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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"plt.rcParams.update({'font.size': 22})\n",
"plt.rcParams['lines.linewidth'] = 3\n",
"from scipy import linalg\n",
"from IPython.display import Audio"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Computational Mechanics Boundary Values - Project 05\n",
"\n",
"![6-string guitar diagram](../images/guitar.png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this final project, we will consider all six strings of a guitar and the deflection of the neck of the guitar. Here are the inputs for each of the strings, all L=0.64 m:\n",
"\n",
"|string|density (g/m)|tension (kg)|\n",
"|---|---|---|\n",
"|E|0.401|7.28|\n",
"|B|0.708|7.22|\n",
"|G|1.140|7.32|\n",
"|D|2.333|8.41|\n",
"|A|4.466|9.03|\n",
"|E|6.790|7.71|"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. The neck of the guitar can be considered a cantilever beam with an applied moment, shown above. At the tip we have a moment equal to the sum of the (tensions in the strings) $\\times$ (bridge height). Here we will consider it as $h=4~mm$. \n",
"\n",
"a. Use a finite difference approximation to determine the deflection of the guitar's bridge if the Young's modulus is E=10 GPa and it is a rectangular cross-section $2\\times4~cm^2$ and $I=\\frac{4\\cdot2^3}{12}~cm^4.$\n",
"\n",
"b. Demonstrate that your finite difference solution has converged. _e.g. decrease the step size $h$ and show the solution converges to a final value._"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"#Givens:\n",
"E = 10e9 #Pa\n",
"L = 0.64 #m\n",
"height = 4e-3\n",
"base = 2e-2\n",
"width = 4e-2\n",
"T = np.array([7.28,7.22,7.32,8.41,9.03,7.71]) #kg\n",
"\n",
"M = np.sum(T*9.81*height) #N*m\n",
"I = width*base**3/12 #m^4"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Part A:**\n",
"\n",
"We show how to derive the finite difference equations, considering a beam divided into 6 elements:\n",
"\n",
"Our ODE is:\n",
"$$EI \\frac{d^{4} w}{dx^{4}} = 0$$\n",
"\n",
"Writing this into a finite difference form we have:\n",
"$$EI \\frac{d^4w}{dx^4} = \\frac{w(x_{i+2})−4w(x_{i+1})+6w(x_i)−4w(x_{i-1})+w(x_{i-2})}{h^4} = 0$$\n",
"\n",
"Where the analytical solution is:\n",
"$$w(x) = C_{1}\\frac{x^{3}}{6} + C_{2}\\frac{x^{2}}{2} + C_{3}x + C_{4}$$\n",
"\n",
"Our Boundary conditions for this problem are:\n",
"$$w(0) = w'(0) = 0$$\n",
"$$w^{(3)}(L) = 0$$\n",
"$$w''(L) = \\frac{M}{EI}$$\n",
"\n",
"Applying the boundary conditions the analytical solution becomes:\n",
"$$w(x) = \\frac{M}{EI}\\frac{x^{2}}{2}$$\n",
"\n",
"Using the central difference method, we can obtain from these boundary conditions the following:\n",
"$$w(0) = w_{0} = 0$$\n",
"$$w'(0) = \\frac{w_{1} - w_{-1}}{2h} = 0 \\rightarrow w_{1} = w_{-1}$$\n",
"$$w''(L) = \\frac{w_{7}-3w_{6} +w_{5}}{h^{2}} = \\frac{M}{EI}$$\n",
"$$w^{(3)}(L) = \\frac{w_{8} -2w_{7} + 2w-{5} - w_{4}}{2h^{3}}= 0$$\n",
"\n",
"Simplifying we have that:\n",
"$$w_{7} = \\frac{Mh^{2}}{EI} + 2w_{6} - w_{5}$$\n",
"$$w_{8} = 2w_{7} + w_{4} - 2w_{5}$$\n",
"\n",
"Plugging in these results into the finite difference form of our ODE, we obtain the following equations:\n",
"$$7w_{1} - 4w_{2} + 3w_{3} = 0$$\n",
"$$-4w_{1} + 6w_{2} - 4w_{3} + w_{4} =0$$\n",
"$$w_{1} -4w_{2} + 6w_{3} - 4w_{4} + w_{5} = 0$$\n",
"$$w_{2} - 4w_{3} + 6w_{4} - 4w_{5} + w_{6} = 0$$\n",
"$$w_3 - 4w_{4} + 5w_{5} - 2w_{6} = -\\frac{Mh^{2}}{EI}$$\n",
"$$2w_{4} - 4w_{5} + 2w_{6} = \\frac{2Mh^{2}}{EI}$$\n",
"\n",
"We can extend these results for higher N as shown in the following code:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"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": [
"N = np.array([21,31,61,81])\n",
"\n",
"for i in range(len(N)):\n",
" h = L/N[i]\n",
" A =np.diag(np.ones(N[i]-1)*6)\\\n",
" +np.diag(np.ones(N[i]-2)*-4,-1)\\\n",
" +np.diag(np.ones(N[i]-2)*-4,1)\\\n",
" +np.diag(np.ones(N[i]-3),-2)\\\n",
" +np.diag(np.ones(N[i]-3),2)\n",
" A[0,0] += 1\n",
" A[-1,-1] += -4\n",
" A[-2,-2] += -1\n",
" A[-1,-3] += 1\n",
" A[-2,-1] += 2\n",
" b = np.zeros(N[i]-1)\n",
" b[-1] = 2*(M*h**2)/(E*I)\n",
" b[-2] = -(M*h**2)/(E*I)\n",
" w = np.linalg.solve(A,b)\n",
" xnum = np.arange(0,L+h/2,h)\n",
" plt.xlabel('Position on Beam (m)')\n",
" plt.ylabel('Deflection')\n",
" shapes = ['p' , '*', '-o','--']\n",
" colors = ['black', 'red', 'purple', 'yellow']\n",
" plt.plot(xnum[:N[i]],np.block([0,w*1000]),shapes[i], color = colors[i], label = 'Finite Difference, h =' + str(np.round(h,3)))\n",
" plt.legend(bbox_to_anchor=(1,0.5),loc='center left');\n",
" \n",
"x_a = np.linspace(0,L)\n",
"w_a = (M/(2*E*I))*x_a**2\n",
"plt.plot(x_a, w_a*1000,'s', color = 'teal',label = 'Analytical')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');"
]
},
{
"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": [
"#Part B\n",
"N_values = np.array([6,10,40,60,100, 500])\n",
"error_values = np.empty(len(N_values))\n",
"for j in range(0,len(N_values)):\n",
" h = L/(N_values[j]-1)\n",
" G=np.diag(np.ones(N_values[j]-2)*6)\\\n",
" +np.diag(np.ones(N_values[j]-3)*-4,-1)\\\n",
" +np.diag(np.ones(N_values[j]-3)*-4,1)\\\n",
" +np.diag(np.ones(N_values[j]-4),-2)\\\n",
" +np.diag(np.ones(N_values[j]-4),2)\n",
" G[0,0] += 1\n",
" G[-1,-1] += -4\n",
" G[-2,-2] += -1\n",
" G[-1,-3] += 1\n",
" G[-2,-1] += 2\n",
" b = np.zeros(N_values[j]-2)\n",
" b[-1] = 2*(M*h**2)/(E*I)\n",
" b[-2] = -(M*h**2)/(E*I)\n",
" w = np.linalg.solve(G,b)\n",
" w_num = np.block([0,w*1000,0])\n",
" \n",
" x_a = np.linspace(0,L)\n",
" w_a = (M/(2*E*I))*x_a**2\n",
" w_amax = np.max(w_a)\n",
" error_values[j] = np.abs(w_amax*1000+np.min(w_num))\n",
"\n",
"plt.xlabel('N-values')\n",
"plt.ylabel('Error')\n",
"plt.ylim(top = 1.43)\n",
"plt.ylim(bottom = 1.4)\n",
"plt.plot(N_values,error_values, label = 'Measured Error');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see that as we vary N, the error is pretty much constant. This is also shown in part A, where despite the changes in h, the convergence of the solution to the analytical was pretty much constant."
