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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": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib import animation\n",
"from IPython.display import HTML\n",
"from IPython.display import Audio\n",
"from scipy import linalg"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"L = 0.64\n",
"E = 10e9\n",
"N = 10\n",
"h=L/(N-1)\n",
"I = (((0.04*0.02)**3)/12)\n",
"g = 9.81\n",
"M = (7.28+7.22+7.32+8.41+9.03+7.71)*g*4e-3\n",
"mu0 = 0.401e-3\n",
"mu1 = 0.708e-3\n",
"mu2 = 1.140e-3\n",
"mu3 = 2.333e-3\n",
"mu4 = 4.466e-3\n",
"mu5 = 6.790e-3\n",
"\n",
"T0 = 7.28*g\n",
"T1 = 7.22*g \n",
"T2 = 7.32*g \n",
"T3 = 8.41*g \n",
"T4 = 9.03*g\n",
"T5 = 7.71*g\n",
"\n",
"A=np.diag(np.ones(N-1)*6)\\\n",
"+np.diag(np.ones(N-2)*-4,-1)\\\n",
"+np.diag(np.ones(N-2)*-4,1)\\\n",
"+np.diag(np.ones(N-3),-2)\\\n",
"+np.diag(np.ones(N-3),2)\n",
"A[0,0]+=1\n",
"A[-1,-1]+=-4\n",
"A[-1,-3]+= 1\n",
"A[-2,-2]+= -1\n",
"A[-2,-1]+= 2\n",
"\n",
"b=np.zeros(N-1)\n",
"b[-2]+= (-M*h**2)/(E*I)\n",
"b[-1]+= (2*M*h**2)/(E*I)\n",
"x=np.linspace(0,L)\n",
"w_ana= (M/(2*E*I))*x**2\n",
"w=np.linalg.solve(A,b)\n",
"xnum=np.arange(0,L+h/2,h)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A matrix\n",
" [[ 7. -4. 1. 0. 0. 0. 0. 0. 0.]\n",
" [-4. 6. -4. 1. 0. 0. 0. 0. 0.]\n",
" [ 1. -4. 6. -4. 1. 0. 0. 0. 0.]\n",
" [ 0. 1. -4. 6. -4. 1. 0. 0. 0.]\n",
" [ 0. 0. 1. -4. 6. -4. 1. 0. 0.]\n",
" [ 0. 0. 0. 1. -4. 6. -4. 1. 0.]\n",
" [ 0. 0. 0. 0. 1. -4. 6. -4. 1.]\n",
" [ 0. 0. 0. 0. 0. 1. -4. 5. -2.]\n",
" [ 0. 0. 0. 0. 0. 0. 2. -4. 2.]]\n",
"b matrix\n",
" [ 0. 0. 0. 0. 0. 0.\n",
" 0. -0.02184418 0.04368836]\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"print('A matrix\\n', A)\n",
"print('b matrix\\n', b)\n",
"plt.figure()\n",
"plt.plot(xnum, np.block([0,w*1000]),'o')\n",
"plt.title('Finite Difference Approximation')\n",
"plt.ylabel('Deflection (mm)')\n",
"plt.xlabel('Beam Location (m)');"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"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 = 80\n",
"h=L/(N-1)\n",
"A=np.diag(np.ones(N-1)*6)\\\n",
"+np.diag(np.ones(N-2)*-4,-1)\\\n",
"+np.diag(np.ones(N-2)*-4,1)\\\n",
"+np.diag(np.ones(N-3),-2)\\\n",
"+np.diag(np.ones(N-3),2)\n",
"A[0,0]+=1\n",
"A[-1,-1]+=-4\n",
"A[-1,-3]+= 1\n",
"A[-2,-2]+= -1\n",
"A[-2,-1]+= 2\n",
"\n",
"b=np.zeros(N-1)\n",
"b[-2]+= (-M*h**2)/(E*I)\n",
"b[-1]+= (2*M*h**2)/(E*I)\n",
"x=np.linspace(0,L)\n",
"w_ana= (M/(2*E*I))*x**2\n",
"w=np.linalg.solve(A,b)\n",
"xnum=np.arange(0,L+h/2,h)\n",
"plt.plot(x,w_ana*1000, label = 'Analytical Solution')\n",
"plt.plot(xnum,np.block([0,w*1000]),'.', label = 'Finite Difference')\n",
"plt.title('Finite Difference Approximation vs. Analytical Solution')\n",
"plt.ylabel('Deflection (mm)')\n",
"plt.xlabel('Beam Location (m)')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');"
]
},
{
"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": 5,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First three natural frequencies of 6-element string (Hz)\n",
" 1st natural frequency: 194.437\n",
" 2nd natural frequency: 379.124\n",
" 3rd natural frequency: 544.801\n",
"First three natural frequencies of 30-element string (Hz)\n",
" 1st natural frequency: 195.995\n",
" 2nd natural frequency: 391.486\n",
" 3rd natural frequency: 585.973\n",
"First three natural frequencies of 45-element string (Hz)\n",
" 1st natural frequency: 196.040\n",
" 2nd natural frequency: 391.852\n",
" 3rd natural frequency: 587.207\n",
"First three natural frequencies of 60-element string (Hz)\n",
" 1st natural frequency: 196.057\n",
" 2nd natural frequency: 391.984\n",
" 3rd natural frequency: 587.651\n"
]
}
],
"source": [
"mu = 1.14e-3\n",
"T = 71.81\n",
"\n",
"N6 = 6\n",
"N30 = 30\n",
"N45 = 45\n",
"N60=60\n",
"\n",
"dx6=L/(N6+1)\n",
"dx30=L/(N30+1)\n",
"dx45=L/(N45+1)\n",
"dx60=L/(N60+1)\n",
"\n",
"k6 = T/dx6**2/mu\n",
"k30 = T/dx30**2/mu\n",
"k45 = T/dx45**2/mu\n",
"k60 = T/dx60**2/mu\n",
"\n",
"A6 = k6*(np.diag(np.ones(N6)*2)\\\n",
" -np.diag(np.ones(N6-1),-1)\\\n",
