZiU1x5f28ze+uJuJdPH8XmkmX0aQnj6NLNP96K2Qm6n3EBIQptqk3V2NudtpqxWNlHFBcYZU9Jj+FzoO11eFnb49o+t7qRptVhd7PlmYqbnI4Tgl2NOH6DRuSbt4dye5yrLa4+vNWwG7W4l01BUq6KZfRoqPQbrLIuCJEkLHCHU6YWF7e8logtCuBZq9A0Bv+5VA0tdq2xW4ixjSnpIElz8PHg5+vPkboXNb7f6cBeT2VFTyXg6u4t3U1AlVyYP9Q1lZNRIgyVqOyMiRyj18gqqCsg6lWWIHO5WMg1PB48ySgsh3hJCpAghUqKiWpfU6DYqi+TwWQAkuYS/B9ZN0gu7sLs8lN1uKlMTcY5rJ81V/4Sy/FYdOjl+Mj4WHwD2ndrH8bL2VXg2cQ/qqLKpCVPxtnS+4iheFi8mxU9SxuroTHfibiXTEJbTXJnghm2tD+HpqtTboDTXOQ6KOavTZVdnd9Fuiqvlbp/hfuGMih5lrECT74EIR2RbbRms+kerDguwBjAh3hnLYiZmejarj61WljujqawBtcmsuyiZbMdnc8V/ep2xb/elLNfV2R/UeUrAaIW6MOGUhClYjA7Z9vaFi/7lHG/7CI63LvdFHcpsmsw8l/yKfPYU7wHAW/JmcvxkgyVqP1PipyA5DEiZhZmcqj7ldhncfcdudXwOlSSpqTT1sWfs2z2prZBNZQ2E9OxWzv4G1uWsU5Y9oTcGAP1mwUBVJd4V94Pd3uJh03pNU274jIIMTlef1ktCkw6gzvJPjk1WIgM7Iz38ejAiagQAAmFIKLNblYwQ4hiQAfgAc8/cLknSNKAncjWADe6UzaNo1NkfYpw8BnG6+jQ7T+4E5LpRE+MmGiyRiguekGeXADnpkPlZi4dE+kcqDmS7sLuEyJp4Dmol09lClxvjzCgzd2OE7eEpx+e/JEnq17BSkqRo4DXH8GkhhF217SlH8cun6A5UFevm7F+yZAmTJk0iIiICPz8/Bg4cyOOPP05tba0m59eSDSc2KG2Wh0UOo4dfD4MlUhHeFybe4Rz/+NdWVQJQR5kZmbtg0jhVtiqXpnidpZRMc6iVzPrc9dS3MvReK9yuZIQQS4DXkbP6d0iS9I0kSV8A+4EhwFfIhTLVxCEXvzwrA1GSpDGSJKU1/AFjHJuePGN958BeD6XqApjRmjr7i4qKmDFjBm+//TYrVqzghhtu4IknnuDee+/V7Bpa4ZGmMjVT/wxBjk6k5fnwy7MtHqL+Hmkn0tx+w5s0T1pumlK1uG9oX3qF9GrhCM9nYNhAov1lf25JTQmZJzPden1D4vKEELdLkrQOuAOYBngBe4F3gdfVs5hWEAKMb2S9m4pbaUx5ATRU6rV4yxFlGnLLLbe4jGfMmEFpaSmvvvoqL7/8sse0lbULu0v12CnxHqhkfIPhvL/Dl45/07TXYMx1cqhzE/Tr0Y/ogGgKKgsorS1lZ9HOTpmD0VVRm8o6c1SZGkmSmNpzKp/v/xyQZ9Cjo91XUMWwUB0hxCdCiMlCiBAhRKAQIlkI8WpjCkYIcb0QQhJCXN/IttWObc3+ueVLdRRbraxkGgiOd4uzPyIiwuPMZXuL91JULQc+hPmGMTRyqMESNcHwedDTEatSXwsrH252d0mSXHIXUnNSm9nbxJ3Yhb3L+WMamNpzqrLs7lDm7lHCt7NQdgJoKOPvDwHhul2qvr6eyspK1q1bx0svvcRtt93mMbMYwGUWMzF+ovGhy01hsbiGNO9bAQebD09Wh8QaWbjQxJU9RXs4WSWXb+rh26NLzTAnxk1UEkqzTmWRV5Hntmt3vjRWD2P4B8ONFoEdv9/R5mMCAwOVTpjXXXcdzzzzjNZidQiP98eoSUiGUb+Vc2YAvn8MbpnW5Cx0QtwEJCQEgh0nd1BSU6KU/zAxDnVr78kJk/HqQikDAdYAUmJSlNYF63LWcdUA9zQP9tDXQxO9SU1NZe3atTz33HMsXbqUO+9sS584fSmtLWV74XZlrDYveSwzHwFrgLycv6PZkOYefj0YFjkMkE006mgmE+PYcMKZNdEpfnNtxKjsf1PJdFPGjBnDlClTuPfee3nppZd4/fXXOXjQM3q+peWmUe+odDA0YigR/hEGS9QKQuJg0l3O8ap/Qm1lk7u7+GVyTb+M0VTWVbK1wJn/7VE5WRqhVjJpJ9KorXePH9Y0l3WQ9piqXLDboXCP7DQGuTlWaM+OC9YGxoyRo74PHz7MOec0HRnlLtR+Co83lamZdDekvwcVBXJJoLTXXAtqqneNn8SbmW8C8vcVQniUT6y7kZ6fjs1uA+QIwKgADyuUqwG9Q3qTGJzI0bKjVNmqSM9Pd8uMzZzJGE3lSaeCkbwgONbtIqxfLz/U+/QxvoWPEKJz+WPU+AbBjIec43UvuEYLqhgeNZwgq1wLNq8ij8Mlh90hoUkTbMjt2qayBtSzGfV9piemkjESuw3KVFEewbFyboyOXHjhhTz77LOsWLGC77//nr/+9a/8+c9/5uqrr/aIWcy+U/soqJQfzCE+IYrvotMw+ncQNUheri2H1U83upvVYmV8nDO9y4wyMxa1kpkY3/VMZQ2oFai7fIGmkjGS8nzXKsuBkbpfcuzYsbz//vvMnTuXefPm8c033/DUU0+xcOFC3a/dGtQP24nxEztfHw8vbzhPVf5/y/tQuK/RXdU3vKlkjCO/Ip+DJbI/0mqxkhyTbLBE+pEck6zcU/tO7VNCtvXEVDJGYauFclUXzuA4cEMuyD//+U927txJeXk5p0+fJiMjg7vuugur1ar7tVtDpzWVqel/PvRxmCVEvVzXrBEmJzjzZbbkbVHKmZi4l4awXoAx0WPw926qQHznJ8Aa4JL/s+nEJt2vaSoZoyg/gdIg1OoP/mGGiuMJVNRVsDXfGeHTaft4SBKc/zhKI9is5ZB99kwlISiBpJAkAKrrq8nIz3CfjCYK6ug+dWO5rsqEOOd3VIdt64WpZIygrgoqi53jkIRu1VK5KdLz0rEJOcJnYNjAzh3hEzcSRlztHP/4N7mFwxmYoczGYhd2l5lMV3b6N6D2OaWdSEM08rvUElPJGIG6pbJvsPxn4nKzdwnn68yHnT1njm+SZzRnoDaZmX4Z97P/1H6lvXeYbxiDwgcZLJH+DI0Y6hLZeKT0iK7XM5WMu6kph5pS5zgk3jhZPAy1klFHXnVaeiTC2Juc41X/kFs5qEiJSVEcsftP7Vci60zcg4upLG6C59bI0xBvizdjY8cqY/V9pwdd/19UYzo0tRQCSnOcY/8wZykSD0fvKfXJqpMcOH0AkG+CMdFjWjiikzD1z+AjvzVSuPescjMB1gCX72qazNxLdwldPhMXv0yuvn4ZU8m0AavVSlVVVftPUF3i2vEy+KwebB5LVVWVrhFo6iiXEZEjCOgkyrdFAiNdy838/CTYXKPIzNL/xlBtq2ZL/hZl3K2UjCrAYXPeZqXagR6YSqYNREdHk5OTQ2VlZdvf7IVwlPJ3EBipacdLvRBCUFlZSU5ODtHR0bpdZ2OeMzGsy0X4TFv3LcYAACAASURBVLwDAhz110qOQfq7LptdEuTyNuo+azSRySjIoNYuV9voE9qH2ED3V9swij4hfYgOkO/nsroydhft1u1anSzTzVhCQkIAyM3Npa6urm0H11ZApdyEC8kCwVbIbbknvCdgtVqJiYlRvr/WCCFIy3XahdVT+S6BbzCc+3/w3QPy+JdnYPRvlYCPgeEDCfUNpaSmhOLqYg6cPkD/sM7Z2LUzof7NdcWCmM0hSRIT4yay9OBSQPbLjIgaocu1TCXTRkJCQtr+sLXVwivJcPqoPJ72AEx4UHvhOinHy46TWyFH3AV4B3S+UjKtIeUG2PAalByVXzZSX4EZ8m/AIlkYFzuOH478AMCmvE2mknEDav9XdwhdPpMJ8RNclMyCEQt0uY5pLnMHGR84FYx/uGw+MVFIy3O+USbHJGO1eEb1AU3x9nUtnrnhFZeKD+NjndF0ekf7mMiBJlmnsgDwlrxJiU0xWCL3o7YYbC3YSmVd060pOoKpZPSmtlI2jzQw9V7w08fs1FlRF+rrEqHLTTFiHkQNlpdry2Hd88qmcXHjlOX0vHRdHbEmrr+5kdEjCbQGGiiNMUT6R9KvRz8AbHYbGQX6VJwwlYzebHpLLoQJcjSZOm/CBLuwu0SWdTl/jBqLF8x6zDne/A6UyCHtSSFJiiO2vK6cvcV7jZCw27Apr