" -np.diag(np.ones(N6-1),1))\n",
"A30 = k30*(np.diag(np.ones(N30)*2)\\\n",
" -np.diag(np.ones(N30-1),-1)\\\n",
" -np.diag(np.ones(N30-1),1))\n",
"A45 = k45*(np.diag(np.ones(N45)*2)\\\n",
" -np.diag(np.ones(N45-1),-1)\\\n",
" -np.diag(np.ones(N45-1),1))\n",
"A60 = k60*(np.diag(np.ones(N60)*2)\\\n",
" -np.diag(np.ones(N60-1),-1)\\\n",
" -np.diag(np.ones(N60-1),1))\n",
"\n",
"e6,v6=linalg.eig(A6)\n",
"isort6 = np.argsort(e6.real)\n",
"e6=e6.real[isort6]\n",
"v6=v6.real[:,isort6]\n",
"e30,v30=linalg.eig(A30)\n",
"isort30 = np.argsort(e30.real)\n",
"e30=e30.real[isort30]\n",
"v30=v30.real[:,isort30]\n",
"e45,v45=linalg.eig(A45)\n",
"isort45 = np.argsort(e45.real)\n",
"e45=e45.real[isort45]\n",
"v45=v45.real[:,isort45]\n",
"e60,v60=linalg.eig(A60)\n",
"isort60 = np.argsort(e60.real)\n",
"e60=e60.real[isort60]\n",
"v60=v60.real[:,isort60]\n",
"\n",
"f6 = e6.real**0.5/2/np.pi\n",
"f30 = e30.real**0.5/2/np.pi\n",
"f45 = e45.real**0.5/2/np.pi\n",
"f60 = e60.real**0.5/2/np.pi\n",
"\n",
"print('First three natural frequencies of {}-element string (Hz)'.format(N6))\n",
"print(' 1st natural frequency: {0:.3f}'.format(f6[0]))\n",
"print(' 2nd natural frequency: {0:.3f}'.format(f6[1]))\n",
"print(' 3rd natural frequency: {0:.3f}'.format(f6[2]))\n",
"print('First three natural frequencies of {}-element string (Hz)'.format(N30))\n",
"print(' 1st natural frequency: {0:.3f}'.format(f30[0]))\n",
"print(' 2nd natural frequency: {0:.3f}'.format(f30[1]))\n",
"print(' 3rd natural frequency: {0:.3f}'.format(f30[2]))\n",
"print('First three natural frequencies of {}-element string (Hz)'.format(N45))\n",
"print(' 1st natural frequency: {0:.3f}'.format(f45[0]))\n",
"print(' 2nd natural frequency: {0:.3f}'.format(f45[1]))\n",
"print(' 3rd natural frequency: {0:.3f}'.format(f45[2]))\n",
"print('First three natural frequencies of {}-element string (Hz)'.format(N60))\n",
"print(' 1st natural frequency: {0:.3f}'.format(f60[0]))\n",
"print(' 2nd natural frequency: {0:.3f}'.format(f60[1]))\n",
"print(' 3rd natural frequency: {0:.3f}'.format(f60[2]))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"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": [
"x6 = np.linspace(0,L,N6+2) \n",
"plt.plot(x6[1:-1],-1*v6[:,0]/np.max(-v6[:,0]),'o',label = '6 nodes') \n",
"x30 = np.linspace(0,L,N30+2) \n",
"plt.plot(x30[1:-1],-1*v30[:,0]/np.max(-v30[:,0]),'o', label = '30 nodes') \n",
"x45 = np.linspace(0,L,N45+2) \n",
"plt.plot(x45[1:-1],-1*v45[:,0]/-np.max(v45[:,0]),'o', label = '45 nodes') \n",
"x60 = np.linspace(0,L,N60+2) \n",
"plt.plot(x60[1:-1],-1*v60[:,0]/np.max(-v60[:,0]),'o', label = '60 nodes') \n",
"plt.title('First Mode Shape\\n')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"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": [
"plt.plot(x6[1:-1],-v6[:,1]/np.max(-v6[:,1]),'o',label = '6 nodes') \n",
"plt.plot(x30[1:-1],v30[:,1]/np.max(-v30[:,1]),'o', label = '30 nodes') \n",
"plt.plot(x45[1:-1],v45[:,1]/-np.max(v45[:,1]),'o', label = '45 nodes') \n",
"plt.plot(x60[1:-1],v60[:,1]/np.max(-v60[:,1]),'o', label = '60 nodes') \n",
"plt.title('Second Mode Shape\\n')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"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": [
"plt.plot(x6[1:-1],v6[:,2]/np.max(v6[:,2]),'o',label = '6 nodes') \n",
"plt.plot(x30[1:-1],v30[:,2]/np.max(v30[:,2]),'o', label = '30 nodes') \n",
"plt.plot(x45[1:-1],v45[:,2]/-np.max(v45[:,2]),'o', label = '45 nodes') \n",
"plt.plot(x60[1:-1],v60[:,2]/np.max(v60[:,2]),'o', label = '60 nodes') \n",
"plt.title('Third Mode Shape\\n')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');"
]
},
{
"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": 9,
"metadata": {},
"outputs": [],
"source": [
"# using 60 node guitar string\n",
"k0 = T0/dx60**2/mu0\n",
"k1 = T1/dx60**2/mu1\n",
"k2 = T2/dx60**2/mu2\n",
"k3 = T3/dx60**2/mu3\n",
"k4 = T4/dx60**2/mu4\n",
"k5 = T5/dx60**2/mu5\n",
"\n",
"E = k0*(np.diag(np.ones(N60)*2)\\\n",
" -np.diag(np.ones(N60-1),-1)\\\n",
" -np.diag(np.ones(N60-1),1))\n",
"B = k1*(np.diag(np.ones(N60)*2)\\\n",
" -np.diag(np.ones(N60-1),-1)\\\n",
" -np.diag(np.ones(N60-1),1))\n",
"G = k2*(np.diag(np.ones(N60)*2)\\\n",
" -np.diag(np.ones(N60-1),-1)\\\n",
" -np.diag(np.ones(N60-1),1))\n",
"D = k3*(np.diag(np.ones(N60)*2)\\\n",
" -np.diag(np.ones(N60-1),-1)\\\n",
" -np.diag(np.ones(N60-1),1))\n",
"A = k4*(np.diag(np.ones(N60)*2)\\\n",
" -np.diag(np.ones(N60-1),-1)\\\n",
" -np.diag(np.ones(N60-1),1))\n",
"E2 = k5*(np.diag(np.ones(N60)*2)\\\n",
" -np.diag(np.ones(N60-1),-1)\\\n",
" -np.diag(np.ones(N60-1),1))\n",
"\n",
"e0,v0=linalg.eig(E)\n",
"isort0 = np.argsort(e0.real)\n",
"e0=e0.real[isort0]\n",
"v0=v0.real[:,isort0]\n",
"e1,v1=linalg.eig(B)\n",
"isort1 = np.argsort(e1.real)\n",
"e1=e1.real[isort1]\n",
"v1=v1.real[:,isort1]\n",
"e2,v2=linalg.eig(G)\n",
"isort2 = np.argsort(e2.real)\n",
"e2=e2.real[isort2]\n",
"v2=v2.real[:,isort2]\n",
"e3,v3=linalg.eig(D)\n",
"isort3 = np.argsort(e3.real)\n",
"e3=e3.real[isort3]\n",
"v3=v3.real[:,isort3]\n",
"e4,v4=linalg.eig(A)\n",
"isort4 = np.argsort(e4.real)\n",
"e4=e4.real[isort4]\n",
"v4=v4.real[:,isort4]\n",
"e5,v5=linalg.eig(E2)\n",
"isort5 = np.argsort(e5.real)\n",
"e5=e5.real[isort5]\n",
"v5=v5.real[:,isort5]\n",
"\n",
"nfE = e0.real**0.5/2/np.pi\n",
"nfB = e1.real**0.5/2/np.pi\n",
"nfG = e2.real**0.5/2/np.pi\n",
"nfD = e3.real**0.5/2/np.pi\n",
"nfA = e4.real**0.5/2/np.pi\n",
"nfE2 = e5.real**0.5/2/np.pi"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First three natural frequencies of 80-element high E string (Hz)\n",
" 1st natural frequency = 329.663\n",
" 2nd natural frequency = 659.107\n",
" 3nd natural frequency = 988.114\n",
"First three natural frequencies of 80-element high B string (Hz)\n",
" 1st natural frequency = 247.075\n",
" 2nd natural frequency = 493.986\n",
" 3nd natural frequency = 740.569\n",
"First three natural frequencies of 80-element high G string (Hz)\n",
" 1st natural frequency = 196.056\n",
" 2nd natural frequency = 391.982\n",
" 3nd natural frequency = 587.647\n",
"First three natural frequencies of 80-element high D string (Hz)\n",
" 1st natural frequency = 146.898\n",
" 2nd natural frequency = 293.699\n",
" 3nd natural frequency = 440.306\n",
"First three natural frequencies of 80-element high A string (Hz)\n",
" 1st natural frequency = 110.017\n",
" 2nd natural frequency = 219.962\n",
" 3nd natural frequency = 329.760\n",
"First three natural frequencies of 80-element high E string (Hz)\n",
" 1st natural frequency = 82.446\n",
" 2nd natural frequency = 164.837\n",
" 3nd natural frequency = 247.119\n"
]
}
],
"source": [
"print('First three natural frequencies of {}-element high E string (Hz)'.format(N))\n",
"print(' 1st natural frequency = {:.3f}'.format(nfE[0]))\n",
"print(' 2nd natural frequency = {:.3f}'.format(nfE[1]))\n",
"print(' 3nd natural frequency = {:.3f}'.format(nfE[2]))\n",
"print('First three natural frequencies of {}-element high B string (Hz)'.format(N))\n",
"print(' 1st natural frequency = {:.3f}'.format(nfB[0]))\n",
"print(' 2nd natural frequency = {:.3f}'.format(nfB[1]))\n",
"print(' 3nd natural frequency = {:.3f}'.format(nfB[2]))\n",
"print('First three natural frequencies of {}-element high G string (Hz)'.format(N))\n",
"print(' 1st natural frequency = {:.3f}'.format(nfG[0]))\n",
"print(' 2nd natural frequency = {:.3f}'.format(nfG[1]))\n",
"print(' 3nd natural frequency = {:.3f}'.format(nfG[2]))\n",
"print('First three natural frequencies of {}-element high D string (Hz)'.format(N))\n",
"print(' 1st natural frequency = {:.3f}'.format(nfD[0]))\n",
"print(' 2nd natural frequency = {:.3f}'.format(nfD[1]))\n",
"print(' 3nd natural frequency = {:.3f}'.format(nfD[2]))\n",
"print('First three natural frequencies of {}-element high A string (Hz)'.format(N))\n",
"print(' 1st natural frequency = {:.3f}'.format(nfA[0]))\n",
"print(' 2nd natural frequency = {:.3f}'.format(nfA[1]))\n",
"print(' 3nd natural frequency = {:.3f}'.format(nfA[2]))\n",
"print('First three natural frequencies of {}-element high E string (Hz)'.format(N))\n",
"print(' 1st natural frequency = {:.3f}'.format(nfE2[0]))\n",