5v85lpA/d3VPiotMZWMnlSXyD1FGph2v1ynzERh/6n9nKo5BUC4X3jX90UMvAgSHFV+62uUWa4kSabJzI10m9lzC5xZYkYPTCWjJ6mvQPVpeTksSe41YuKC+oc9LnZc18+4liSY+YhzvHUhFMsNy9QmM3dUx+2u5JTnkFMuzyD9vf0ZFtEFA01aSUpMCt6SHP+VdSqLoqoiza/Rxe9oAykvhA2vOsczHgavLujQ7iBdrpRMa+g7A3o72hjYbbDmX4Cr839rwVa39WDvbqgV+JiYMVi78X0ZYA1wCV3Wo5GZqWT0Yt0LUFchL0cPgWFXGiuPB1JXX+eScd1tlMyZs5nMz6Awi7igOBKDEwG59P/2wu0GCdi1UftjxsWOa2bP7oE6+VkPk5mpZPSgNBfS33GOZzwsO31NXNhxcgdVNrlMT0JQAr2CexkskRvpPRH6zZaXhV0uN8MZJrM802SmNUIIl5mMevbYXVEnourxmzOVjB6sfQ5s1fJy/GgYdLGx8ngo6ql5t4zwmfGwc3n3V3Biu8tszvTLaE92aTYFVXKl62BrcLco7d8SQyOHcu3ga3lx+ov879f/0/z8ppLRmtNHYcsHzvGMR8yGZE3QLf0xahLGwKBLnOOfn2RsjLMEe2Zhpm4Jct0VteJOiU3By7QwYLVYeWDcA8zqPYsQH+1z+EwlozW/PAN2R12zXuOh3yxj5fFQKusqySzMVMbd1jY+42GUNs37viPi5CEljNsm9EuQ666Y/hj3YyoZLSk6CFs/do5nmrOYpsgoyFBaLfcP60+Ef4TBEhlEzBAYfpVz/NM/XfwEpslMO+zCzua8zcpY7f8y0Q9TyWjJmn+DcHQ+TJoKfc41Vh4PxnS+qpj+IEgOs83hNYy3ONtxm0mZ2nFm4m9DSRUTfTGVjFYUZsEOldNMHaJqcham2UJFxDkw8jfKMHnH10pS6t7ivZTUlBglWZdC/ZsbGzu26yf+egjmv7JWrH5KDkUFOTQ1sRtGS7WSstoy9hTvAeQy98mxyQZL5AFM+z+wyJnXwUc2MCxIzpcRCNLz0o2UrMtgvtgYg6lktCBvJ+z60jlWl3Q3OYst+VuwOxTyoPBBukS0dDrCkuRGZg7GlTjbAKi7hpq0D5vd5qKsTSXjPkwlowWrn3IuD/yVswCiSaOYb5RNMPU+8PIBYFz+IWW1HqU+uht7i/dSXlcOQHRANL1DehssUffBVDIdpeoUHFeZM8xZTIuoI3zGxo5tZs9uRo9eMOb3AIyuqcUq5NWHSg5xsuqkgYJ1flyqLseORzKjPt2GqWQ6in8Y3L0Vzn8cUm6E2OFGS+TRlNSUkFUsdyT0krxIjjFnfS5MvRe8fPETghHV1cpqtWI2aTtnOv1N3IepZLTAJwAm3QWXPN/yvt2c9Lx0BPIr+tCIod2yI2GzhMTD2BsBGFddo6w265i1n7r6OrYWbFXG3bK6hIEYpmQkSZovSdJaSZJKJEkqlyQpXZKkOySpfXGFWp/PRB/MN8pWMPmP4O3PWHMmownqQqw9g3oSHxRvsETdC0MewJIkvQp8DKQAa4EfgAHAK8ASSZLaVFBI6/OZ6Ifp9G8FwTEw7mZGVtfga5ej8I6UHiG/It9gwTon6ug8cxbjftyuZCRJuhK4HcgDRgghLhFCzAH6A3uAOcCdRp3PRD+Kq4s5cPoAAN4Wb0ZFjzJYIg9m8j34WAMZVeNsXGaazNqHGWhiLEbMZB50fP5FCLG/YaUQIh+4zTF8oA1mLq3PZ6IT6pt9eORwAqwBBkrj4QRGwvhbXE1mZh2zNlNTX8P2AmfzN3P27H7c+uCVJKknkAzUAovP3C6EWAPkALFAiynzWp/PRF/MN8o2Mukuxtmct+imY6uNk6WTsr1gO7V2eTaYFJJEVECUwRJ1P9z9dj/a8blLCFHVxD6bz9jXnecz0RHTH9NGAsIZNvpG/B1+mZza0+SWHDVYqM6F+ZszHncrmT6OzyPN7NNwF/VpZh+9zmeiE4WVhRwuOQzITZJGRo00WKLOgXXSXYyurVfGm7a8bqA0nQ+X2XOcOXs2AncrmSDHZ0Uz+5Q7PoOb2UfT80mStMAR8pxeWFjY1G4mHUB9s4+MGomft5+B0nQi/MNcTIubDy6DepuBAnUeqmxVZJ50NsZTdx01cR/uVjINtRyEJ51PCPGWECJFCJESFWXabPXANFu0n3EptynLmyx1iO2fGihN52FrwVZsdlkh9+vRr/s2xjMYdyuZMsdnUDP7NGwra2Yfvc5nohNmEmb7GRI3jkDJCkCetzfH1/0L6usMlsrzMQNNPAN3K5lsx2dzJVB7nbGvO8/XLmz1dv78v+38ss80tTVGXkUex8qOAeDr5cuIqBEGS9S58LZ4MyY2RRlvqi2C7YsMlKhzYM6eW8/KXXk89OUO7HatjExO3K1kGgoIDZUkyb+Jfcaesa87z9dm6u2CPy/ezucZx7npw3R+zirQ4zKdGvXNPip6FD6OcvYmrWdc/CRleZO/H6x5Bmy1zRzRvamoq2DXyV0ASEikxKS0cET3ZcWOE9zxcQafbDzKw1/t1FzRuFXJCCGOARmADzD3zO2SJE0DeiJn729w9/naQ1F5DenZct/wWpudWz7cwo+7zfIfajadMN8oO4o6Mmqzny+i5ChsXWigRJ5NRn4G9UKOyhsQNoAefj0Mlsgz+WZ7Lncu2orNoVjSDhVRUqWtKdaILPiGDl//kiSpX8NKSZKigdccw6eFaOhlDJIkPSVJ0l5JklTdwdp/Pi2JDvHj0wUT6BkmT6Rq6+3c9vEWVu7K0+NynQ4hhMtMxqwd1T4GhQ0i2CoHSBZ6e5Nt9Ya1z0FddQtHdk9Mf0zLLN2Wwz2fbqXeoWD6RgXy6YIJhAVqa2lwu5IRQiwBXkfOwt8hSdI3kiR9AewHhgBfIRe2VBMHDHR8anE+TekVHsCnCyaQGC6XSamrF9zxcQYrdpzQ87KdguPlxzlRIf87BHgHMCRiiMESdU68LK69dzb7+UFpDmR8YKBUnou6KKY5ez6bz7cc50+fbaPBMtYvOohPF0wgJkT71AJD6nkJIW4HrkU2dU0DLgAOIBeyvFIIUd/M4bqfrz30DAvgs1smkBQhKxqbXXDnoq18m5mr96U9GrWpLDkmGavFaqA0nRv1G/kmP195Ye1zUNdUsYvuSWltKXuL9wJgkSwkx5qN8dT8L/0Y9y3ZriiYgTHBLB2RRnRBKojO7/hXEEJ8IoSYLIQIEUIECiGShRCvNmbWEkJcL4SQhBDXa3E+vYgL9eezWybSN1JuxFVvF9y9aCtLt+W4SwSPwyyzrh3j4pxv5JsDAuTksPJ8SH/XMJk8kS15W7A7bvtB4YMI8QkxWCLPYdGmo/zl80xFlwyOC+GzK8MJXPcULJwD718MtZWaXtOsTKwxMQ4fTb9oOT3HLuBPn23j8y3HDZbM/QghXGYypm28YwwIG0CobygAxRaJg1bHrHDdC1DbXNGL7oUZutw4Czdk8+AXOxQFMzQ+hE9uGk+Pjc+i5LNbA+ROvxpiKhkdiA7xY9HNExgYIztq7QLuW7KdzzZ3r+KGh0sOU1RdBECITwgDwwYaLFHnxiJZXB6aG8Ni5IWKQtj0X4Ok8jxMp//ZvLvuMI8u3aWMR/QM5eObxhNWlgW7vnTuOOMhza9tKhmdiAr25ZObxzM4Tp6qCwF/+XwHH6U1V8uza6E2lY2NHYuXxWxQ2lFclExsf+eG9f+BGrOoxenq02SdygLAS3INluiuvPXLQf7x7W5lPDqxBx/dNJ4eAT7wsypgd9AlkDBG8+ubSkZHIoJ8WXTzeIYlOG3Cj3y1kw9Ss40Tyo2Y+THao/ZrpVfnU98jUR5UFcPGNwySynNIz09XlodGDCXQGmigNMbz6s8HeHL5XmWc0juMD28YR4ifFXIyIGuZc+fpDzZyho5jKhmd6RHgw8c3TWBkL2cy2F+/3sXbaw8ZKJX+2IWdzflOs4WpZLQhKSSJaP9oAMrqytk79jrnxtSXoeq0QZJ5BmaNPBkhBC/+uI9nVmYp68b3CeeDG8YR7Ofw5f38hPOAoXMgdpgusphKxg2E+ltZeOM4xiQ6Fc3jy/bw6s8HDJRKX/ad2kdJTQkA4X7hnNPjHIMl6hpIkuQSZZYW3APCHf+21SWw4VWDJPMMzNmzrGCeWZnFiz8q3eiZ3C+C9/8wjkBfb3nF0Y1w4Ed5WbLoNosBU8m4jRA/Kx/eOJ5xfcKVdc+szOL5H/YhdIhNN5qNJ1Shy7HjkSSpmb1N2oLaZLYpPx2mP+DcmPYaVBQZIJXxFFYWcrDkICA3xhsd0/2a4QoheHzZHl5bfVBZd+6AKN75/Vj8fVQ+0Z8fdy4PnwdR+gXlmErGjQT5evP+H8YyuZ+zr8VLq/bzr++yupyicTFbmB0JNWV8rFPJZORnUDv41xA1WF5RWw7rXzBIMmNRB5qMjBqJv3dTNXO7Jna74LGlu3hn3WFl3ezB0fz3umT8rCoFc/gX+Q9A8oJp9+sql6lkNEAIwf5T+1m8b3GL+wb4ePPO78cybYCzOdoba+Toj66iaGx2G1vytyhj9UPRpOPEBcWRGCw7/Kvrq8ks2uUaerrpv1DW/Wrnucyeu1nib71d8NCXO1ioil69aFgsr12bjK+3SsEIAT+pfDGj5kOEvqZsU8l0ECEEl3x5CVd8fQX/2PAPpW9Kc/hZvXjrumRmD45R1r23PluXMttGsLtoNxV1cnJgbGAsvYJ7tXCESVtR+2U25W2Cwb+GuJHyCls1/PKsQZIZgxCCtBNpynhC3AQDpXEvtno79y3ezqebnc+ey0bF8/JvRuPjfcYj/uAqOOb4d7JYdZ/FgKlkOowkSSSGJCpj9dtUc/h6e/H6b8dw8XBnzc9PNh7lviXbsdW7rRKOLpyZcW36Y7RHPTvceGIjSBLMfNS5w5b34XT3Sf49WnaUvAp59hbgHcDQyKEGS+Qeam127lq0lS+3OktXXZXck+fnjcLb64zHuxCw6p/OcfLvoUciemMqGQ1QvzWp36Zawupl4T/XjOLyUfHKui8ycrjn023UdWJFo1a03TXCR2/U4bmZhZlU1lVCv9nQy/FbtNfBmn8ZJJ37Uf/mxsaO7RaFWKvr6rn1oy2s2Ok0jc4fn8i/rxyBl6WRF7s9X8OJbfKytx9Mvc8tcppKRgMmxk9Uljee2KgU52sN3l4Wnps3imvGOk1Ky3ac4LaPtlBdp3vxaM2pra9lW8E2ZWwqGX2I8I+gf5ic8W8TNrYWbHXMZh5x7rRtEZzsumHyatQvd93BH1NZa+OmD9L5aa+zE+8Nk/vwxOXDsDSmYOz18JMqomzcAgg5q3OKLphKRgP69+hPuJ8cmny65rRSZry1eFkknpwznOsnJSnrftxTwM0fplNV27kUTWZhJtX1ciOtxOBE4oLc80PujpxlMgPoMxX6TpeXRT2sbqzPX9fCLuwu9cq6upIpq67j9+9uYt2Bk8q6O2f049FLBjdtms78DE7uk5d9gmHKn9wgqYypZDRAkqR2m8wasFgk/vrrIdw6zRnpsXb/SX7/7ibKqrVth6onZsa1+1A/TNXhuy6+mZ2fQ/4uujJZxVmcrpErHYT7hdO/R/8Wjui8nKqo5bdvb2Szo+U7wH3nD+C+CwY2rWBsNa41yibdBQHhje+rA6aS0QgXJZPbdiUDsrL6y4UDufe8Acq6TdnFXPv2Rk5V1HZYRnfQ3cwWRpIck4xFkm/hPUV7lAoL9EyBARc59jrD2dsF6S6JvwVl1VzzVhrbj5co6x69ZAh3zmxBqW75AEocQSABETDxdh2lPBtTyWiE2i+TUZBBTX1Nu84jSRJ3z+rPw78arKzLPF7C1W9toKDUs/u5l9WWkVmYqYxNJaMvwT7BDI2Qo6gEgvQ8Z3FI2TfjeNjuWwFH2/fi0xlIy+v6LzbHT1Uy740NZOXLlbYlCZ6YM4wbp/Rp/sDaCvjlGed46p/BN1hHSc/GVDIaERsYS1JIEgA19TWyI7YD3HxuX56cM5yGl7J9+eXMe3MDx09p27VOSzbnbabe0el6cPhgxU9loh9Nmsxih8GIec7xj3/TpbWu0dTV15GRn6GMJ8R3vfyYQ4XlzHtjA9lF8r3vZZF4Yd4orh3fu+WDN74JFY7ggJAESLlRR0kbx1QyGqKFyUzN/PGJvDBvlBKOmF0kv80cKizv8Ln1YEPuBmVZPbMz0Q919J66OCQgFz1sCOU9ugH2f+9GydzD9sLtVNmqAOgZ1JOEoASDJdKWPSdKmfdmGrklshXDx8vCa9eO4fLRrfieVadh/YvO8bT7weqnk6RNYyoZDVG/RbXH+d8Yl49O4LVrx+DjSKzKLalm3psb2J1bqsn5tWTDCVPJuJvR0aOVnJCDJQcprCx0bgzvAyl/cI5//DvYO2/+VWOoZ29dzVSWcfQU17yVxsly2fTub/XinetTuGBobOtOkPqSXJkbILwvjLpWJ0mbx1QyGjI2dqziiN1dtNvpiO0gFwyN5Z3rU/B3FLk7WV7L1W9tID27WJPza0FOeQ5HSuW6SX5efoyO7n4VcI3Az9uPUdGjlLFa0QNw7v9BQ+Ougl2wc4kbpdMftdO/K5WSWbf/JL99eyMlVXJkabCvNx/eOI6p/aNaONJBaS5seM05nvEweBmToGoqGQ0J8QlhWKTc+EcgWl1ipjVM7R/FwhvHEewn94Moq7bx23c2sjqroIUj3YPaVJYck4yvl6+B0nQvJsVPUpbX56x33RgU7RpN9NPjYOsckYotUVlXyY7CHcpYXc+tM/PdzhPc8P5mKh05cuGBPnxy8wTGJrXBx7n6aXCYEYkdAUOv0EHS1mEqGY3paL5Mc6QkhfPpgglEBvkAUF1n5+YP0/k2M1fT67QH0x9jHGolk3Yi7eyKE5PuAn/HA+r0Ecj4wI3S6Ud6fjo2YQNgYNjALhFo8r/0Y9z+cQa1jrJScaF+/O+WiQzvGdr6kxRmwdaFzvF5fweLcY96U8lojJ5KBmBofCj/u2UiCT3kXhl19YK7Fm1l0SbjiiHW2+tdvqupZNzLoPBBygO2uLr47IoTfqFy6GoDa/4FNZ4ZPNIWulpO1ttrD3H/kkwaCrH3iQxk8a0T6Rcd1LYT/fh3aHjR6DsdzpmppZhtxlQyGqNulnSs7BjHy45rfo2+UUEsuW0i50TJtnYh4MEvdvDa6gOG9KTZU7yH0lo5ECHSP7JLZ1x7IhbJ4qLYU3NTz95p7E1yCCtARWGXaNPcVfrHyO2S9/L4sj3KuiFxISy+dSI9wwLadrKjaZC1zDme/XeNpGw/ppLRGB8vH8bEjFHGWvpl1MSF+svT6ATnNPrf32Xx+LI9bu9Jo36oTYyb2GUzrj2ZyfGTleWz/DIgh66q+7iv/w+U5btBMn0oqCxg3ym5Fpe3xZuUmBSDJWoftno7D36xg1d/drZLHpsUxqIFE4gMaqNfUwj44THnePhciB/V9P5uwlQyOjAxzvlWeVa0j4ZEBPnyyc3jmdjX2c75nXWH+fPi7W5tFWD6Y4xH/e++rWCb0jTOhVHzIXqIvFxX0amLZ6oVaXJ0MgHWNr7xewDVdfXc/nGGS7OxmYOi+fCG8YT6tyMSbO8yOOZ4qbVYXStyG4ipZHRA7Zdpa+n/thLsZ+W9P4zlomHO2Pkvt+Zw84fpVNbadLtuA5V1lWwrdJb270phpJ2JSP9IBoUPAuTS/2clZgJYvOA8VR2zjA+goG0Vwz2FdTnrlOXJCZOb2dMzKXVUUv5+t3M2ecWYBN78XTL+Pl7NHNkE9TZYpTKNjb0JwpI6LqgGmEpGB/qHuZb+zyrO0vV6flYvXpk/hvnjnV3uVmcVuqWwZnp+Oja7rMz6h/UnKqCVcfwmmuMSypzbiMkMoN8s6DtDXhZ2V/NKJ8Fmt7lYCKYkTDFQmrZTUFbNNW+msfGwM8/t5ql9ePaqkVjP7GbZWrZ95Czl7xsi50d5CKaS0QGLZHFxRDZ5w2uIl0XiicuHcffMfsq6rUdPc+UbqRwr1q/emYupLM40lRmJ2i/TqPMf5MqK5/8TpXjm/pVwaI3+wmnIjpM7KKuVC0XGBMTQr0e/Fo7wHA4VlnPFa6nsPuGs2PHgRYN4+OIhjTcbaw01ZfDzk87x5HsgMKLp/d2MqWR0Qn3Drz2+1i3XlCSJe88fyN8vHaoU1jxUWMGVr6fqVoZG/TBTv0mbuJ9R0aNcIhuPlR5rfMfY4bJ/poHvH+lU5WbU99OUhCmdJtBk69FTXPl6KsdPyUmSXhaJf181gltUPaTaxboXodxhdguOgwm3dVBSbTGVjE6op/DbC7drVmKmNfx+UhIv/2a0Uu+soKyGq9/cQKqqk54W5FXkcajkEABWi9Ulqs7E/fh4+bg0imt2Bj3jYXAoJPIyYcdinaXTDrU/prOYylbtyec3/03jVKVcJsbPauG/1yUzL6VXC0e2wOljsOEV53jWX8EnsGPn1BhTyehEhH8EwyLkEjP1ot7FrOQOLhkRzwc3qMrQ1Nj4/Xub+Hq7dtUB1N9pTMwY5S3axDha5ZcBCE2AiXc4x6v+AXVVOkqmDSerTrKnWM4n8Za8O0V+zKebjrJg4Raq6+TZYnigD4tunsDMQTEdP/mPfwObo89U/GgYcXXHz6kxppLRkXN7nqss/3L8F7dff+I5ESy+dSIxIXK8fV294O5FW3nrl4OaJG26VF02/TEegdpMu+nEJurqm2ndPeWPEOgI1Cg9DmmvNb2vh6A2z46MHkmwj3sbcLUFIQQv/LCPB77YQb0jd61XuD9Lbp3I6MSwjl/g2GbXgqcXPGlo+Zim8DyJuhBTe05VltflrNM1lLkpBsWG8MXtk11KUzy5fC+PLd2FrQO5NDa7zTUJ08yP8Qh6h/RWeqpU2lzDy8/CNximP+Ac//IclJ7QWcKOse545zCV1drs3Lc4k/+s2q+sGxofwue3TaJvVBvLxDSGELBSlVw75DLo7Zk+UVPJ6MiQiCFE+MlRHqdqTrHz5E5D5EjoIb89jVNVcV2YdoRbFm5pdy6N2s8U7R/N4PDBLRxh4g4kSXIxmbVoph1zPUQ5/u/qKmTzi4dSb68n9YTzxcZTlUxJVR3Xv7eJzzOcJaWm9o/ks1smEh2sUdOwnZ/D8c3yspePR5SPaQpTyeiIRbK43Ahrc9wTZdYYPQJ8+PDGcfx6ZLyybtXeAq5+M42Csuo2n2/NMWfY67m9zu00ET7dAZcSMy2Fz3t5w0VPO8eZn8pmGA9kZ9FO5cUmyj+KgWEDDZbobHJOVzH3jVRSDxYp665O6cW7148lyNdbm4vUVcEPf3WOJ9wmN6jzUEwlozNqk5kRfhk1flYv/nP1KG6b7gyZ3JFTwpxXU9mXX9amc60+vlpZnt5zukYSmmjBuLhxeEly1vieoj0UV7fQ3K7vdBh0iXO84n6PDGk+M8vf015sduaUMOfV9ezLd1a4vu/8ATx95fD2J1k2xoZXZB8aQEAkTL1Pu3PrgCFKRpKkgZIkfSRJUq4kSTWSJB2RJOl1SZLi2nGuQEmSrpUk6UVJktZLklQpSZKQJOlbPWRvK5PiJ+EtyW8wu4t2u7bHNQCLReIvFw7iyTnD8XIkf+WcruLK11JZs691sh0tPcrhksOA3AWzM0T4dCeCfYIZETUCkJvnNVow80wueAIaGs3lZsD2T3SUsH2ov4enlZJZuSuPuW9soKBMbpVs9ZJ48epR3Dmzv7bKsCQH1r7gHM98GPxCtDu/DrhdyUiSNA3YClwLnAC+BCqBW4HtkiQNaOMp+wMfAfcAkwCPiqMN9glmdIyzFbH6bcxI5o9P5O3fpxDoqJNUVmPjhvc3s3BDdovHrj62WlmeEDcBP2+N7MwmmjE1wTmD/vnYzy0fEJYkNzdr4Me/Q7U+Cbztobi6WPFpWiSLx0QzCiF4Y81Bbv1oC1V1cifLED9vPrxhPJePTtD+gisfkn1nANFDYfR12l9DY9yqZCRJCgQ+RVYEdwkhkoUQ1wghBgPPAVHAIqltqr8MeBe4HRiPrKw8CvUNb6Rf5kxmDIxm8a2TiA+VlUS9XfDo0l387evmI8/WHHf6Y6b1mqa7nCZtZ2ais1HVupx11NTXtHzQ1Hsh2OGzqyiAX/6tk3RtJzU3FYEcBjwyaiShvm3oFKkTtTY7f/k8k6dX7KUhI6B3RABf3D6ZiefoUNbl4M+w+yvn+OJnZZ+ah+PumcwfgFhgtRDilTO2/QU4CIwBLmrtCYUQB4UQNwohXhdCbAJacTe5J+PHZwAAIABJREFUF3W+TGpuavO5C25mSHwIX90xmZGq9q7vp2Zz04fplFWfLWdpbSkZ+RnKeFpPU8l4In1D+9I7pDcAVbaq1vU18gl01DVzkPY6nNzf9P5uxMVUFm+8qex0ZS3XvbuR/6U7I8jGJYXz5RnpApphq4XlqqKXI6722JDlM3G3krnc8fnRmRuEEPXIsxz1fl2CvqF9iQ+U3xAr6irYWrDVYIlciQ7x49MFE/nVcGe7gNVZhVzxWipHilz7kqzPWa/0VR8aMdSsuuyhSJLEjF4zlPFPR39q3YHDroREhynKboMVfwEDuq2qqbfXu+RkTelpbOjy/vwyLnt1PWmHnAEVV4xJYOFN4wgP9NHnommvQpFD4fuGuLZs8HDcrWQanBNNxUhuPmO/LoEkSR4VZdYY/j5evPKbMdw5w1nRdn9BOZe+sp71qppnan+MaSrzbNQms9XHVrcuGViS4KJ/oVRpPrgKdn2pj4CtZFvhNiVCLtwv3NCcrFV78pnzWipHipyVzf/vgoE8N3ckvt7t6APTGkqOwxqV6XLGQxCsQUkaN+E2JSNJUgjQkA14pIndjjo+PTfou52oTWae5JdRY7FI3HfBQJ6fNxIfb/mnUVJVx3XvbuL99Yepq69zCVwwQ5c9mxGRI5S+RkXVRWQWZrbuwLiRctOrBr57AKrdV+D1TH488qOyPDNxJhbJ/UGxQgheX32Qmz5Mp7xGnsn7W7147dox3DGjn77h1CsfgjqHUoseCmNv1u9aOuDO/y21obKR3rAANASYu7UgkSRJCyRJSpckKb2wUJ8Q47GxY/F1hIgeKjnE8bLjLRxhHFeM6clnCyYQHSzLW28X/O2b3dz++ReU1soRRzEBMUonRhPPxMvixfRe05XxT8daaTIDmPUoBDnMp+X5sMoY84wQglVHVynj8xLPc7sM1XX1/PGzbfzrO6eDP6GHP0tum8ivhrc566JtHPwJdi91jjuJs19Nq5WMJEn/liRpbzv+GuL4PCtzSoUQ4i0hRIoQIiUqSh8fg7+3P+NixyljTzSZqRmdGMY3d01xCQj4RR1V1nOaxyXDmZzNzF5Ok9nPR1sRytyAXyhc+JRzvPltOL5FQ8lax66iXZyokOuphfiEMDZubAtHaIucwb+Bpduc1cvHJYWz9M7JDI3XOcLNVgPL73eOR1zTaZz9atoyk4kHBrbjz+o4Xp1S3lTDg4bZTtvSzzsJapNZqx2xBhIT4sdnt0xkjiPe3ztoj7It3ifZKLFM2sD4uPFKC4bs0myl/0+rGDoH+s12DAR8e4/cS96N/HDkB2V5eq/pWC3WZvbWlvUHTvLrl9exI8dpKpw/PpGPbhpPZJCv/gL88swZzv5/6H9NHWi1khFC/FYIIbXjL9txfCnQEI7Ru4nLNHTwyW7vF/JkZibORHJM6Dbnb+ZklbZNxPTAz+rF8/NGctt5wVh8ZXmF3cpTX9Tx4YZsTVoGmOiHn7efS8hvm15uJAkufk7V3GwHbHxDYwmbRgjh4o85r7d7TGUNCZa/e2cjxRW1AHhbJP55+TCenDNc8VfqSt5OWKfK7J/1WKdy9qtxtwetIXa3qTnvuDP261JEB0Qr3SPtwu5yA3kykiQRG3tYGdsq+mOr9+axpbv48+LtVDsynU08E3WUWauy/9WEJcE0lcnm5yflboxuYN+pfRwtk2OBArwD3NJOorzGxh2fZPD0ir04WsAQFezLpwsm8LsJTb0ba0y9Db6+Uw4hBzmkPOVG91xbB9ytZBo8WNeeuUGSJC/gGsfQ2JhJHbkg6QJleWX2SgMlaRvq0OVYb2eb5S8ychrNpzHxHM7tea5SMDOzMLPt9fMm3eXaDmDF/W7JnfnxqPMlbFrPaUrgjF7szy/j8lfXs3xHnrIupXcYy+6aQoqqTYbubHwdch3v2V6+cOnLHtmMrLW4W/L3gDxghiRJd5yx7WngHORZzAr1BkmSxjUEErhHTP04r/d5SgjmlvwtFFQWGCxRy5ysOklGgTPL/6P51zM3uacy3n2ilEteWsd3Oz274VV3JdQ3lOQYpw+tzbMZLyv8+kXnOGs57FiskXRNo57pz+o9S9drfbn1OJe+sp4DBc4Kyr+f2JtPbp5AdIgba/MVH4KfnnCOp90Pkf3dd30dcKuSEUKUI89WqoBXHGHDiyRJ2g3cB5wEfiPONvQH4AwkOAtJkr6UJClNkqQ04FHH6skN6xx/F+vypdpIpH8kKTEpgFwhV+3Y9FRWZq9UEvmSY5LpGRLDv68awRNzhuHjKGFeVmPj1o8y+Ps3u6i1eV6Z+O5Oh0xmAIkTIOUG53j5fbp20cwuyebA6QMA+Hr5utT/05Lqunoe/CKTP322XSlw6We18Nzckfz9smHu8b80IAR8fTfYquRxzHCYfI/7rq8Tbp+DCSHWIGf0fwL0BK5Ajip7ExghhMhqx2lHIxfHHA/0dazroVo3Hrn4pkfQ2Uxmyw4tU5Yv7ivrakmSuHZ8bz6/bRK9wp2Fr99bn83cNzdw/FTlWecxMQ51iZmNJzZSXlvezN5NcN4/oEeivFxdAt/crZvZTG0qmxw/mQBrgObXOHyygjmvpbJok9PH1DcqkK/umMyVqpm628j4ELIdidqSBS57WZ5FdnIMMfQJIbKEENcKIWKFEL5CiEQhxK1CiEZfjYQQqxui1ZrYntSKKLf3df1SbWB279mKjXxrwVbyKvJaOMI4jpQeYcfJHQB4W7w5v/f5LtuH9wzl27umcv4QZ+TL9mOnufildXy303O/V3cjPiheSZ6ts9e1r+WEbzBc9ppzvP972HpWGUJNUM/wZ/ee3cye7eOrrTn8+uV17DnhbGdw6ch4vr5zCoNiDejPUpID3z/qHE+6C+K7RnWtzutN6sSE+4W7JGZ+n/29gdI0z/LDy5XlKQlTGi2xHupv5c3fJfPIxYPxdjRCK6mq49aPtvDwlzvM6DMPQZ2Yqf5/bRN9psJ4VTeN7x7UPNospzyH3UW7AfnFRssaeeU1Nu793zb++Nk2pTyMj5eFxy8fxn+uGaVdi+S2YLfDV7eCo7U04X1h+oPul0MnTCVjEC4msyOeaTITQrD8kPNh1GAqawxJkrhpal8+u2UCCT2c5rOPNx7l0lfWsTfPcxpgdVcu6uPsoLH2+NqW2zI3xay/yg9CgNoyOdxWQ7OZ2uE/IW4CIT7azCwyj5/mkpfW8kVGjrJO7v8yid9O6G1cBYsNr8BhRwUQySLPFq0e1XuxQ5hKxiBmJc5S2jJnFmaSW57bwhHuZ3fRbrJLswE5T6E1vWOSe4ez/O6pLm0D9uXL1ZzN5E1jSQpNYlTUKABswubyAtEmfALg8tdRKkUdWg3p72oiI6B5AqbdLnjrl4Nc8Voq2arqyVeMSWDZ3VMZlmBgA7QTmbBKlck/5V7o7RldP7XCVDIG0cOvB+PjxytjTzSZfXvoW2V5du/ZSnmSlggNsPLq/DE8fcVw/KzyT6zWZuexpbu4/r3N5JdW6yKvSctc2u9SZfnrg1+3/0SJE2DSnc7x949q0uAsvyKfbYXbALnNsrrAZ3s4fqqS+W+n8eTyvdgc2ZVBvt7855pRPD/PIPNYA3VV8PlNYHc0B4wfA9MfME4enTCVjIFcmHShsuxpUWb19nq+y/5OGV/cp20R4JIkcc24RL69awqD45zmjjX7CrngxV/4NtPzZm7dgQuSLlCSGvcU7yGruD3BnA5mPAKRjqyCugpYfL384OwASw86Kw6PjRmrtCpoK0IIFqcf48IX17o0FxvZqwfL757KZaMSmjnaTfzwGJx0/PtbA+CK/3aJaLIzMZWMgczoNQNvi/wmtbNoJ8fK3FOuozVsytuk1FYL9wtnXNy4Fo5onH7RwXx5+yRumtKHBpP36co67vxkK3cv2srpylqtRDZpBSE+IS45M+qHepux+sGVb8tZ6QD5O+VAgHZiF3a+2P+FMp7Tf067znOyvIZbFm7h/5ZkKs59iwR3zujHklsnkhihfTh0m9n3PWx6yzm+8CmI7Nf0/p0YU8kYSKhvqEvxQk8ymalzYy7qc5GiDNuDn9WLRy4Zwic3uQYFfL09lwte/IWf9uZ3SFaTtnHZOZcpy8sOLaOuwVzTHuJGwIVPOsdb3oOdn7frVGm5aeSUy075UN/QdoUur9hxggte+IXvdzt/U33+v70zD4+iShf3e7LvIQlJWJMQIvsqa5BVBGQVxAVGFHfRGRUZuNy5+tOrd4ZRR1R8htFRGRFkk4BsMwIqJoLIKsgS9rCELYSE7Gunz++PanoJSSCkq7vTOe/znKf6VFedOvV1dX1V53xL40CSnu/HzBFt8fZ0gVteQSasfcFSbzsa7pzqvP7ojAtIvGFjbWW27tQ6l5gYLzGU2DjD1XaorDoSW0ewcfoAHrBydMvIK+XJhXuYvnyfOeKtQl/6Nu1LlH8UANkl2fx84ee6NdjzKegw3lJf9zJknap1M0knksyfx8aPrVWssiv5JUxbvJfnl/xKltV19GjfWP79Un/ujAmrdX90ocIASU9AoSl+XFC0FpvMjXMzKSXjZO6OuZtAby29TlpuGjsv73Ryj7SEaoXlWsDLlsEt6dS4k93aDvbz5r0Hu/LPR3sQEehjXr9m/0WGvZ/ChgMXXULRujOeHp6MbT3WXF97sg5DZqDdIMd9pEVsBs2seeXjUH7rBh5Xi6/aJFV7oM0Dt7SflJKkvecZ9v5PbDxscf6NDvHlyyd783/jOxHg40KZJL973eLVj9Cs9AIjnNolvVFKxskEegcyrrXF4mfZkWVO7I1G5TAyevgPjOjYhO9mDOK+bs3M67IKy/jD0n08t3ivskDTGWsrs+TzyeSU5NStQb9QeHAheJoeHC4fgM2v3fLu606twyC1+ZPuUd1p3aj1Tfc5f62IqV/sZubK38gttgz5PdyzJZtfGcSgNi4TSUrjYBLsmG+pD3kVEvQN/OkKKCXjAkxqN8n8Ofl8slN9ZrJLstl6Yau5PqrVKN2OFR7ow7xJ3VkwtSdNrCLdbk7NYOjcFP617TSGChVsUw/iQ+Pp0rgLAAaj4fYjAFjTrDsM/7Olvvsz2H/zhyYpJauOW+ZxJt4xscbtywxG/pF8knveT+Gn45a0BS3D/VnydB/eeaALof4uZqV1+RCstTL5bjsKBvzRef1xIErJuADxofEkNtUcsIzSyNfHvnZaX1YcXWGeCO4U0YlWoa10P+bQ9tFsnjGQyb1jzOsKSg28tSGVcX//mV/PXdO9Dw2R+xIsBgB18pmxpvez0N4yFMe6F+Hs9hp32X15tzk5WbB3MMPjhle77Y60LEZ/tJV3Nx6jpFx7ABECnrgrjk3TB3JXQuO6n4O9Kb4GKx6xRFeOSIAJn9TrHDG1oWGcZT1gcrvJ5s+rTqyixOD44aJiQzHLjlqePB/t8KjDjh3i581f7+/Msmf60joy0Lw+9VIeEz/ezp9WH1TmznZmRNwIfDy04a3DWYc5ca3uzpQIoYVFieqg1Y3lsPwRLU9KNVhP+I+OH12l0+/VglJmfL2fSZ/u4IRVzpd2TYJJmtaPN8Z2dK25l+sYK2DVM3DtjFb3CYKHl2jDiw0EpWRchIEtBtIsUJufyCnNsXGEdBTrT63nWqn21tA0sGmNT5R6kdg6gm9fHsisEW3xNeXykBKW7TrH4PeS+XL7GTWEZidCfUMZEmNJAfDNSTslpPULgcnLIdA0J1KcDUsfhuIb531ySnJswshUnvAvMxj59KdTDPlbsk3MsUAfT14b3Z4NL/anR6yLWI5VxXevw0mrnFHj/wFR7ZzXHyeglIyL4OnhycPtHjbXlx5Z6lArqwpjBYtSF5nrj3Z4tE6+MXXBx8uD3w9J4PsZgxjaLsq8PqeonDfWHWbkvK2kHK9lCmFFlYxPsJgeJx1P4lqJnYYmw2Jh0lKLo+bV45rFWYWtT866U+vMw7OdG3embbgWQUBKyebDlxn+QQpz/nOUfJNTJcDozk35/o+DeHpAPF6u4PdSHT9/pAW/vE7/V6DDfdVv76a48C/U8Lg/4X6bkB8Hrh5w2LGT05M5m3cWgGCfYO6/436HHbs6WoYH8PnUnvzz0R42idFOXClg6r928cQXu2zS5SpqT79m/bgjTEvvW2woZnHqYvs13rK39uR+nbQf4dv/MkdsllKy6sSNE/5HLuUxZcFOnl281yagZXxkIAuf6MX8R+6kaaiLRynevwy+s8oP024M3P3/qt/ejVFKxoVo5NfIxppr6ZGlDjv2wsMLzZ8favOQ2XfH2QghNHPnVwYx+952NgENfzyWyfAPUpiddICLOXWLmdVQ8RAePNflOXN96dGl5F7Pa2IPOj9gmxtlz78g5V3tY8Ye0nK1uZoArwA6hQ7ilRX7GfXRVn4+mWXeJcTPi9fHdGDT9IEMbhuFy3N8M6z9vaUeexdMXAAens7rkxNRSsbFsDZn3nx2szl+mJ7sv7LfHPnWy8OLR9o/ovsxa4uftyfPD27NlpmDmNSrpdlB2ihhxZ50Br+XzJ83pKqoAbfBsNhhtA7V/FIKywv56oids10Omg2drOZakucgU/7GvF/nmVdFeSQy5qNdfLPvgjk1jaeHYGpiLCmzhvBk/1auERLmZqTvhq8fA2lK1BfVURs29