"print(' 2nd natural frequency = {:.3f}'.format(nfE2[1]))\n",
"print(' 3nd natural frequency = {:.3f}'.format(nfE2[2]))"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure()\n",
"N = 60\n",
"x0 = np.linspace(0,L,N+2)\n",
"plt.plot(x0[1:-1],-v0[:,0]/np.max(-v0[:,0]), 'o', label='E1')\n",
"x1 = np.linspace(0,L,N+2)\n",
"plt.plot(x1[1:-1],-v1[:,0]/np.max(-v1[:,0]), '--', label='B')\n",
"x2 = np.linspace(0,L,N+2)\n",
"plt.plot(x2[1:-1],-v2[:,0]/np.max(-v2[:,0]), 'o', label='G')\n",
"x3 = np.linspace(0,L,N+2)\n",
"plt.plot(x3[1:-1],-v3[:,0]/np.max(-v3[:,0]), '--', label='D')\n",
"x4 = np.linspace(0,L,N+2)\n",
"plt.plot(x4[1:-1],v4[:,0]/np.max(v4[:,0]), 'o', label='A')\n",
"x5 = np.linspace(0,L,N+2)\n",
"plt.plot(x5[1:-1],-v5[:,0]/np.max(-v5[:,0]), '--', label='E2')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left')\n",
"plt.title('First Mode Shape \\n');"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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wPA31txJreZL0nedtdqUxJlv56KI8HFihqh8AiMh9wDTgrW7qnwfcm4fP7dfSSwIqWn1iW9+hLOFy0W9/SXDo8EKHVhSagg1UsTte+bEkIktBW0EqBkSXrTEmP/LR3zMSWJXxenWqbBsiUgGcCvwlo1iBJ0VksYhc0t2HiMglIrJIRBbV19fnIezC+WwD5QriTY+AuMSGXMBP571Q6NCKRnp2pRuaTHDQBYhTMWC7bI0xOycfCU66KNNu6p4OvNSpe/IoVT2EZBfn5SJybFcnqurtqlqrqrXDhg3LLeICSy8JSESWov4mApVfJODsYuNLGdLbejWFGkA8mrx6KrfezZUnHFjo0Iwx/UQ+uihXA3tkvB4FrO2m7rl06p5U1bWpr+tF5CGSXZ7P5yGuopUeR3JDh+J4u+N4u3coN0mZsytX3vtr5j7UwB+vvo7Nw88nHKuxpQPGmO3KR5NhITBORPYUkSDJJDavcyURqQaOAx7OKKsUkar0c+DzwLI8xFTUWmQN6jciIu3JDQbGkoCdNfa8y6iqGEaTRChv/AhBbGNmY8x25ZzgVDUOXAE8AbwNPKCqb4rIpSJyaUbVM4EnVTVzD6bhwIsisgR4FXhMVR/PNaZiloi0UrXhIaJb70U10V5u40s7trHqdJzAnsRbn8OPrwds6YAxpnt5WeitqvOB+Z3Kbuv0+vfA7zuVfQBMykcM/cUL376IFidGVfWubAo12i4dPRCO1UDFqUS23k2s5RmCVeciIta1a4zpku1k0gfalwS0tBFrbCOsIS7+9a9xXLfQofUr6d1eguEvgYT79b3xjDG9z/p2etlnSwIqiTc/DlJO6+B/4Sd3P1To0Pqd9NIBxxuJ41ajqsR0i3XtGmO6ZAmul6WXBIAi3nAClacSkGobN9oJne8IHm9+DG/j77nqjGMKHZoxpghZF2UvS48PiQQJVp62TbnpmcylA8tvfZlHn/d5+ttfZ+rdjxY2MGNM0bEE18uavY0Et7yCV3Y4jvfZAnUbN8rd+Mv/k3dePo2321ze/sathNwJNmHHGNPO+sl62ZCGh/Fjy8lcHWFLAvJn+edmIM4gpOll0LitjTPGtLME14tWP3w3jZEtVEk5LZU1dpeAXuC/W0Og8guoJtDEZsDWxhljkqyLspckWpp54g/3EBCX8/77+1SNO6DQIZWkcLQaCdQQqv46yTs3fVZujBnYLMHlWXrNW3njR8QDIcK7jLHk1ovSa+NEXFQTJKJv4gYPoCm0tdChGWMKzPpx8ii95q0qWoMb3J9AxWm0+F+y8aBelF4bB+DHVhJveZp4ZLGNcRpjLMHlk9Q5eIkAqjFEPNzQfgQ1ZONBvShzbZwE9sRxd0ebX+DSg3YtdGjGmAKzLso8Cker8WPvEmt5nmDVDBy3pr3c9J7MtXH1z0f44y9v5ckbf8w5Dz5Z2MCMMQVlCS6Pmt16vJZnEacScQa1l9uat74z7NgvMunPd1G3uY2fXXwzQe9AWxtnzABlfWd5NKThYdBmAhUnIZL81tqat7638JAv4wTGEWC43TfOmAHMElyerH3szzRGtzJIKmiuKLc1bwWkyyoIhk/H8Ya3l9naOGMGHuuizJPXH/gznu9z7g+/R9WEAXWLu6KTHvNUv5V428u4ock47hAbCzVmgMlLghORU4FfAC5wh6re2On48cDDwIepormq+sNszi1m6TVv4Wg1TYNmUjHufUtuRSC9Ng58EpG30UQDwaqzbCzUmAEm5z4bSW4fcStwGjAROE9EJnZR9QVVPTj1+GEPzy06n93nrQL8Jqpig/HXHmTjPEUgvTZOnEq88in48ZXEYu/aWKgxA0w+BiUOB1ao6geqGgXuA6b1wbkFlb7PW7z1n0Qa/oD6rTbOUyQy18Y5oYMRGYTbMJ/vTj+l0KEZY/pQPn4bjwRWZbxenSrr7HMiskRE/iYi+/fwXETkEhFZJCKL6uvr8xB2bsLRavzEZhKROtzgvohT3l5uCm/WzOlce8tZ/MdvP8+pU/Ym6vq8dO0lhQ7LGNOH8pHgpIsy7fT6NWCMqk4Cfgn8tQfnJgtVb1fVWlWtHTZsWFdV+lRTsIF463OAh1d+VIdyU1wmfutHHDq0gv0v+NdCh2KM6UP5mGSyGtgj4/UoYG1mBVXdmvF8voj8WkR2yebcYlUT+CfNsQ/wyo9GnErA1rwVs+N//UByUtB9c5OTgmzxtzElLx8JbiEwTkT2BNYA5wLnZ1YQkRHAp6qqInI4yZbjRmDLjs4tVvtsfZ+3Ew4t4b2ojKv9wixys++aQ/kC0Ka/o+Wfo4rdiC2MMps59jMzA9rixYt39TzvDuAA+tfaaB9YFo/HLz700EPXd1Uh5wSnqnERuQJ4guRU/ztV9U0RuTR1/DZgOvDvIhIHWoFzVVWBLs/NNaa+cPLv5nLU2pWU7z620KGYLEidg0cFkUQ9sZZnCVadS8AP0lbntO9jacxA5HneHSNGjNhv2LBhmx3H6XKIqBj5vi/19fUTP/nkkzuAM7qqk5d1cKo6H5jfqey2jOe/An6V7bnFrGXV+2xa9AKjzvyaJbd+JBytRkTwyo8i3vIkfuxd3OB4mxRkDBzQ35IbgOM4OmzYsIZPPvmk2xtu2k4mWUov6i7bspREZDHu8s1869pvFzosk6X04m83OJFE5DXirS/iBPamKdRU6NCMKTSnvyW3tFTc3Xar9qf+1oJJL+qubBUSkTqc4AT4eD9b1N2PtC/+Fgev/FjUbyAeqbNJQcYUAdd1D50wYcLE9OO6664bAfA///M/w0aPHn2AiBy6bt26HjfIrAWXhfSi7mjrk4AQKD8asfGbfmXWzOnMZg5tdQ5hxuBUHEnskF1sgokxPfTHBR8NueWZ90bWN0aCw6pC0StPGrfmX6aM2ZTLe4ZCIf+dd955q3P5cccd13T22Wc3nHjiieN35n0twWUhHK3Gj69NjtuUTUGcqvZy039k3hgVTgLATyRwXLdgMRnTn/xxwUdDfvToW2Micd8BWN8YCf7o0bfGAOSa5Lpy1FFHteZyvnVRZqEp2