PareT83ph78ag2LDhEdLDk/jAaSjifdZI+6Y/0WMyZ+DJEBLubEZkVUsB9vT+zC+j/0Z8AdFnPVMoORz7edZuC7P/LBd8fJLapDPK4Ghofw4Nkuz5rrS1KXkFdmxyRzQsB986G1JTDnlp1z+S3zNwCk9ORQag/KKyxzkEPbRfHtywN4875OhFlFhnBprhyFpQ9aTJUbxcCUVeDfyLn9cjJKybgg1ubMy44us+8fvhJn886y5dwWc31qh/oRqK9T81AWP9WHpU/3oWtLy5+4oNTAvB9O0P+dLfxt01H1ZnOLjIgbQVxIHAD55fksObLEvgfw9tOe6FsNxADMC7P8ZuXZichyLaR/77hwkqYlsuDxXrSJDrZvH/Tk4j5YOErziQEIiIAp30BIU+f2ywVQSsYFGRY7jCaBWmbJ7JJs5u+bf5M9bp9Fhxch0Z4gBzQfQEJY/Qo33i+hMWte6McnU3qQEBVkXp9famD+j6e46+0t/OXfqVxRYWpqxNPD0+ZtZnHqYgrK7GtUcbEQ/hzyBu8H3sFpH80jP8ho5P5rkvZNQ/jiiV6seK4vPeNuL4eM0zi9FRaOhSLTPJJ3IDyy0m1D99cWpWRcEG9Pb2b2nGmuLz+2vG7JpaohsyjTJp/I4x0ft/sxHIEQgns7NWHT9IF88HBXG2fO4vIKPtt6mv7v/Mislb9x9LJ+b4X1nZGtRhITrEVdyC/Lt3HMrQsHz+cyffk+Br77I5/vSmdRmCXky1M5efzVcxn/7r6LIW0idYmTpytH/wNfTdSCggL4NYLH1kLzHs7tlwuhlIyLMjx2OH2aaumZjdLInJ1z7Oo3I6XkrV/eorSiFNDmgno16WW39p2Bp4dgQvcWbH5lEPN/dyftmliGW8oqjKzce557P9zKI5/vYMvRDIxGFe3ZGi8PL57p8oy5/mXql+Zo3LWlwijZeOgyD33yC2P/vo01+y9iMEp8wn9GeGtvSBFGDx7J027OHlvegm+mgaG07ifiKH5bDiumgOk/RFATeOJbaFm//0f2RikZF0UIwf/0+R+zQ+SvV35lQ9oGu7W/IW0DyeeTzfUZPWbUv6fIavD0EIzu0pT/vDSAzx7rSbeWthOvP5/M4smFe7jn/RQ+35qm5m2sGB0/mhZBWr6f3NLcWr/NXMkv4R/JJxnyXjLTvtrLrjOW1MfCsxD/yBRz/Q+9Z+EfY0nax4Hl8OVYLamXK2M0wrYP4JvnLFZkYa3gqU0Q3cG5fXNBhMrdYUvPnj3lnj17nN0NM+/vfZ8vDn0BQIRfBOsnrCfYp24TohmFGUxYO4H8cu0pclLbSbza99U699VVkVLy67lrLNh2mo2HLlP5BcbH04PhHaOZ3DuGxPgIPDzcQ9neLqtPrOaN7W8A4Ovpy5JRS8ye+FVRYZRsPZHJ8l3pfH8kA0MlAXuZlL5v1Aa+TdeCv7YKbcXqcavxMhrh3zNgn5UTaGgM/G45RHe0/8nVlcIsWPM8nNhkWRfdCaashuBo5/XLyQgh9kope1b5nVIytriakikqL2LsmrFcKboCwJT2U5jde/Zttyel5IUfXmDbhW0AtAhqwapxqwjwdoG85w4gPbuIL7efYcXudJtQJdeJCQ9gfPfmjOvazMaQoCFRXlHOQxse4mTOSUBLXLd8zHJCfEJstjt2OZ+1+y+wdv9FLlThDBvq783v+sQwNTGOco9M7ltznzmEzIdDPmRojCmXipSw4x+w6VUwGaHgEwRj50Gnia6TNfLsdkh6CvKtUnHEJMLkZeDvwvHTHIBSMrXA1ZQMwMYzG5mVMgsAT+HJ12O/pk1Ym9tqy/opFeCLEV/Qs0mV14ZbU1hqYMOBiyzdlc5v6VUn7OrYLIRxXZsxtmszmjVy8TAmdiYtN43JGyZTZNDCugxpOYR5Q+aRnl3M+gMXWbf/Iscy8qvct1dcGJN6xTCqc1P8fTzJLc1l6rdTOZWrpWTuGtmVxSMX3zg8e3wTJD0J1lZtbUbC6LkQ2lyX87wljEbYNhd+nAPSKjhrvxdh6Bvg6WK5a5yAUjK1wBWVjJSSZzY/Y07N3CWyC58N+6zWbx+XCi4xYd0E82RuXd+K3IUjl/JYvusc3+y7QF7JjW83AF1bhDK0fTR3t4uiY7MQt5m/qolNZzYxM8Vi5dioeDzpZ/pWuW1YgDcT72zBpN4tSYiyDOcWG4p5dvOzNhElFt67kK6RXas+aEYqLJsEOWct63xDYNibcOfjjs/BcmGv9oZ17hfLOv9wLR9MmxGO7YsLo5RMLXBFJQOQlpPGxHUTzSlqOzfuzPyh8wnzu7XXdKM08tx3z7Hj0g4AYkNiWTl2ZZW5OxoqJeUVbDl6hXX7L7Ll2BXKDFWnFGga6sfd7aIY2CaSPq3CaRRQTzzSb5GsglJ2ns7mp+OZbLz0TyqCfwJASkHxuaepKNJC0Ph5e3BP+2jGdW3GoLaR+HrZxuYyGA1M/3E6Kectk/3vDHiHUfE3ybZakgc/vAm7P7ddH9sfRr3rmLmaa2fgh7fg0Crb9TGJWhwyZ75ZuSBKydQCV1UyAAsPLWTu3rnmelxIHJ8M+4TmQTVf8FeKrvDattf45ZL2NCYQLBq5iG5R3XTtb30mr6SczYczWPfbRX4+eZWKasydhYB2TUJIjI+gb3w4PePCCa8vYVBMXC0oZc+ZbHakZfPLqaxKw2AV+Md+ileA9mYhDUF083yTB7t15J720QT6Vp0OQkrJ69tfZ83JNeZ1s3vNZkqHKbfesbPbtcyaWSdt1yfcow1VtRpk//maomzYOhd2fQoVVlaHHl5w13Qt2KenCyZHczJKydQCV1YyoKVH/svOv5i99CP9I/n4no+rtf754ewP/O8v/0tOqWXe4YmOTzCj5wyH9NcdyC0uJ+V4Jj8cySD5WCa5xTXHRWveyJ8uLULp1DyULi1Cad80hIhAH6cPsUkpySwo5cilfA6ez+HA+VwOXsjlUm7N0RAaBRfh2eJDytAcWZsHNeeFbi8wqtWoanMOfbj3QxYcWmCuP935aV6+8+Xad7q8BFLe1nKzXDcXvk6TztDvJegwHrzqoNgNpXBiMxxcCcc2WvxertN+LNzzJkS0vv1juDlKydQCV1cyAJvPbOa/t/632VIn2DuYP/X5E/Gh8UQFRBHuF05pRSnv7H6H1SdWm/cTCB7v9DgvdX/JaQnJ6juGCiN7zl4j+VgmO9KyOHght9q3HGtC/LyIjwwiPjKQ+MaBxEYE0iTUj+hgP6JCfPHztk8Y+OKyCjLySsjIK+FyXglns4o4fbWQtMwC0jILq7Soq4yXh6Bry0YkxkcwuG0k3WPC2Juxm2e+ewaj1cR3bEgs07pOY2TcSIQQHLp6iOT0ZJLPJ9ukcp6QMIE3+71ZNyV76QD89C4c2YDZAu063gHQsg+0GgBxA6FZt5on4yvK4dpZuHoMjn0LqeugqvQGLXrB8D9DTNXzUAoLSsnUgvqgZAB2X97NS1teoqD8xvhSHsIDX09fig0Ws9LogGjm9J9D76a9HdlNt6eg1MDuM9nsSMtiZ1o2qZfyqp3LqYkQPy8aB/sS7OtFoK8XQabi7+OJR6Wbs1FKisoqKCg1UGgq+SUGMgtKya/GcKEm/Lw96NgslD6twklsHUGP2DACfG58CFl/aj1v73r7hoCtMcExFJYXklWSdcM+g1sM5oMhH9jvoSbrlGbuvG+JJdpxZXyCNOdIn0DwDdLqvkHaUNjVE3DtNBhrkFOTzjDgj9obUgMw8LAHSsnUgvqiZACOZR9j2vfTbppz5t64e3mt72uE+oY6qGcNl/IKI8cz8jl0IZcD53M5dCGXk1cKKCyruPnODiDI14uEqCCb4byEyKBbTmOcX5bPV0e+YvHhxWZn3qrw8fBhZKuRvNr3VX2MSwqzYM8C2L9Em6SvK41iofODWolqV/f2GhhKydSC+qRkAC4XXmZR6iLSctPILMoksyiTa6VauPFQ31Bm95rNmPgxTp8PaMhIKcnIKyUts4BTpqGriznFZOSVciWvhCv5pTd4yd8u3p6CKNMQXHSwH83D/E1DdEG0jgwkMtjXLtdCXlkeX6V+pUVrNr1Nh/uFM7DFQAa3GExis0THOfjmnIMz27RoyGe2Qm76zfcJbqZFSY7uDB3Ha0Nj6j9y2yglUwvqm5KpirKKMrJLsmns31jNvdQDjEZJdlEZWQVlNkNgBaUGistvfAMSgL+PF0G+ngRaDa9FBPoQFuDj0LA4uaW57L+yn1DfUDo37oyns1MMSwl5F6HoKpQWaI6dpfna0icIIhK04tswoznohVIytcAdlIxCoVA4kpphLNlzAAAGFklEQVSUjIrCrFAoFArdUEpGoVAoFLqhlIxCoVAodEMpGYVCoVDohlIyCoVCodANpWQUCoVCoRtKySgUCoVCN5SfTCWEEJnA2ZtuWDWNgZpjvCj0QsneeSjZOw9XkX2slDKyqi+UkrEjQog91TkkKfRFyd55KNk7j/ogezVcplAoFArdUEpGoVAoFLqhlIx9+dTZHWjAKNk7DyV75+HysldzMgqFQqHQDfUmo1AoFArdUEpGoVAoFLqhlEw1CCF+J4TYKoTIFUIUCCH2CCF+L4S4LZnZuz13xh6yEkJ4CyGGCiHmCiF2CCEuCSHKhBAXhBBJQojBOp5CvUXP61QIMUcIIU1lpj36607ocM/xF0L8lxBitxAiRwhRJIQ4LYRYKYS4y979rxYppSqVCjAfkEAxsAH4BsgzrVsNeDqzPXcu9pIVcI9pHwlcMrW1Ajhotf4tZ5+vKxU9r1OgF2AAjKb2Zjr7fF2p6HDPaQWcMO2fAawFvgZ2AWXAaw47N2cL19UKMNHqxnSH1fpoINX03cvOas+diz1lBdwNJAEDqvjuYdMNTwJDnH3erlD0vE4BX+AwcMF081RKRkfZA4HAyesPUoB3pe8jgDYOOz9nC9jVCrDH9OM8VsV3g6wuBg9ntOfOxZGyAj43tbfA2eftCkVP2QPvmPYfCyxUSkZf2QN/Ne3zpbPPTUqlZCr/OC1MP04p4F/NNudN2/RzdHvuXBwtK+D3prY2OfvcnV30lD3QB+2tcYmprpSMjrIHfNBimUmgvbPPT0qpJv4r0d20PCylLK5mm92VtnVke+6Mo2V1h2l5yQ5t1Xd0kb0Qwg/4EsgGXr797rk19pZ9D7ThsHQp5REhRD+TwcU/hRBvCiES69rh2uLl6AO6OK1My5qiMJ+rtK0j23NnHCYrIUQT4HFTdVVd2nIT9JL9X4C2wCQppStECnZF7C37zqblCSHEQmBqpe9fF0KsAh6tQanZFfUmY0uQaVlYwzYFpmWwE9pzZxwiKyGEF/AVEAr8IKVcf7ttuRF2l70Qoh8wHVgjpVxRh765O/aWfbhpORB4DHgPSADCgPvQjC8molmzOQSlZGwRpqW9Yu3Yuz13xlGy+gQYCqQDU3Q+Vn3BrrIXQvgDX6CZ4L5gjzbdGHtf99fv6V5oRi2zpJSnpJQ5Usp1wHjTsaYKIeLtdMxb6pBCI9+0DKphm+vf5dewjV7tuTO6y0oIMQ94CrgMDJVSXr6ddtwQe8t+DtAGmCGlVHNeNaPXPQfgs8pfSin3AHvR7v2Db6G9OqPmZGw5Y1rG1rBNy0rbOrI9d+aMaamLrIQQc4GXgEw0BXOitm24MWdMS3vJfgKa0+VUIUTlOYF2puXzQogxwEkp5dO32E935Ixpae97DsDparY5DfQEmtxCe3VGKRlb9pmWHYUQ/tVMjPWqtK0j23NndJOVEOJdYAaQBQyTUqbefjfdEj1k74Hm41Ed8abS6Bbbc1fsLftfrT5HoD1UVaaxaVlQxXd2Rw2XWSGlTEf7kXyAByt/L4QYhGbXfhn4xdHtuTN6yUoI8TYwC7iGpmB+s0uH3Qgdrvs4KaWoqqCZNAPMMq3rZr8zqX/oIPsLwE5TdWgV7YUBd5qqe26v17XE2Y46rlaAB7B42CZYrY9CC41xQ4gHNA/bo8Bf7dFeQy06yP7/TPtcA3o4+/xcudhb9jUcZyHKGVNX2aNFVpBoMcu6Wa33A5abvtuDKZ+Y3kUNl1VCSpkkhPgYeB44KIT4HihHeyoIAdYAf6+0W1M0f4CmdmqvQWJP2QshxgGvmaongReFEFTBUSnl23Y7iXqKva97xa2jwz1nvRDiPWAmsFMIsRNtqLg30AzNjHmyNGkevVFKpgqklC8IIbahhR4ZBHiiPTX8C/hYSml0ZnvujB1lFW71uaepVEUK0OCVDKjr1JnocM+ZJYTYDryIFikgAM2p833gbSllVXM1uqDSLysUCoVCN9TEv0KhUCh0QykZhUKhUOiGUjIKhUKh0A2lZBQKhUKhG0rJKBQKhUI3lJJRKBQKhW4oJaNQKBQK3VBKRqFQKBS6oZSMQqFQKHTj/wOKJ7+6+6BhOgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#60 node\n",
"N=60\n",
"L=0.64 #m\n",
"mu=1.14e-3 #g/m\n",
"T=71.81 #N\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",
"e,v=linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e=e.real[isort]\n",
"v=v.real[:,isort]\n",
"print('First 3 Natural frequencies of {}-element string (Hz)'.format(N))\n",
"print(e.real[:3]**0.5/2/np.pi)\n",
"\n",
"x=np.linspace(0,L,N)\n",
"plt.plot(x,v[:,0],label='1')\n",
"plt.plot(x,v[:,1],label='2')\n",
"plt.plot(x,v[:,3],label='3')\n",
"plt.legend(prop={'size':15});"
]
},
{
"cell_type": "code",
"execution_count": 153,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"180 nodes causes convergence. This can be determined by changing N until convergence happens\n"
]
}
],
"source": [
"print('180 nodes causes convergence. This can be determined by changing N until convergence happens') "
]
},
{
"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": 175,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First 3 Natural frequencies of 180-element E string (Hz)\n",
"Nat Freq 1:329.6952\n",
"Nat Freq 2:659.3655\n",
"Nat Freq 3:988.9862\n",
"\n",
"\n",
"First 3 Natural frequencies of 180-element B string (Hz)\n",
"Nat Freq 1:28472.0572\n",
"Nat Freq 2:28468.8406\n",
"Nat Freq 3:28463.4799\n",
"\n",
"\n",
"First 3 Natural frequencies of 180-element G string (Hz)\n",
"Nat Freq 1:22592.7966\n",
"Nat Freq 2:22590.2442\n",
"Nat Freq 3:22585.9904\n",
"\n",
"\n",
"First 3 Natural frequencies of 180-element D string (Hz)\n",
"Nat Freq 1:16928.0723\n",
"Nat Freq 2:16926.1599\n",
"Nat Freq 3:16922.9727\n",
"\n",
"\n",
"First 3 Natural frequencies of 180-element A string (Hz)\n",
"Nat Freq 1:12678.0188\n",
"Nat Freq 2:12676.5866\n",
"Nat Freq 3:12674.1996\n",
"\n",
"\n",
"First 3 Natural frequencies of 180-element E2 string (Hz)\n",
"Nat Freq 1:9500.7782\n",
"Nat Freq 2:9499.7049\n",
"Nat Freq 3:9497.9161\n"
]
}
],
"source": [
"muE=0.401e-3\n",
"muB=0.708e-3\n",
"muG=1.140e-3\n",
"muD=2.333e-3\n",
"muA=4.466e-3\n",