ICf2IQ41XhltR3KTf+16i93cOf0U6l/8W+FDsWYfuGWZ94bmU5uaZG479zyzHtd7kCVrUgk4mR2Uf7ud78bnFukSdaCy4JO9tGF+xIM7kdyf2hb1F0KwmP3ZWsgxJ9+Mx/vj0Fby2jMDtQ3RoI9Kc9Wd12UubIW3A4kWpo5s+VNWg/dSlOo0W5kWkJuW7oep6yWRPxDNP6J3fnbmB0YVhWK9qS80KwFtwOLf/hNXvjwE8463mX8LdcXOhyTR1Ln4JVPIRF9i1jr8wTDX7HF38Zsx5UnjVuTOQYHEPIc/8qTxq0pZFzdsRbcdkTWr2Xhe6sZEosw7pJZhQ7H5Fly8XcQr/xINL4GP/5Re7kxZlv/MmXMpv/80sSPdq0KRQXYtSoU/c8vTfwo1wkmncfgLrvsspEAP/7xj3cdPnz4QZ9++mlw0qRJE88555wxPXlfa8Ftx8vf/yZtnscXTjnRZtqVoM8Wf++PEMDxRreXG2O69i9TxmzK94zJRCKxuKvy66+/fv3111/f5T6T2bAE10l6x5LKtiDRhjiVGmSfi68udFimF+hkn9jCKAE/iBvaD4CoRGzykDElwrooM6R3LKmK1oC/BaSMtuqzbdJBicq887eiRGKvEaq/javOOrHQoRlj8sASXIb0jiUAjrc7oeqvE3B3Q+rs21Sq0nf+vuK2k5h6SDOtboJXv39locMyxuSB/ebOkJ5ckIh9jGoCEadDuSlt+156PcNiEepWbaB17cpCh2OMyZEluAzJHUs2Emv6C4m2VzuUm9LnuC7HTj+TqOfx0g3/X6HDMcbkKC8JTkROFZHlIrJCRK7t4vgFIrI09XhZRCZlHFspIm+IyOsisigf8ewsnewTb3kR8HBDyRBtx5KBZez5lxHWEEsalF9e8hg3XjnXxmCN6adyTnCS3LvqVuA0YCJwnohM7FTtQ+A4VT0I+BFwe6fjJ6jqwapaSwGdH96IH38fJzQRnHLbsWQAmn3XHFprphMIn4HjlNvuJsb0gfTtcsaPHz9x4sSJ+z311FOV+XjffCwTOBxYoaofAIjIfcA0oH1fMVV9OaP+AmBUHj437168bw4B8bj4xzOpGL1PocMxBSB1DgFneIc//Wx3E2N6V+ZelH/5y18GXXfddaNOOeWU5bm+bz66KEcCqzJer06VdefrQOb27Qo8KSKLReSS7k4SkUtEZJGILKqvr88p4K60rl1Jm8Kk4dWW3AawzAlFsdYXibX8fZtyY0zvaWhocKurq+P5eK98tOCki7Iub38uIieQTHBHZxQfpaprRWRX4CkReUdVn9/mDVVvJ9W1WVtbm/fbq5fvPpaZ9z2GH23L91ubfiS9uwkAGiURWYIbmkxzeVf/zI0pQbefsO3NRfc7fRPH/H/1RJoc/nD6uG2OTzpnA0dcupHGTzzuPW/vDscu+ccOW2LprboikYhs2LAhMH/+/HdzuIJ2+Uhwq4E9Ml6PAtZ2riQiBwF3AKep6sZ0uaquTX1dLyIPkezy3CbB9Yb0riUVrXHagjEStSEbbxvgMnc38cqOIBFZRrz1JfTIIwsdmjElK7OL8umnn66cOXPmnu++++6bjpNbJ2M+EtxCYJyI7AmsAc4Fzs+sICKjgbnAhar6bkZ5JeCoamPq+eeBH+Yhph1K71riJQJEm/+I1ywEXp3BbOZYkhvAZs2czmzm0FbnEI5W44YmkGhbxld3ObTQoRnTN7bX4gqF/e0erxoRz6bFtj0nn3xy8+bNm71169Z5I0eOzKmrMucEp6pxEbkCeAJwgTtV9U0RuTR1/Dbgv4ChwK9FBCCemjE5HHgoVeYBf1bVx3ONKRvpXUsSseVoop5Axam4GiJS12qTCQa4WTOnt/8baF4xgjuu/Q4v3v17zjn9gsIGZswAUFdXV+b7PsOHD895HC4vmy2r6nxgfqey2zKeXwxc3MV5HwCTOpf3hXC0GlWfeOs/EWcoTnBCe7kxaZX77M/xh05k18lHFDoUY0pWegwOQFX5zW9+s9Lzck9PA/ZuAk3BBioa16L+JgKVX2rflst2LTGdTZr100KHYExJ6+52ObkasAlOJ/v4f1+LuMNwAslJQbZrielOw9JXuO/HN9FUfRIhdzxNwQZ0sm/jtcYUsQG7F+WsmdNpPfEQYkNOBcF2LTHb9dsX36HJcZCWpaDYDifG9AMDsgUXbdjElsXPd5hMYMz2+O9UESqbQrz1H/jxj3EDY2yHE2OK3IBMcAt/8C1eWb2Rc1tb2P2L5+/4BDPghaPVEDqQeNsi4q0v43ijERGblGRMERtwXZTRjZ/y+kfrGRKPMuLUcwodjuknmoINiHh45UegiXX48ZXt5caY4jRgWnDpXUvKtr5PwvNwRh+M47qFDsv0E+kdTrzg/uC34LjDbVKSMUVuQLTg0ruWhCMVJNoW4nijiTQfbxMETNZmzZxO62FNNIUaccuPoKksapOSjMmTVatWeaeffvqeo0aNOnD//fff7+CDD55w99131+T6vgOiBde+a0n8I9AIXvmRODZBwPRQ5qSkFXfcxNInnsG/4AycYLCwgRnTh+5ffv+Q25bcNnJj68bg0PKh0UsnXbrmnPHnbNrZ9/N9n9NPP32f888/f+MjjzzyIcC7774bfPDBB3NOcAOiBZeeCOAGxhCq/gaOt3uHcmN6asvHH/KhBnjj/64pdCjG9Jn7l98/5KaFN43Z0LohqCgbWjcEb1p405j7l98/ZGff85FHHqkKBAJ69dVXt98Hbd99941+73vfW59rvAMiwWVOBBCnostyY3pi8vd+RjgW5ZVFb+JHo4UOx5g+cduS20ZGE9EOeSOaiDq3Lblte/cA3a433nij/KCDDmrJPbptDYguysxboKTZBAGTCzdUzuEHT+Dvb37AzZfeTDB4qO1uYkrextaNXfbHd1e+My688MLRr776ajgQCOiyZcvezuW9BkQLLj1BoDG4BUVt1xKTF4/vfjTiDIHWN0DVdjcxJW9o+dAuuyu6K8/GgQce2Lp06dL2rrV77rnn42efffbdzZs359wAGxAJDpJJ7tpbzuKK207i2lvOsuRmciZLPbyK4xLvDLMAACAASURBVHBDB5O+iX3ADyJ1A+a/lRlgLp106ZqgG+zQ9RV0g/6lky5ds7PvefrppzdGIhH5yU9+Mixd1tTUlJf/RAOii9KY3hCOViOBGghsW25MKUrPlsznLErHcXjkkUfev/zyy/e45ZZbRgwZMiReUVGRuOGGG1bnGq8lOGN2UlOwgapoDao+ieibiJThBsfZ5CVT0s4Zf86mXBJaV8aMGRN79NFHP8jne0KeuihF5FQRWS4iK0Tk2i6Oi4jckjq+VEQOyfZcY4qVTvaJOVFASESWEG99nqi02uQlY4pEzglORFzgVuA0YCJwnohM7FTtNGBc6nEJ8JsenGtMUfpsd5MG3PLPoX4DlYmHbXzXmCKRjy7Kw4EVqvoBgIjcB0wD3sqoMw24W1UVWCAiNSKyGzA2i3ONKVrp3U38RILfz3iAtg0fEW9swKuycThjCi0fXZQjgVUZr1enyrKpk825AIjIJSKySEQW1dfXd1XFmIJxXJcpx32O1kCAhT/4ZqHDMcaQnwQnXZRplnWyOTdZqHq7qtaqau2wYcO6qmJMQU244vvs5cSpGTO20KEYY8hPF+VqYI+M16OAtVnWCWZxrjH9guO6nHnv48y+aw4PXzmXcLTadjcxpoDy0YJbCIwTkT1FJAicC8zrVGce8NXUbMopQIOqrsvyXGP6jdl3zaF8gUd5w3LQhO1uYkwWXNc9dMKECRP32Wef/cePHz/xhhtuGJ5IJHJ+35xbcKoaF5ErgCcAF7hTVd8UkUtTx28D5gNTgRVAC6mbjnR3bq4xGVMoUufgxLcQa3sJJIBXdggBuzWTMdsVCoX8d9555y2ANWvWeDNmzNiroaHB/fnPf55Tj15eFnqr6nySSSyz7LaM5wpcnu25xvRX6d1NEt4o4m0LcUMHIhKw3U2MydLIkSPjd9xxx8ojjzxy4k9/+tO1jrPzHY22k4kxeZTe3cQrO5Jo0wMkIkvwymptdxPTb3w44yvjO5dVnXLypl0uuaTeb252PvrazHGdj1efcfqGIRdeuDFeX++tuuzyvTOP7fngA8t7GsPEiROjvu+zZs0ab4899oj39Pw0S3DG5FH7rZkCo3C8McTbFqJlE2x3E5Oz2XfNQeqcATN5KdnxlxtLcMbk0ayZ05nNHNrqHCrKPwctL6B7fcismbY2zuy82XfNoXxhuP2ellXRGmILo8xmTt6T3PZaXE5lpb+9496wYfGdabF19tZbbwVd12XkyJE73XoDS3DG5F16d5OkfylkKKZESJ3T4YbNQMlOXlq7dq33jW98Y8zMmTPX5zL+BpbgjOl19c8/xqevvsAB37mx0KGYfqq7SUqlMnkpEok4EyZMmBiPx8V1XT3nnHM2fv/73/801/e1BGdML3vmlptZj8eeK5dTOXab8XtjdqgpsIWq2OBty0tk8lIikVjcG+9rCc6YXnb0BRdw/31zuP2/7iZQceKAmCBg8mto4zyaYoMIhE9HJPlrO+ZEbfLSDuTlfnDGmO7dsyWM4+2NH3kb/Dbb3cT0SMvHK2htWk95dA1NoSYUpTG4hdbDmuyPpB2wFpwxvUzqHLyKo4huvZt4ZDGB8qNLdoKAyb+Xf3Q1Mdfly9NPY/SMswodTr9iCc6YXhaOViOu4AQngiY6lBuzPc0r3uTNza2MkjijZ3yj0OH0O5bgjOll6d1NAhVfQEQ6lBuzPS/P/h5xx+HoC79W6FD6JUtwxvSy9t1NUuuY/PgaEm45OrnAgZmilLljSUvZDGpCLzPy9AsKHVa/ZJNMjOlls2ZOp/WwJhqDW/D9JqKND1K59UGbIGC2kd6xpCpagyBUJnajhdMHxISku+++u0ZEDq2rqyvL13taC86YPpC5u8m8C37DiliC+ucfY9ixXyxsYKaopHcsUb+JaNOjBCpOIOANL6oJSW88t3rIovkrR7Y0RIMV1cFo7dSxaw48btSmXN/3vvvuG3LIIYc03XPPPUMmT56clxtfWwvOmD52zHeuR1R54de3FDoUU2TSE4/iba+giU9AQh3KC+2N51YPeenBFWNaGqJBgJaGaPClB1eMeeO51UNyed+GhgZn0aJF4bvuumvlQw89tO2K9p1kCc6YPjZ48lGMr3D40PdY9/gDhQ7HFJGmYAN+ooFE5A3c4AE4bk17eTFYNH/lyETc75A3EnHfWTR/5chc3vdPf/pTzfHHH99w0EEHRWpqahIvvvhiRW6RJuWU4ERkiIg8JSLvpb5uk3lFZA8R+YeIvC0ib4rINzOO3SAia0Tk9dRjai7xGNNfHDPrvwn4Lvc+uJpfXfoMN145d0CMs5jt08k+8daXAMErPwIorh1L0i23bMuz9cADDww577zzNgOcffbZm+65556cWoRpubbgrgWeUdVxwDOp153FgatUdT9gCnC5iEzMOP5zVT049bA7e5sB4Vf/fI/EsEsJBQ5GENvdxADwtd18/Og7uMEJ4ISLbseSiupgtCfl2fjkk0/cBQsWDLr88svHjBw58sBf/epXI+bNmzfY93NP6rlOMpkGHJ96/gfgWeCazAqqug5Yl3reKCJvAyOBt3L8bGP6LalzCGoZqoofX4UbGG27mxiGHfUFPvfUoxz4jfOpmjCp0OFso3bq2DUvPbhiTGY3pes5fu3UsWt29j3vueeewWedddbGP//5zx+lyw477LDxTz75ZPjUU09tyiXeXFtww1MJLJ3Idt1eZREZC0wGXskovkJElorInV11cWace4mILBKRRfX19TmGbUxhpScNJKJLiTXNwY+v7VBuBiavqpojf3p3USY3gAOPG7XpqBn7fJRusVVUB6NHzdjno1xmUT744INDzzrrrM2ZZdOmTducj27KHbbgRORpYEQXh77Xkw8SkTDwF+Bbqro1Vfwb4EeApr7+FPjXrs5X1duB2wFqa2tzv5e5MQWU3t3EDU4k3vpPYq0vEAx/haZQcUwmMH1v7rlfYPS4Pan90W2FDmW7Djxu1KZ8LAtIe/XVV7e5A/j111+/Ph/vvcMEp6ond3dMRD4Vkd1UdZ2I7AZ0GZSIBEgmtz+p6tyM9/40o87vgEd7Erwx/VXm7iZe2RTirX8nHl+BThla6NBMH0rvWlLRvJWYBti4uo3aQgdVQnLtopwHXJR6fhHwcOcKktx87/8Bb6vqzzod2y3j5ZnAshzjMaZfyNzdxAkdgEiYQMN8rrngjEKHZvpIeteScKQ6OXNSwjSFpttEozzKNcHdCJwiIu8Bp6ReIyK7i0h6RuRRwIXAiV0sB7hJRN4QkaXACcC3c4zHmH5j1szpXHvLWfzHbz/PceOH4vqtbFnyUqHDMn0kvWuJH/sQTazDK59CkAqkzpYn50tOsyhVdSNwUhfla4GpqecvAtK5TurYhbl8vjGlYvL3fs6kaBteeFChQzF9JBytRtUn3voC4tTgBvdvLzf5YX8qGFMEnGAQLzyIyKdr+OjB3xY6HNMHkruTCF7FMXgVJyLiZpSbfLDNlo0pIr//jytpFiHw9GiaQ63oZL9oFvma/NLJPvGFMQKyV3tZMe1aUgqsBWdMkZh91xxaB30JpQ2/7XXb3aTEHbPkr4S33k1jYBOKFt2uJX3Jdd1DJ0yYMDH9uO6660YAnHHGGXuOHTv2gHHjxu0/Y8aMsZFIpMvhru5YC86YIiF1DgFvDBrYm3jbQtzQQQQot91NSlDzh2/z2uqNDNU41/5x4CW0zkKhkP/OO+9ss7vVBRdcsOmvf/3rhwDTpk3b8+abb97lmmuuyXqnD2vBGVMk0pMLvPKjgRjxtgUdyk3peP4HVxNzHI77qs2z255zzjmnwXEcHMehtra2efXq1T3a1NlacMYUifTuJo47FDd4AJrYhKra7iYlZtOCZ3inOcGeboJR075a6HC28afrvj2+c9k+hx+56Ygvz6iPtrY6D/7ounGdj+93zAkbDjntjI1Nmzd5D//vj/bOPHbB//x8m51KOotEIs6ECRPaN+G/6qqr1n3jG9/YnHFc7r///qE/+9nPVvXkWizBGVMkOuxuUnEC4BJ3YzbpoESkdy0p27wA3/H4+OBTCh1S0eiuizLtoosuGj1lypSmnm6+LKr9b1vH2tpaXbRoUaHDMCbv0r8Ew9FqmoINhEat4tyDdmO3U79S6NBMDtK7lgT8IH6iHj++Hi0f1+eTSkRksap22A1syZIlKydNmrShz4LoQkVFxeSWlpa6ro5dddVVuy1ZsqTiiSeeeN913W2OL1myZJdJkyaN7epca8EZU0RmzZzePqHEj0a5/dzTeXyBz0WnnI3TxX9u0z+kdy0BcNxhOO4w8LEJRDvws5/9bJe///3v1S+88MLyrpLbjtgkE2OKlBMMMnnfUWwKhFh641WFDsfkIBytJhFbSbTpMdRv7VBuPhuDSz8uu+yykQBXX331mA0bNni1tbX7TZgwYeJ3vvOd3Xb0XpmsBWdMEav9wa9Yet40Xqj7gMeveJBwfAhNwQZbAN7PNAU2E2x4DkiAfDYR0HYtSUokEou7Ko/H412WZ8tacMYUMTdUTmLMgURdn/KmjxDEFoD3Q0Nb/ob6G/HKj2nfkst2Lel9luCMKXJb4kfieGNQv7G9LOAHbdf5fqJ55XJat6ylwvdoqdxlwO9a0pesi9KYIheO1UD4TEQ6JjQbv+kfXvjBd4m5Dmee8yX2OPvsQoczoNifgMYUuaZgQ3ty8+Of4Cc2t5eb4nfkd7/PsfuOYo+zLy50KN3xfd/v0R6PxSIVd7f9vDm14ERkCHA/MBZYCXxFVTd3UW8l0AgkgHh6HUa25xszkKUXgHsJIdo0F8cdDoO+ZOM3RSy9nrEyMojm0FZ08ikcVuiguresvr5+4rBhwxocx+k3C6N935f6+vpqYFl3dXJa6C0iNwGbVPVGEbkWGKyq13RRbyVQq6obdub8zmyhtxlo2nfB2Po+idbnqByxD5f+4uZCh2W6kF7U7UQ+Jd76IsHKLxIPlBXFmFtXC70XL168q+d5dwAH0L969XxgWTwev/jQQw9d31WFXMfgpgHHp57/AXgW2GGCyuP5xgwI6QXg8aat3PnVp/BXvU20YRPB6iGFDs10InUOXsIj2vos6reBU07ADxTtou5Ucjij0HH0hlyz9XBVXQeQ+rprN/UUeFJEFovIJTtxPiJyiYgsEpFF9fVZ3y3BmJLihQdx7ElH0RwI8NK1/1bocEwXwtFqEpGlaKKeQMWxiATay03f2mELTkSeBkZ0ceh7Pfico1R1rYjsCjwlIu+o6vM9OB9VvR24HZJdlD0515hSMuHy77Ps+c+zIjKMV66c275vpS3+Lg4tzjrctpdwvNE4gX3by21SUN/bYYJT1ZO7OyYin4rIbqq6TkR2A7rsB1XVtamv60XkIeBw4Hkgq/ONMR29d+ollC8MUxVN7opRFa0htjDKbOZYkiuwwVvns1VjeBUnIJKcnGiLugsj1y7KecBFqecXAQ93riAilSJSlX4OfJ7PZr3s8HxjzLaS4zwBEtF38ePrAFv8XSwu+uUvqBw1geZy1xZ1F1iuk0xuBB4Qka8DHwMzAERkd+AOVZ0KDAceSv0l4wF/VtXHt3e+MWb7kuM5cWItzyJOOcGqCxBxbJyngBKRVuINmwntujuX/vSmQodjyDHBqepG4KQuytcCU1PPPwAm9eR8Y8z2pe/+Hag4gVjzIyQir+GV1do4TwGkl3CUb/2QRNuryKFH8e3vXlnosAz9a82DMSZFJ/vEnChOYB+cwF7EW18m5m+wcZ4+ll7zFm4LEm97GXGHwgfjbCPsImEJzph+aNbM6bQe1kRTqAGv/AQAyrbcxzVfPbPAkQ0s6RuZxltfAI3hVZxIUEM2FlokbLNlY/qpzLt/L7h6HsHKysIGNAAlb2S6ikT0TdzQYTjukPZyU3iW4IwpAVNuugv4bDzI1sb1jaZgA2XNbyNONV75lA7lpvCsHW1MiZh91xzKn3uPsoZldmPUPqKTfTR8HMGqc9p3LLE1b8XDEpwxJULqHEg0kmhbiB//FLC1cb1p3eMP8G8HDKPt8GaayuK25q0IWRelMSUiHK2G8qNJxN4n1vIkwarzEXFtPKgXxJu28thv7yAhcM19j+LMDBY6JNMFS3DGlIjP1sadRKx5HvG2VwiUH2njQXnUftuihuUkgkHCw/fGCVpyK1bWd2FMiUivjXOD++AE9yPRtpCYbrbxoDxJr3mrbPVJtC3ACexLa/w0G+MsYpbgjCkR6bVxjcEteOXHw6Av0DpFbTwoT9L7f8ZangLxCFScYGOcRc66KI0pIZlr49I2LXiGIVNsR7xcpff/FKcaN3gA4lRmlJtiZAnOmBJW96Nv8vc33oea9wg542xtXA7SY5zBylNR1Q7lpjhZ29qYEvZ0zYGIE0YaXwKN29q4nRTd+CmDP/0zsUTy1kR2n7f+wRKcMSUs8d4QvMovoP5m4q0vAbY2bmc88c2ZNNFGKFxHY3CLrXnrJ6yL0pgSFo5WI4Ea/NAkEpHXcAKjcQN72bhRD7x183/ybsxhfFD50s//r9DhmB6wBGdMCUuPG3nlx+HHP0X9lvZy0730erfKtgCxhrcJJVw+f8sdhQ7L9FBO/RQiMkREnhKR91JfB3dRZ7yIvJ7x2Coi30odu0FE1mQcm5pLPMaYjtJr40Q8glXn4oUOsHGjHUivd6uK1pBoW4QSIz54Bj/963OFDs30UK4d8dcCz6jqOOCZ1OsOVHW5qh6sqgcDhwItwEMZVX6ePq6q83OMxxiTIXNtHCI0BrdQLo9wxIJ7Cx1a0Urf4w3AKz+KYPhsAu7uNm7ZD+XaRTkNOD71/A/As8A126l/EvC+qn6U4+caY7LUeW3cX8+7nTrfo+7iWwh5+9vSgU7C0Wr8+HrEqUKcciQwqr3c9C+5/kkyXFXXAaS+7rqD+ucCnf90vEJElorInV11caaJyCUiskhEFtXX1+cWtTED2PJjz0OcodD0AvjNtnSgkxZZQ7RpLrHmv3Uot3HL/meHCU5EnhaRZV08pvXkg0QkCJwBPJhR/Btgb+BgYB3w0+7OV9XbVbVWVWuHDRvWk482xmTQt6sIhE8HjRNtfgzVhC0dSIk2bCJcPxc0hldxXHu5jVv2TzvsolTVk7s7JiKfishuqrpORHYD1m/nrU4DXlPVTzPeu/25iPwOeDS7sI0xOyscrUZcIVB5MrHmv+HH3scN7jtgu+Ay74Ieb5pPwo0THrYnmx2XcFStC7cfy3UMbh5wEXBj6uvD26l7Hp26J9PJMfXyTGBZjvEYY3YgvXTADe6HOINxvBHt5QNNesZkwA+SiLxFIrYcN3QImw49iFkzzyp0eCZHufZJ3AicIiLvAaekXiMiu4tI+4xIEalIHZ/b6fybROQNEVkKnAB8O8d4jDE7kF46ALQnt3hiNTXui4UMqyAyZ0w6gTG4ocPwyo+17toSkVMLTlU3kpwZ2bl8LTA143ULMLSLehfm8vnGmJ6bNXM6s5lDW6pbrimwheqNc2ndEuf//u13lMleA6ZbLhytRv1GkArEqSRQcUx7uen/bCcTYwagzksHfv6/a9DFLyMNz8Cg4VRFa4gtjDKbOSWd5FpkLW7j33C8kQQrT2svH4jdtaXI2uHGGCKrRhEIfxk0QrTpYVSjJT+zsnnlcirr54Dfihea3F5uMyZLh7XgjDHJmZWeEKicSqx5Hom2xXjlnyu5rrr2PSYjlcS33o86CSpG7ktDvMxmTJYgS3DGmIyZlXsjMgPxdmsvLxWZMyajLY/j++txw59ny4G724zJEmUJzhiTnFm5MNkt6aS2porpFobW389PftOIvl2VnJDSj1s4HfaYDB2C7+2OFzyAtrotHcYjTeko3Q52Y0zWMjdlTt/Mszz4D7Ymmgm+uIBwJIwg/Xpbr8pIJYnI2wA43q54oYMAmzFZyqwFZ4wBtp1ZCWfxs5mz8VteItY0j0D4DEQ8An6QtjqnX7V6WteuJN74IH7iE8QdiuN9tm1uKXXDmo4swRljuhUMHU6CcuItTxNtfIBgeBriVPaLVs9nNy0NppLbRtzKUzokN5sxWdoswRljutUUbKCKgxApI972CulRjWJv9aQnlHjxCNHGB1C/ATf8RdaMDjB005Z+P55osmMJzhjTrfbJJ8F9cQL7IOIQpRUnXseNV1K0iSI9oSSRWI1qM8Hw2TiBUQzdtIVrb7EZkwOFJThjTLc6b+vVGNxC+ZancCOrCJWHIVRbFLueZN4RoCmwmYrWVvBqcAN74Qz6GuJUAjahZKCxBGeM2a7Ok09+ckWc4JZXiLe+gB9fQ6DiJAJUFWziSeb6NvWbCG16hlh8DTLoIhx3cHtyg+LvWjX5ZQnOGNMjlfGhUDmVRGQE8daXiDT8gUDlVMLsyY1Xzu3zbsv27sjYh8SaH0/drPQUcDq21mxCycBjCc4Y0yPpXU+8skNxAnsTb/kH4g4GIBypRkR6tduyQ3dksIHKyCCizY/hx5YjzlACVV/CcYe2r+cr1nFC0/sswRljeqTDriduDcGqM1EUFGItf0OcQXihyQSoJL4oyI11+WvVdeyObCUcqQYBxx2G4w7DLZuMSABIJmKbUDKwWYIzxvTINveTCzakJm8kQH0Sba+SaFuMG9yPYNkhlLu7APS4Vde5paaTfaTOwYtHiEcWE29bRKDyi7jBvXDLD0OQ9nOtO9IAiKru/MkiM4AbgP2Aw1V1UTf1TgV+AbjAHaqavvP3EOB+YCywEviKqm7e0efW1tbqokVdfpQxpgBuvHIuVdEaAPzEZhKR10hElgEJApVTcYMT2uu2uk3E3XiHxAV0SGYbh2xi5PpR7XtHqvrEo0vR6Hv48VUAOIF98MqPwXEHo2h7orXuyO6JyGJVrS10HH0l1xbcMuAs4LfdVRARF7gVOAVYDSwUkXmq+hZwLfCMqt4oItemXl+TY0zGmD7WsdtyME7FSbhlU/Ajb+B4YwCIR5aQiCzD80YRDIwGN0A4EibxCoiAq8lfR+FIJRWro+CvJKFx3NBEQPDbFgGCWzYFN7gfTmrcD6w70nQtpwSnqm8DiMj2qh0OrFDVD1J17wOmAW+lvh6fqvcH4FkswRnT73TVben5AcqdKe11RMpAPBKROhKRxalSl7LB30yN3z1HIvouaONnbyxh3NBERIRg1bmoVJBw4ziplh1Yd6TpXl+MwY0EVmW8Xg0ckXo+XFXXAajqOhHZtfPJaSJyCXAJwOjRo3spVGPMzuq8Xm72XXPwFgbauxnd4Hic4L6gcfz4WjSxCfgsMYkzCCcwCsepQdwhiDO4fXZm8niYpuAWdLLfIZFad6Tpzg4TnIg8DYzo4tD3VPXhLD6jq+Zdjwf+VPV24HZIjsH19HxjTN/qtlUXr8QNjIHAmA71vbLJHV4r2uXEkW3vemBM13aY4FT15Bw/YzWwR8brUcDa1PNPRWS3VOttN2B9jp9ljCkiO2rVAcSJdxiDg2QyW7PraoZuGmItNbPT+qKLciEwTkT2BNYA5wLnp47NAy4Cbkx9zaZFaIzpp7pq1XU1i1In+/zvzIsLHK3p73JdJnAm8EtgGLAFeF1VvyAiu5NcDjA1VW8qcDPJZQJ3qup/p8qHAg8Ao4GPgRmqumlHn2vLBIwxpucG2jKBnBJcoViCM8aYnhtoCc4pdADGGGNMb7AEZ4wxpiRZgjPGGFOSLMEZY4wpSf1ykomI1AMfZVF1F2BDL4fT2+waikcpXIddQ3Eo1DWMUdVhBfjcguiXCS5bIrKov88YsmsoHqVwHXYNxaEUrqE/sC5KY4wxJckSnDHGmJJU6gnu9kIHkAd2DcWjFK7DrqE4lMI1FL2SHoMzxhgzcJV6C84YY8wAZQnOGGNMSSqJBCcip4rIchFZISLXdnFcROSW1PGlInJIIeLcniyuYYKI/FNEIiLynULEuCNZXMMFqe//UhF5WUQmFSLO7cniGqal4n9dRBaJyNGFiHN7dnQNGfUOE5GEiBTdTday+DkcLyINqZ/D6yLyX4WIc0ey+VmkruV1EXlTRJ7r6xhLmqr26wfJW/C8D+wFBIElwMROdaYCfyN5d/EpwCuFjnsnrmFX4DDgv4HvFDrmnbyGI4HBqeen9dOfQ5jPxq4PAt4pdNw9vYaMen8H5gPTCx33TvwcjgceLXSsebiOGuAtYHTq9a6FjruUHqXQgjscWKGqH6hqFLgPmNapzjTgbk1aANSk7iBeLHZ4Daq6XlUXArFCBJiFbK7hZVXdnHq5gOTd3YtJNtfQpKnfREAlUGyztLL5/wDwH8BfgPV9GVyWsr2GYpfNdZwPzFXVjyH5/7yPYyxppZDgRgKrMl6vTpX1tE4hFXt82ejpNXydZKu6mGR1DSJypoi8AzwG/GsfxZatHV6DiIwEzgRu68O4eiLbf0ufE5ElIvI3Edm/b0LrkWyuY19gsIg8KyKLReSrfRbdAOAVOoA8kC7KOv9VnU2dQir2+LKR9TWIyAkkE1yxjV9ldQ2q+hDwkIgcC/wIOLm3A+uBbK7hZuAaVU2IdFW94LK5htdI7qvYJCJTgb8C43o9sp7J5jo84FDgJKAc+KeILFDVd3s7uIGgFBLcamCPjNejgLU7UaeQij2+bGR1DSJyEHAHcJqqbuyj2LLVo5+Dqj4vInuLyC6qWiyb/2ZzDbXAfanktgswVUTiqvrXvglxh3Z4Daq6NeP5fBH5dZH9HCD7300bVLUZaBaR54FJgCW4PCiFLsqFwDgR2VNEgsC5wLxOdeYBX03NppwCNKjqur4OdDuyuYZit8NrEJHRwFzgwiL9CzWba9hHUpkhNRs3CBRTot7hNajqnqo6VlXHAnOAy4oouUF2P4cRGT+Hw0n+LiumnwNk9//6YeAYEfFEpAI4Ani7j+MsWf2+BaeqcRG5AniC5KylO1X1TRG5NHX8NpIzxaYCK4AWYGah4u1KNtcgIiOARcAgwBeRb5GckbW12zfu/LVMHQAAAJNJREFUQ1n+HP4LGAr8OvW7Ka5FtKN6ltdwNsk/lmJAK3BOxqSTgsvyGopaltcwHfh3EYmT/Dmc+/+3c8c2EAIxEEVn+2+BQqgDnUQ3mAJIyDiN3qvAKwdfcrD/tIfk3Ttm5lxr7UmOJFeSbWZ+303dxVddAFRqOFECwIPAAVBJ4ACoJHAAVBI4ACoJHACVBA6ASjcdzmbTQsS2ZAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure()\n",
"plt.plot(x0[1:-1],-v0[:,1]/np.max(-v0[:,1]), 'o', label='E1')\n",
"plt.plot(x1[1:-1],v1[:,1]/np.max(-v1[:,1]), '--', label='B')\n",
"plt.plot(x2[1:-1],v2[:,1]/np.max(-v2[:,1]), 'o', label='G')\n",
"plt.plot(x3[1:-1],v3[:,1]/np.max(-v3[:,1]), '--', label='D')\n",
"plt.plot(x4[1:-1],-v4[:,1]/np.max(v4[:,1]), 'o', label='A')\n",
"plt.plot(x5[1:-1],v5[:,1]/np.max(-v5[:,1]), '--', label='E2')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left')\n",
"plt.title('Second Mode Shape \\n');"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"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": [
"plt.figure()\n",
"plt.plot(x0[1:-1],-v0[:,2]/np.max(-v0[:,1]), 'o', label='E1')\n",
"plt.plot(x1[1:-1],v1[:,2]/np.max(-v1[:,2]), '--', label='B')\n",
"plt.plot(x2[1:-1],v2[:,2]/np.max(-v2[:,2]), 'o', label='G')\n",
"plt.plot(x3[1:-1],v3[:,2]/np.max(-v3[:,2]), '--', label='D')\n",
"plt.plot(x4[1:-1],-v4[:,2]/np.max(v4[:,2]), 'o', label='A')\n",
"plt.plot(x5[1:-1],v5[:,2]/np.max(-v5[:,2]), '--', label='E2')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left')\n",
"plt.title('Third Mode Shape \\n');"
]
},
{
"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": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
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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": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"freq = np.array([nfE[0], nfE[1], nfE[2], nfB[0], nfB[1], nfB[2], nfG[0],\n",
" nfG[1], nfG[2], nfD[0], nfD[1], nfD[2], nfA[0], nfA[1],\n",
" nfA[2], nfE2[0], nfE2[1], nfE2[2]])\n",
"N = 10000\n",
"dt = 3/N\n",
"t = np.linspace(0,3,N)\n",
"samplerate = int(1/dt) \n",
"waves = np.sin(2*np.pi*freq[0]*t)\n",
"for i in range(1,18):\n",
" waves += np.sin(2*np.pi*freq[i]*t)\n",
" \n",
"Audio(data = waves,rate = samplerate)"
]
},
{
"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
}