"muE2=6.790e-3\n",
"\n",
"g=9.81\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",
"TE2=7.71*g\n",
"\n",
"N=180\n",
"L=0.64\n",
"dx=L/(N+1)\n",
"\n",
"#E\n",
"kE=TE/dx**2/muE\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",
"eE,vE=linalg.eig(AE)\n",
"isort=np.argsort(eE.real)\n",
"eE=eE[isort]\n",
"vE=vE[:,isort]\n",
"\n",
"E1=eE.real[0]**0.5/2/np.pi\n",
"E2=eE.real[1]**0.5/2/np.pi\n",
"E3=eE.real[2]**0.5/2/np.pi\n",
"print('First 3 Natural frequencies of {}-element E string (Hz)'.format(N))\n",
"print('Nat Freq 1:{0:.4f}'.format(E1))\n",
"print('Nat Freq 2:{0:.4f}'.format(E2))\n",
"print('Nat Freq 3:{0:.4f}'.format(E3))\n",
"\n",
"\n",
"#B\n",
"kB=TB/dx**2/muB\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",
"eB,vB=linalg.eig(AB)\n",
"isort=np.argsort(e.real)\n",
"eB=eB[isort]\n",
"vB=vB[:,isort]\n",
"\n",
"B1=eB.real[0]**0.5/2/np.pi\n",
"B2=eB.real[1]**0.5/2/np.pi\n",
"B3=eB.real[2]**0.5/2/np.pi\n",
"print('\\n\\nFirst 3 Natural frequencies of {}-element B string (Hz)'.format(N))\n",
"print('Nat Freq 1:{0:.4f}'.format(B1))\n",
"print('Nat Freq 2:{0:.4f}'.format(B2))\n",
"print('Nat Freq 3:{0:.4f}'.format(B3))\n",
"\n",
"#G\n",
"kG=TG/dx**2/muG\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",
"eG,vG=linalg.eig(AG)\n",
"isort=np.argsort(e.real)\n",
"eG=eG[isort]\n",
"vG=vG[:,isort]\n",
"\n",
"G1=eG.real[0]**0.5/2/np.pi\n",
"G2=eG.real[1]**0.5/2/np.pi\n",
"G3=eG.real[2]**0.5/2/np.pi\n",
"print('\\n\\nFirst 3 Natural frequencies of {}-element G string (Hz)'.format(N))\n",
"print('Nat Freq 1:{0:.4f}'.format(G1))\n",
"print('Nat Freq 2:{0:.4f}'.format(G2))\n",
"print('Nat Freq 3:{0:.4f}'.format(G3))\n",
"\n",
"#D\n",
"kD=TD/dx**2/muD\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",
"eD,vD=linalg.eig(AD)\n",
"isort=np.argsort(e.real)\n",
"eD=eD[isort]\n",
"vD=vD[:,isort]\n",
"\n",
"D1=eD.real[0]**0.5/2/np.pi\n",
"D2=eD.real[1]**0.5/2/np.pi\n",
"D3=eD.real[2]**0.5/2/np.pi\n",
"print('\\n\\nFirst 3 Natural frequencies of {}-element D string (Hz)'.format(N))\n",
"print('Nat Freq 1:{0:.4f}'.format(D1))\n",
"print('Nat Freq 2:{0:.4f}'.format(D2))\n",
"print('Nat Freq 3:{0:.4f}'.format(D3))\n",
"\n",
"#A\n",
"kA=TA/dx**2/muA\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",
"eA,vA=linalg.eig(AA)\n",
"isort=np.argsort(e.real)\n",
"eA=eA[isort]\n",
"vA=vA[:,isort]\n",
"\n",
"A1=eA.real[0]**0.5/2/np.pi\n",
"A2=eA.real[1]**0.5/2/np.pi\n",
"A3=eA.real[2]**0.5/2/np.pi\n",
"print('\\n\\nFirst 3 Natural frequencies of {}-element A string (Hz)'.format(N))\n",
"print('Nat Freq 1:{0:.4f}'.format(A1))\n",
"print('Nat Freq 2:{0:.4f}'.format(A2))\n",
"print('Nat Freq 3:{0:.4f}'.format(A3))\n",
"\n",
"#E2\n",
"kE2=TE2/dx**2/muE2\n",
"AE2=kE2*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"eE2,vE2=linalg.eig(AE2)\n",
"isort=np.argsort(e.real)\n",
"eE2=eE2[isort]\n",
"vE2=vE2[:,isort]\n",
"\n",
"E21=eE2.real[0]**0.5/2/np.pi\n",
"E22=eE2.real[1]**0.5/2/np.pi\n",
"E23=eE2.real[2]**0.5/2/np.pi\n",
"print('\\n\\nFirst 3 Natural frequencies of {}-element E2 string (Hz)'.format(N))\n",
"print('Nat Freq 1:{0:.4f}'.format(E21))\n",
"print('Nat Freq 2:{0:.4f}'.format(E22))\n",
"print('Nat Freq 3:{0:.4f}'.format(E23))"
]
},
{
"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": 176,
"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": 176,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Audio\n",
"r=20000\n",
"tsig=np.arange(0,1,1/r)\n",
"Audio(data=100*np.sin(E1*2*np.pi*tsig) \n",
" + 100*np.sin(E2*2*np.pi*tsig)\n",
" + 100*np.sin(E3*2*np.pi*tsig)\n",
" + 100*np.sin(B1*2*np.pi*tsig)\n",
" + 100*np.sin(B2*2*np.pi*tsig)\n",
" + 100*np.sin(B3*2*np.pi*tsig)\n",
" + 100*np.sin(G1*2*np.pi*tsig)\n",
" + 100*np.sin(G2*2*np.pi*tsig)\n",
" + 100*np.sin(G3*2*np.pi*tsig)\n",
" + 100*np.sin(D1*2*np.pi*tsig)\n",
" + 100*np.sin(D2*2*np.pi*tsig)\n",
" + 100*np.sin(D3*2*np.pi*tsig)\n",
" + 100*np.sin(A1*2*np.pi*tsig)\n",
" + 100*np.sin(A2*2*np.pi*tsig)\n",
" + 100*np.sin(A3*2*np.pi*tsig)\n",
" + 100*np.sin(E21*2*np.pi*tsig)\n",
" + 100*np.sin(E22*2*np.pi*tsig)\n",
" + 100*np.sin(E23*2*np.pi*tsig),rate=r)\n",
"#Sounds like a strum with one string being extremely loose and clashing with another"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}