]
},
{
"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",
"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": {},
"outputs": [],
"source": [
"#Givens:\n",
"L = 0.64 #For all Strings\n",
"mu_g = 1.14e-3 #g/m\n",
"T_g = 71.81 #N\n",
"\n",
"mu_e = 0.401e-3\n",
"T_e = 7.28*9.81\n",
"\n",
"mu_b = 0.708e-3\n",
"T_b = 7.22*9.81\n",
"\n",
"mu_d = 2.333e-3\n",
"T_d = 8.41*9.81\n",
"\n",
"mu_a = 4.466e-3\n",
"T_a = 9.03*9.81\n",
"\n",
"mu_E = 6.790e-3\n",
"T_E = 7.71*9.81"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 6-element string (Hz)\n",
"f1: 194.4370866109145\n",
"f2: 379.12428580059105\n",
"f3: 544.8006102150752\n",
"Natural frequencies of 30-element string (Hz)\n",
"f1: 195.994645953565\n",
"f2: 391.48617646194407\n",
"f3: 585.9727675700807\n",
"Natural frequencies of 45-element string (Hz)\n",
"f1: 196.04043698528574\n",
"f2: 391.8522995904132\n",
"f3: 587.2072799426845\n",
"Natural frequencies of 60-element string (Hz)\n",
"f1: 196.0568723200582\n",
"f2: 391.9837461956978\n",
"f3: 587.6507093798888\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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d7jwi+4K3bNtbtdY/eFG3stfwR0oN3K/GPZ7O3/G+RQDXeSgnCN7j72li3iwY76yOKYtz8TxNWGFcqv/llG73w/OYm7qP28oMcpHvckqlU5mLbeUSPJT7yCqzErjb2i4AmnmoM9sqVwT8vYxrFs3JzshGOmQrxzWfY5U9jgvP0BjjwnTbuT7qoswnVl4ucEEZx2sONHZKe9Sqn1ZG3eW4mZqNmVGnMX54zvHQhrMLgdaU+h35DogsQwaXfpHKqGP3w3OSp2iMs8oVNvlP8m/j6dzLKUM4xj+UW59MVrk2mAC9GtNjGurje213QTHWQ11Pfnj+h+tp811t93K+i/wUyjElHjdexfGjHx5bnsL0rnTEyceRlT/S3bF9dA3L44cnxybDSBfyr7Py9rlqw6l8AmX4hpJFFsfidwG8EtZ8lL+yvSxpGDfo3ayPZ3Nr+z5sYRec2lCUOqHTGMd6Z2Gm23YFXrPlfeJGDl8qPHbfF9ut9Um+f5zqNMTMgnD8SP4H4zSuBWYKfCKmt+B1TO/BNU71Sz565bjmcVYbGjNb7i6MEhCD6QX7w0r35Gm5je1Dmo9xvX8exmlhU0wX943Au5gfdGdHiY867ncZsi7HvcJj97Scg3Fc5rjvLTH+P2bhInQJcKftHm0B7sAM8TWy6l6ACT3xM7CuAs+13dNyNiZu3ClW+iWUenLWwAPenns5ZYikVLFdhPEYfKZ1n5tY2/fb7qPGhR8oH9xrZ0/Lb2Oe7Rirje7W9dnIyZ6Wb7TVW4OZseTwknwHpcpIFtDehewpVELhsfLsnpZ/xkyzboqZgTaFKvC07GXdkZ6O7YNraPe0vAfzpzMW857chPF/Vpan5W6UOic8ivFQ7fCKHmM9i6MwrjIK8fDnUBZZ7IvfBfBaYPNv99+4j3NjX7LdfJTKE0vra8qOpTXSg5wXl+ejhvlXddjp2NeV4zq05MSQA56WK53qlnz0ynnN+3HivzL7cgwYSGkvz2Q3bXTEKEdlyVoMdHWq+yiVVHis/LMwoSc8Hd9dLK3by/nMra7gc12eWFqzcIqlVd5zL8fx7Y7cyloKcREWwhf32qrf1HY+npYqi6VVxrVKw43CY+V7iqW1Dh/H0vKy7siyjl2Za2jVvwb3sbQOU75YWheU431wPIuNvb0OstTPpTbZ8ACgtT6utb4f04sxCfNh3I35MTqG+UH7GBP/qI3W+lEXbRzB/HO+CTNmvB/z4uy39kcAfXXVGSvbZcnnRIdzf+HZyZ+j3l6MA7qrrfo7MNegAPMvahnGQVyi1rrM9so41leYf1VzMde6wFq/iwk38QllzCDSWm+w2rgZ04Owx2onHxOa4jPgHsw9W+Oqjcqitf4d82M8DtNrchDTo7EH8298OqW+S5zrzsH0uiRj/B8dwvwoZGF+3FMwtkwuo5qXQ7Z1mN6PSZjhzaOY67MTc517aa3/pbXWFWm/HMc/hvn3fCXwDMbR4l5LhgLMu/EDJhZWZ631ZA9tVepea60PYt7PazFDvo76BzEKw6uYMBdHXdSdhekNeAPTY5qHUeTWYuKnddBaf1PuC1MBtNbjMddxKcaLdi7G98xjmN6uw+5r+5/KXkOt9YeYmFfvYjzGF2C+T68DSdrM9CtLhh8wvahjMbZhmZh39Zgl00JMiJIWWusafT2FmoOqou+nUI9QSjWm1DnkNVrr+f6URxAEQRCcqXU9PEKNZJBte7XfpBAEQRAEN4jCI5SJUqqJh7wYTFc9wEqtdVq1CCUIgiAIXlBbYmkJ/iVZKRWP8fHhsF9pgrGjmAw4wgs87B/xBEEQBMEzovAI5UEBl1uLKzQwXmv9efWJJAiCIAjlR4yWPdCsWTOdkJDgbzH8zrFjxzh06BBZWVkUFBRQWFiIUooGDRoQFRVFTEwM4eGuAsILglDfWL169QGttUQwF2oc0sPjgYSEBFatWuVvMQRBEGoNSqn0sksJQvUjRsuCIAiCINR56pzCo5Q6TSl1r1LqHaXUBqVUsVJKK6WuKbu2IAiCIAh1kbo4pHUXcK+/hRAEQRAEoeZQ53p4gPWYWFtDgVMxMbMEQRAEQajH1LkeHq316/Z9pZS/RBEEQRAEoYZQF3t4hFpA1t4sUnqnkJ2RbRJSUyEhgSwVTUroXWTPfvOE8rGxsSilTlpiY2P9IL0gCIJQ2xCFR6h6LGWGgACzTk3lm8e+IWPNJtamvgSfTYWnb4XCdH6IPp+dx5ux4t7/mnoWmZmZLpt2ly4IgiAIdurckJZQc8jam8X8Pi9xTfpTRAbvBw3J6cMpHL4FgPaX7uCC8Y+bwpeZ1aV8Qf/iL9i3vjk/Lc0k/erPGfrf2QBEEsk1XMOHfEg22f44JUEQBKGWIj08TiilbldKrVJKrdq/f7+/xanV/Pj0Ilr0XcHxZcfhd0DBPTxHZ9YSpAo5sKGZy3oqAFqcuY/zxv3E0P++DTThu+/gpk5nE09bXqM3RcB24IZqPB9BEASh9iI9PE5orecAcwC6d+8ucTcqwNzed3L+uOX0nbGZwAbFJelvXzicEd+8Qwj5FOkAcvY1Zef3bYgKyaFR5CHyokJQ0ZqQqAKnFgvp2j6CZVsupIgANtKDx+hBEMd5jWQz9DVsWPWepCAIglCrEIVH8CE7gYncsmLeSTnFBYrrOv8ffAM5RJAUuZGk755l9Zyzyf7lT4b+8QgLc68gkmy6R6wk/eJTiL4+hI7D/wJ+57/PJEC+0T+DKOB0NnBp4mdEZAOTJonCIwiCIHhEhrSEipOaSlbr03knYjgFzzSDwlOBE5WdXT+24ZO7BvBVy36EvGR6boaGL2bgK4OI7RrLwNkDGbryXzBnDkPjf2agWkKLZuGcc8NYOg5fAfwG7OPz/yRSTBBBHKeIIELIJ+LpXPgT8vpmkNJ7bumML0EQBEFwQhQeoWKkpsLtt/Nn5yiu3PQxweMOQlDpUNTOH85l+bSXCQr/BTb34/CxOFAK4uNhzpyTe2SGDYO0NCguNusT8mMYdNH1JEVuZDSvk8QqArschyuAhhD6n3x6PTiDn5+fXw0nLgiCINRGlNZ120xFKbUc6A1cq7X+0Ju63bt31xIt3TXJAQ9TqINo2yudm5elEBBknqOMX2OJPft94CLfH9RSssjNhbPh4LtNaNrhUEl23pEQPvvnZfzv/e5MOjbZ98cXBKFMlFKrtdbd/S2HIDgjPTxChbhHm9lWe75ryVcT+5GdEcHqW84mskcWVaLsgOn1mTPH9BL9pgge0IzN712ELjbetEMb5TM4ZSETDv8CMm1dEARBsFHnFB6l1NlKqZ8cC3C2lTXDKV2oEEaRiIpvYmZbEcTKp3ow+7QxZKS0JLKN66nmPsM29BW1ZSMbV9zPm5fcwqGtTUqKBIUugoNdoEfrE5wdCoIgCPWXOqfwANHAubYlykpPdEoXvCBrbxY/Pn0TxUXtgR2QnExOQDRJrGI0/6HzX+vJDoiG5ORqlSsnM4eYzkM4nruStBUDSzOapsH83eScEUpK+iVk3zZOlB5BEIR6TJ234akMYsNTyp8LRnH6kLnW3rnAN5D6gZkSvmMHtG1rlB2/Tw+fA4V3lDhcOLi8CbMvGUMSvzIwfr3pHRIEocoQGx6hpiIKjwdE4YHksOn0fGApF09dXpK26+c4PrjmJsbtnOE/wTxxuSL//4LJPxrC6+feRtae6JKsoNAgJh2b5EfhBKFuIwqPUFMRx4OCBzT37z9AcOTykpS0Fe1Y89Zj3LbyKv+JVRZ/xlPYax+/0INje0IBy1lhxE76b3nJz8IJgiAI/qAu2vAIlSU1FdrFw+wAgiOfK0ne+nki8wYMIyikEZGxkX4UsAySk4nYoshbG0aR3Vnhed2IjC3yt3SCIAiCH5AeHuFEUlPh9tvgyWMwpjQ549suRLRcRNeR68neW8OnfFt2RDm3fUXSsVUktdzD6jNuIrznQSABSAUG+FFAQRAEoboRGx4P1EsbnoQEuD4dZtrS5gFT2sKWdD8J5Qu+BAYB+UAo8ClwiV8lEoS6iNjwCDUVGdISSsjam8XSru1PVnZGANt2+kkqX3E60NLazgMGkXNgKSm9UyQGlyAIQj1AFB6hhG8e+4ZVy3twYGlTk7AMuAUoxkw7r9W0BpYCraz9HBqEXk3Wnt9ZMW2FH+USBEEQqgMZ0vJAXR7Sio2NJTMzE4BJTKIBDUryAhoU0nvKCn6ZdQ7/OvoUhIe7DvhZK9lAzr7uRDTPAWDf+hj+c/6tFGSHyJR1QfABMqQl1FSkh6ee4lB2AJ7jOdaylgJMtPMA1YADMxO48+ir7qOb11o6QsAiigqMgte8836GvD2fLmoN9zZ7R7wxC4Ig1FFE4annBAdDtwuzySffmsB9nKJCCLlpKJE6y3gmrjPKjiGi2SWsnXd3yf5pgzfRZeo6IndtMNHYRekRBEGoc4jCU8+ZNQuWL4eRj27n14CVvM7rJN2ZVOcNeTd9fC7bXuhQsp/48Ba4BsjNNeEyBEEQhDqF2PB4oC7b8CilGDoU3nuvNO266+CDD6DePBMNFCwGLrX2ZwCTAKWguNh/cglCLUZseISaivTw1FM6doTXXy/d//BDo+zUK+Li4XpgHTASo+xAHZiRJgiCIDgjCk+9JIePPgok0ooOsXkzjB5ttlu0aOE/saqb5GQoCIduwJtWWni4SRcEQRDqFKLw1CdSU8lq3ZGtb5/Jaac5YkqFkpj4O0eParTWZGRk+FXEamXYMDMDrXW8GcayZqRl9blSHBIKgiDUMSqk8CilgpVSrZVSnZVScUqpYF8LJviY1FS4/Xa2Xx5M+xHbStN/HAF09ZtYfmfYMDMTrbi4ZEba909+RucbZ7PqFZmtJQiCUFcod/BQpVRf4CqgD8ZPv3P+HxjfvAu11kt9JqHgE5JHbCDqlNHc+ewrJWm//acbn97WgklinwtAclgyzTru5Jr/+4CmiYfYs3o3jwXvIiAwVBwSCoIg1HI8ztJSSgUCdwD3AImAsmVnA38B0UCkLV0Dm4DngTla6yJqKXVpllZWYBT53wTTrOchAPb/rxnfd+9Jv7ylxt+OQNbeLH5+4VUufmQiQSHmsd30yZW0SkolMjayjNqCIIDM0hJqLm6HtJRSA4D1wItAPLAAuAs4CwjWWkdrrVtrraOBEIzp5z+Aj4B2Vr31VjuCn4m6IpLG3Y8AUHQ8gP+OuJoGeYVExjf1s2Q1h6iWUeQd7sjSiX8rSesw8GMiY3/wo1SCIAiCL/Bkw7MYiMD07rTUWl+rtX5Va71Wa11oL6i1Pq61XqO1fkVr/XdMWOpxmJ6fRVUlvOAF183ii+6XcXR1NLlTw4j7bTfZAdEyI8mJnMwcCgvGkP9XH1vqzcBhf4kkCIIg+AC3Q1pKqXHAS1rr/Ao3rlQIcJfW+tmKtuFP6tKQFmAMlx95CNJ3GB80ycl1LmyE79gHnAk4Yo6NBOb6TRpBqC3IkJZQUxFPyx6ocwqP4CUfAVfb9j+j1C2zIAiuEIVHqKmIH546ze/AZn8LUYsZDFxXurtrIEQrSEiQAKOCIAi1DFF46iwFwI0YHzsvAjL3vGK8AHnWDK3WRSbeVnq6RFUXBEGoZZTbD48DpVRP4BKgFRDqppjWWo+ujGBC5cjPmk5I1J/W3oPAEMwtE7yjOUwIgeeM1+XCMwOY12AYQ3L/S+SkSWIDJQiVZPXq1cHADQ0aNBgAnKm1DvO3TELtQil1uLi4eElRUdGcpKSkNLflymvDo5SKBD4A+juSPBTXWuvA8gpbU6m9NjxbKDp+BoENjlv7zwL3+lOg2k2AglTge/jkpQGs1t1JYjUD1acSVV0QnPDGhmf16tWNg4KCUqKjo7s0adKkICIiIjcwMLBYKU8/L4JQitaagoKCBkeOHInKzMw8cvz48SHulB5venhmYiw2DwHvYIxDJNhQDSM5bDrXfzyX9n8zys6eVS15/dxDBAYni7fgitI2nuQbh1NIg5KkVfRgle5BUJhcV0GoKAEBATc1adKkS+vWrQ+JkiNUBKUUISEhx1u0aHEIaLJ3797bgYdclfVG4fk7xhnJWVrrXT6QU6gC7tsTS1hjEyuruEix5N6r6XxDV/rP6l9GTcEtycncc9s4vjh2IRvoSCHBBHGc00JGj4gAACAASURBVC9oTP/5d/hbOkGotQQGBg5v1qxZtig7gi9o1KhRVmZm5uW4UXi8MVqOBr4RZacmc4iwxqX3eeXs89n9UwtCokMkNEJlGDaMqNeeISQymCKCCKKQ4sBA4m8+SGRshL+lE4Rai9a6WWhoaIG/5RDqBsHBwce11o3d5XvTw7PVy/JCtTMB2A/AsUMxJFzyFkl3biB7r4w8Vpphw8iZH0RSy0jOuzeAwJB7aRS/GTgDGO5v6QShtqKkd0fwFWU9S94oMHOBaUqpWK11RqWkEnxLaip8NB4+yCxJCmvyOmFN2jNwdns/Cla3GLpgqLX1AKX+jf4FDAIa+kUmQRAEoXx4M6T1LMbV7NdKqb5KKfHhUxNITYU7b4MppcoOCwMhVSKgVx0PA3HWdibwiB9lEQRBEMpDuZUWbeav3wEUAl8AuUqpNKXUNhfL1qoSWHBi0iTIPmZMtLZg5s2NKTLpQhURBTxt238BWOMnWQRBEITyUG6FRymVgIlV0AnjgycYaAskuFmE6mDHDrNejLkz/YDdtnShirgW6GttFwNjAIlLJwiCb4mLi+uilEpSSiW99957bsfOExMTOymlkhYvXhxVnfI5s3///sB77723VYcOHc6IiIjoFh4e3i0+Pr7z4MGD261evdqds+JqwZthqX8DrYFvMBEVuwDt3Cyn+FZMwS1t25ZuFwA/u0gXqgCFCdnh8M3zPfC2/8QRBKHOM2XKlLiioiJ/i+GWb7/9Nrxjx46dn3/++ZbZ2dmBvXr1+uvCCy/8Kzw8vHjRokVNfv7553B/yueN0fIlwHbgUq21TCOsAWTtzWJ+2F1cE/YUkcf2l2aEh0Nysv8Eqzd0BMYBTwJQXPQv3r0ih6vmjhA3AIIg+JTQ0NDizZs3h73yyitNxowZc8jf8jiTlpbWYNCgQR2ys7MDZ86cueP+++/fHxAQcEL+8ePH/Tolz5sengbASlF2agqaI9uHEHb676y4YCLEx4NSZj1njsR4qjZKDZgDAvcTf9G7rJi2wr8iCYJQ5xg1atQ+gMcffzwuLy+vxs3lHzt2bOujR48Gjh07du+ECRNOUHYAEhISjicmJvpVf/BG4VkDtKgqQYTykxyWzP/9/XraXPAVQxe8R4fxLzNt580khzwGaWmi7FQrkSy85fySvfPG/cDmT75iqppKcpj0sgmC4BuGDh16uEuXLjm7d+8OnjVrVoy/5bGzY8eOoCVLljQODg7WkyZNyiy7hn/w1obnQqXU+WWWFKqUe7bdxsBXlpXsH94eQ+cbunLvdgkQ6g/6zHidQ1tPpaggkJUv9aDoL0WXiK3cO6u1v0UTBMFGs2bNujoMgO1Ls2bNuvpbtvKQnJy8G+CZZ55pefTo0RrjGmbJkiXRRUVFqkuXLjnNmjUrmj9/fvQdd9zR+sYbb2w7ceLE2JUrV/rVWNmBNzY8a4CngC+VUs8AnwO7MFNUTkJrLdOEqoiolnNweFTOPRDO8od702mohI/wF1EtG7LitsGsW36Mo1saUUQgIWwi8oF/QKMg6XEThBrCwYMHXf7muUuvaQwaNCirZ8+ef33//ffR06ZNa/HUU0/trUx7ixcvjho0aFAHb+uNGzdu79NPP73Hsb9u3bowgFatWhX06tUr8fvvv4+2l3/yySfjhg8fvn/u3Lk7AgMDKyNypfDmJm+31grj9cVlcC4L7WXbQrnJBJ4o2TueN4VO13eW8BF+JiP1AO2O7SOJ1awmiWwiITfX+EMShUcQBB8xc+bM3RdddFH0q6++Gjt+/Pj9rVq1KqxoW3FxcceHDBly0Nt63bp1y7XvHzp0KBDg008/bayUYtKkSbtGjhx5KCIiQs+fP7/hQw891Obtt9+Oad68+fFZs2ZVSkmrDN4oJTsRRyM1gKkY74IAnWjYejwDZ4tu6W+G5r2J4/UYyKelGeIPSRAEH9KrV6/cAQMGHP7kk08aT548ueUbb7yxs6JtdevWLW/+/PlplZVJa60AioqK1AMPPLB7+vTpJXY8d99998HIyMiiW265pf3LL78cO2XKlMzo6GiXI0NVjTeelhO01u3Ku1Sl0PWXjcAc2/6TSEdaDcHZ71Er4ClID9YopVBKERsb6xfRBEGoW8ycOXN3YGCgTk1Njdm0aVOwv+WJjIwscQ50zz33HHDOHzly5JFGjRoV5ubmBixfvjyieqUrRX4taxUPAo7n6hLgcj/KIpxAcjLcfrsZxvonMB2IgB8ycbjpITOzxk5eEAShFtG5c+f8oUOHHpg3b17MxIkTWy1YsCCtIu389ttvodOnT/f6n9jgwYOPjBgx4ohjPyEhoQCMr6C4uDiXQ2ytW7cuOHLkSNCePXsauMqvDkThqTV8D/zXtv9vjDmVUCNw2OlMmkRxfjoB1n+YgZOg6X/goNej5IIg+JqmTZsWujJQbtq0aYXtYPzFjBkz9i5YsKDpwoULm65cuTKjIm3s3r27wYIFC5p6Wy8+Pr7ArvCcc845OQD5+fkB2dnZKjIy8iTzl8OHDwcBREVF+c1VtFuFRynVUWu9obIHUEqdrrX+s7LtCFNs2zcCSf4SRHDHsGEwbBjBQYq1d8MZZ0B0NDz0EIwf72/hBEE4cOBAnYnyGx8ff3z06NH7Zs+eHTthwoQK+cC44oorsrTWqysrS58+fXJiYmKO79+/v8HixYujr7/++qP2/PXr14fs3bs3GKBnz565rlupejzZ8KxXSr2hlKqQPY5Sqp1Sai6wtmKiCSfyJnALEAaIQ7uaTFGRUXIcjBkjoc0EQfA9U6dOzWjYsGHRsmXLGu7atctvtjyBgYHce++9GQAPPvhg6w0bNpTIsn///sDRo0fHFxcX079//yMJCQnH/SWnJ4XnNWAEsFkp9aVSarhSqqWnxpRSrZRSNymllgKbgeGcaGUreENqKiQkkKWiSQlNJnt2byAdCUZf81m4EH780WyHhEDq1PZEIn6SBEHwHU2bNi0aO3bsXoC8vDy/OiKcOHHivgEDBhxOS0sLPfvssztdcMEFHfr06XNqhw4dOv/yyy9R7du3z0tJSUn3p4xuL5DW+i6gO/A10BfTxbBLKZWmlFqilHpHKfWStV6ilErHTF2fi7Go/RI4W2s9pupPow6SmmqMYNPT+YaL2JHfnBX3/hdSv/C3ZEIZtGhhIrBMnFiadsFNW7ktSZyUC4LgWx588MF9LVq08FuviYPAwEAWLVq07emnn05PTEw8tnbt2ogffvghOiYm5vh99923Z/Xq1X+2bNnSr7ZSSuuyXesopc4AxgBX4oiU6JodwEfAy1rrjT6R0I90795dr1q1yj8HT0ggOX04hZxs0B4UGsSkY5P8IJTgDclhyVw3P4XEAVsA2PhxB9676ka5f0KdRim1WmvdvTxl16xZk9a1a9eTpjELQkVZs2ZNs65duya4yivXLC2t9R8YhWeMUupU4CygOdAQOALsA37VWm9334rgFTt2MH7cv9nRMp7FTwwk62AjgijgdDbQf/ub/pZOKAf3bLuHn58P5dTL7kcFaE67chMXTw0i6XaJeSYIglDdeD3mp7XeorX+UGv9ktb6ca31y1rr+aLs+JjOcYROKaDD/ZsZs+0l4s7aSRFBhEQ2kJhZtYSollHkHTmNde92KUnrcuM8ImP95ndLEASh3lJjoq0KTszrBo3M5vGMIK5Yt4ikwN/J7liunmKhhpCTmcOBjfegixuQndGaP+Zf5m+RBEEQ6iXieLBGkgGdl5bsRU7JJbJ1DAOTr5NAlLWMoQuGWltnEBnbg14T5JUTBEHwB/L1rZHMABy+mbrCe78inXG1HZmhJQiC4E/kV7TGkQ68YttPRm6TIAiCIFQO+SWtcUwFHC4VLgAG+FEWoUpIfQdGNYcrFSQkGJ9LgiAIQpUiQ1o1ig0Y/44OZiABQusYC5+CxAdgWDGkAR3SjYNJEPssQRCEKkR6eGoUjwDF1valQG8/yiJUCQ89B+2se5wAjAZyc2GSOCIUBEGoSkThqSHk7P8F+D9bynR/iSJUJX/ugpmlu8WTFW+HDic7/aD/ZBIEQagHiMJTQ1gxNYOFowaTe6AFcBUmjJlQ52jbFl4G9prdgDhN8zv2sSJyoF/FEgRBqOt4ZcOjlAoErsMEE20FhLopqrXWfSspW70gOSyZwjxHPLWzWPt2F0Ib5VGQnSzxluoiyclw++18ntyLS180gWB7Pvg9z792L6vUVImzJQiCUEWUW+FRSjUGvgDOpmxL2rIjkgqAibf0xb++YMNHGyjMLSQgOIT2l55F/1n9/S2aUBVYhskXPDyN3B1hhLc9RmSLHM67bxVHtt8h910QBKGK8GZIKxlIAnYBEzDjLpe4Wfr4Vsy6S1TLKEKiQyjKKyIoNIiivCJCokMkXlZdZtgworZtZMs3o0uSzvvnt0Q0L5L7LgiCUEV4o/BcCRwGztVa/1trvUhrvcLdUkXy1kEmERHzC0l3JjH6p9Ek3ZlEdka2v4USqoENC88jZ38sAOFNj9Eyab6fJRIEoaYRFxfXRSmVpJRKeu+99xq6K5eYmNhJKZW0ePHiqOqUD6C4uJj777+/Zb9+/drHx8d3joqKOisoKOjsmJiYM/v06XPqvHnz3MoNUFRUxOOPPx7TuXPn08PDw7tFRUWdlZSUdNqrr77axJdyemPD0wz4XGud4UsB6jc/AzO4ZBqYTrHPGDhbjFfrC9d9MAzjZPIWAM4c9iXwFxDtR6kEQaipTJkyJe7aa689GhgY6G9RTqCoqIhZs2a1CgkJ0YmJiccSExOPNWjQQKenp4csW7as4bJlyxp+/vnn+958882dznULCwu59NJL23/99deNIiMji3r16vVXQUGB+vHHH6PvvPPOyB9//DEiJSXlpHoVwZsenj1AYZmlhPKRmgorLi7d354HNPCXNILfGA60BwIxnah5/hVHEIQaSWhoaPHmzZvDXnnlFZ/2eviCwMBAFi9evPHw4cO/rVu37s+vvvpq65IlS7b98ccffy5evHhjWFhY8VtvvdV80aJFJ/U+PfbYYy2+/vrrRu3bt8/7448/1n/xxRdbly9fvmXVqlX/a9q0aeGbb77Z/J133mnkCzm9UXjmAxcppcJ8ceB6TWoqvDEaels/bkXA1b9KiIF6SRAwF+Nley7Q3L/iCIJQIxk1atQ+gMcffzwuLy+vRrngDwgIYODAgdlhYWEnTVgaOHBg9hVXXHEI4PPPPz+h+7qwsJAXX3wxFuCFF15Ib9OmTUmnSpcuXfIfeeSRXQBPPPFES5/I6UXZqZhenveVUvJVrgyTJsHE/NL9VGBNnnjbrbdcCJzqbyEEQajBDB069HCXLl1ydu/eHTxr1qwYf8vjDUFBxnomNDS02J6+dOnSyEOHDgW1aNHi+OWXX36S8erIkSMPBwUF6fXr14dv37690kMg3ig8zwNbgCuAzUqpr5VSKUqpN1ws/6msYHWauHT4m7VdCDxmbe/Y4SeBBEEQ6gmvvNKEVq26EBCQRKtWXaiBQ0TuSE5O3g3wzDPPtDx69GitcBz87bffhi9atKixUoqrrrrqqD1v1apV4QBnnnlmjqu6UVFRxaeeemoewM8//xxeWVm8MVoeSal/nSjgYg9lNSZKkOCKx0MpsdVIxaiRYLzwCgKHgLV4fsUEQfCaV15pwrhx8eTlGWVh795gxo2LB+DOOw/5U7TyMGjQoKyePXv+9f3330dPmzatxVNPPbW3Mu0tXrw4atCgQR28rTdu3Li9Tz/99B5XeQ8//HCLP/74Iyw/Pz9g586dwevWrYsICgrSM2bM2HHhhRfm2stu3749GKBNmzYF7o7VqlWr/A0bNoRt27Yt2Fs5nfFG4bmlsgcTAH6Ci2y2O46QWeHhxguvUI/JBWZgOlODgO2Ax9mcgiB4w7RpcSXKjoO8vACmTYurDQoPwMyZM3dfdNFF0a+++mrs+PHj97dq1arCk4ni4uKODxkyxOtAft26dct1l7d06dKGP/74Y4lxcmhoaPFjjz2285///OcB57I5OTmBABEREUXu2ouIiCgGyMrKqvTUtHIrPFrrNyt7MAGMKZTFwgjYmgvxbY2yY3nhFeorwcB7QJa1/wIw2X/iCEJdIyPDdS+Bu/QaSK9evXIHDBhw+JNPPmk8efLklm+88UaFp2x369Ytb/78+Wk+FI8ffvhhE8DRo0cD1q9fH/L88883v//+++Pnz5/f5NNPP93SuHHjEjserc2gkVLVY4NdK8YA6wo5B5YBn1l7CoasguJiSEsTZUfA/P94uGQvP+txsjNd9hoLglARYmNdD524S6+hzJw5c3dgYKBOTU2N2bRpU41U1ho2bFjcs2fPY++//376TTfdtO+nn36Kuv/++1vZy0RGRhYBZGdnu+29ycnJCQCIiopy2wtUXrwKHupAKRWMCTMRZyXtBlZrrWvVQ1Pd/PLCZpp36sQZ1/yBCrge6OhvkYQaxzDMOOcWQqJy2f71g3S8SjpXBcEnTJmy+wQbHoDQ0GKmTNntR6m8pnPnzvlDhw49MG/evJiJEye2WrBgQVpF2vntt99Cp0+fHuttvcGDBx8ZMWLEkfKWv/XWWw++9dZbzT/99NPGmPBUACQkJBQA7Ny5063Stnfv3mCAdu3aVVq/8DZaegPgUWAMxnDZTrZS6gVgqtb6eGUFq0ucGBH9Wpqdvo/CYw3IzpCI6MKJJIc9QaehnRicYizZ2/b6gMej4igujJBnRRAqi8NOZ9q0ODIygomNLWDKlN21xX7HzowZM/YuWLCg6cKFC5uuXLmyQhEQdu/e3WDBggVNva0XHx9f4I3CExsbWwhw6NChE6aW9+jRIxdg7dq1Ea7qZWVlBWzevDkM4LzzznNrN1RevImWHggsBvphoqXvBbZZ2+2AlsCDQA+l1ACtdaW7n+oKzhHRj6S34vSrT5fI2MJJ3LPtHr6c8CmHt39D43aHCW96jCvuWkS7dwshNUGGPgWhstx556HaqOA4Ex8ff3z06NH7Zs+eHTthwoTWFWnjiiuuyNJar/a1bM4sWbIkCqBt27YnuJLv27dvdpMmTQozMzMbLFmyJNLZF09KSkrjwsJC1blz59x27dpVuiPFGxue2zHeYzYDA7TWcVrrC7XWvbTWccDlwCaMQnRbZQWrS0hEdKG8RLWMIjgigu9m9CpJ6/CvTUQe2gC33y7euAVBKGHq1KkZDRs2LFq2bFnDXbt2+c2WJzU1tWFqamrDwsKTJ4y99957DR955JHWACNHjtxvzwsKCmLMmDEZAGPHjo3fvXt3SSfMunXrQqZNmxYHMGHChEpNv3fgjcJzE5AD9NVaf+acqbX+HKPs5AI3+0K4usMH5B89IBHRhXKRk5lD4PwQitLN6xnSvADuAHJzxRu3IAglNG3atGjs2LF7AfKcp9tXI6tXr44YPnz4qc2bN+964YUXJl511VXtevfufWqbNm0633DDDaceOXIk6Prrrz8wYcKE/c51p0yZknnJJZcc3bp1a2jHjh079+/fv32fPn1O7dGjR6cDBw40uPnmm/cNHz683MNnnvDGhucMYJnW2q1xl9Z6t1JqGdC70pLVGX4HruPv85oA9wEDJCK64JGhC4ZCwA3wuIZXrMQHgJcRb9yCIJzAgw8+uO+1115rkZmZ6bfo09dff/3h3NzcgF9++SVy48aNYUeOHAkKDAzUzZs3P37VVVcdGj169IFBgwZluaobFBTEl19+ueWJJ56ISU1Nbfbtt99GBwYG0qlTp5zbbrtt/50+HH70RuFpgOm9KYtcJOy3DYdnwUPArxiTJ0Eog7ZtYW66ccPTGsjHhNvKEm/cglCf2L179zpP+eHh4TojI2NtdcnjinPOOefYOeecs6vskq4JDAzkoYce2v/QQw+d1APkS7zpAksHLrSmpLvEyutllRVYjwky7+BhdwUF4USSkyEo3PTs3AYkAtvEG7cgCEJF8Ubh+RgzE+tNpVQj50ylVEPgDavMQt+IV3GUUjcqpb5VSh1VSmUrpVYppcYopapxnNP+4zQIOKv6Di3UboYNgzlz4Id4+I+CVvFmX2ZpCYIgVAhvhrSeBG4ArgMuV0otwgT70cApmF/0KIxToSd9LKdXKKVmA//AROhcChwH+gIvAn2VUtdW/bT5DcD7tn3p3RG8ZNgwUXAEQRB8hDextA4qpfoA84DuGJewjujpDsOUlcCNWmu/+ThQSv0do+xkABdprTdb6S2AZcDVwN3Ac1UryQxKL8/lQI+qPZxQjzgENPG3EIIgCLUKrzwta623AOcopXphZmLFYZSdXcAKrfV3vhfRax601hMcyg6A1jpTKXUXsByYqJR6QWtd7KqByrMFsPtLkd4dwResAB4DtmJcXsncAEEQhPJSIXsWrfV3WutkrfU/tNZ3Wdt+V3aUUq0xMb4KgA+c87XWKzBxv2KB83x9/NjYWG5UisNvnA4YXWrdlxAbe7WvDyXUO44Bf8eM0Kbx3cw7xZeT4FMc368/VBRz1S38qaK4USliY70OtSQINZK6Fi29m7X+n9b6mJsyK53K+ow+mZm8ngANR5SaB506zaQLQuUIA8aX7J1xzUd8M/1r/4kj1Dn6ZGbyGrCd3uykLdvozWvI90uoO1QoWnoNpp219jQt3uG5rZ2HMhXiDCbxYfsdXH3gv0S1zCZteTxvfncLZyCxVIXK8+/mudy9IZSwJnk0OfUQeUdSmKp+Iyg0SAKLCpXmDCbxdtcDhDbMR38TwCp6sIoe8v0S6gxuFR6lVBHG6vYMrfUma7+8aK21P5QpR3CqHA9lHOMAztHeAVBK3Y6JG0bbtt45eRvLc3y1tD8vnXIXZ966nn2/NaMLa+nHF5Q6IBSEinHnmgfY9vVmOl1jZv9d9PC3oG6g/78v97NkQl1gLM+R92Q4LfrvI21FPF+O/RtN1x2S75dQZ/A0pKWc8pUXi7+GyhyzxbTHUh7QWs/RWnfXWnePiYnxqu5hsgkhn/y8MH598WzSv29HCPkcQmwthMoT1TKKnT8MJu9oCADNTjtAwsWrJAit4BNyz82mRf99ALTttYP8YyHy/RLqFG4VE611gLVsctov11J9p3ACjlgdnn4BHHku43pUhoeAo0SQxCpG8zpJrOIIETzk6wMJ9ZajaYqdPwwu2W//t3k4DOQFoTJk2CaT5r8bQrst2+X7JdQp6poNT5q1jvdQpo1TWZ/xdYsWkPl/zACaA534lIcc6YLgA4YuGAr0Az4BsmnYdhfwETDEr3IJtZ3VdLNiGutiCEnOk++XUOcod0+MUuompdQF5Sh3nlLqpsqJVWF+s9adlFJhbsr0cCrrMzIyMpinNQlaE2Ct52lNRkaGrw8l1GuaAmNs+9OoxCiuIGD8OxlUwHUE/CnfL6Hu4c3QUwpwaznKjQbmVkiaSqK13okJSR4MXOucr5TqjYk9nQH8WL3SCYIvuQ8It7bXAD/7URahdrOGE8MfTvaXIIJQpVSFrY0qu0iV8ri1fkIpdaojUSnVHHjJ2p1ZdV6WBaE6aI6JoPJ3TGelz/1oCvWG123bQ4Au/hJEcEFcXFwXpVSSUirpvffea+iuXGJiYielVNLixYtdzkD2B4MGDWrnkH3u3LmNXZU555xzTnOUcbVceOGFib6SpypseFqD/8z6tdYfKqVeBu4C1imlvqI0eGg0xuDhRX/JJwi+40lAQWoqTBoMO3ZA27aQnCxBRwUveAajMCcjvTs1mylTpsRde+21RwMDA/0tSpm89dZbjRYvXtxEKYXWZQ+59+rV66/mzZuf5PSpc+fO7pwIe41HhceFLc6pHuxzgoDTMYrFSjdlqgWt9T+UUt9hDB16A4GY8OVvAC9L745QN7CUndtvh9xck5SebvZBlB6hnARhYkHfiP876AV3hIaGFm/evDnslVdeaTJmzBi/BeguD3v37g0aN25cfMeOHY+Fh4cX/frrr2X6zpgwYULGFVdc4fPZ03bKGtJKwdjjOGxyetr2nZfXML7vFTCrCmT1Cq31PK11T611tNY6QmudpLWeLcqOUKeYNKlU2XGQm2vSBcErRNmpyYwaNWofwOOPPx6Xl5dXo2/Wrbfe2vbo0aOBr7/++vaa1BtV1pDWW5RO/7gZE6b5ezdlCzCBORdqrdf4RjxBEDyyw4qUEoEZxD0fY9bjSBcEoU4wdOjQw99++23UunXrImbNmhUzefLkff6WyRVz585t/Omnnza+++67M3r27Omz4Shf4FHh0VqPdGwrpW4GvtNaj6pqoQRBKCdt20JGOmwE4kzS533603PTDo/eN4X6zmYKC25i2eTzOf++qUTG1hg712rhSPqRBh9c88Ep182/bmvDtg0L/S1PeUlOTt595ZVXdnjmmWdajh079kDDhg1r1IjFnj17gsaPH9+2Xbt2eU8++eQeb+rOnz+/0fz58xvl5+erVq1aHe/Xr1/WZZdd5lN7YG9mabUD7vflwQVBqCTJyRAYDotKkzpO2cCK0273n0xCLWA6QcE/8bcnn2H/H8P9LUy18/Wkr1vuWb0nculDS1v5WxZvGDRoUFbPnj3/OnToUNC0adMq7RFy8eLFUZ5mSLlb7rvvPpfXbdSoUW2PHj0aNGfOnLSwsDCvnIOlpKQ0T0lJaf7uu+/GPPXUU60uv/zy05KSkk7bsmVLg8qep4Nyz9LSWnuKQC4Igj+wDJNfmPQT/xj9EoENionvvYNlU9YyVU2VSOrCSbzU6T7uXPM2AdbX/+vJzdj1Y/14VqaHTD+7qKCoxP5lXeq6mHWp62ICgwP15PzJv/pTtvIyc+bM3RdddFH0q6++Gjt+/Pj9rVq1qnAPVVxc3PEhQ4Yc9LZet27dcp3T5syZ0/jzzz9vPGrUqH39+vXzFMD7BM4///ysG2+88UDfvn2z27VrV7B3794Gy5Yti5g2bVrrX3/9NbJfv36nrV279o/o6OhK92Z5ipbuCBW+W2tdZNsvn+LVcgAAIABJREFUF1prMSIQhOpg2DBG9rmSHd/9SbtLlgJw8bQV/PraIPrP6u9n4YSaxm0r9xEQZP58b/3yFDLWnEKXYafXi2fl7k13r1sydknrrV9ubVSUVxQQGBpYfGr/U49c/sLlO/0tW3np1atX7oABAw5/8sknjSdPntzyjTfeqLDs3bp1y5s/f35aZWXauXNn0IQJE9q2bt06/9lnn93tTd3nnnvuhKGvxMTEgsTExIIhQ4b81a1bt9PT09NDZs2aFTNt2rTMysrpaUgrDdgGtLftby/nsq2yggmCUH6iWkax/evrKS40r3RC7+20PHuzRFIXnNhKg/D3Sva+m9mHorwiQqJD6sWz0ii+0fGQqJCiovyigMDgQF2UXxQQHBVcVJvseMD08gQGBurU1NSYTZs2BftbnlGjRsUfPXo0aPbs2elRUVE+sStq1qxZ0R133LEP4IsvvnDrcNEbPA1p7cDM0DrutC8IQg1k//+i2P1LX9pc8CUAp/R7G5jgX6GEGsYMoAiAAxvP5NKnH2P1nNVk7/Wbr9hqJ2d/ToMzh525v8c/euxf+dLKmOzMbJ/ZiFQXnTt3zh86dOiBefPmxUycOLHVggUL0irSzm+//RY6ffr0WG/rDR48+MiIESOOOPa/+uqrRqGhocXTp09vNX369BPK/vnnn2EAycnJrV5++eXm5513Xtbzzz9fLoPmM844Iw8gIyPDJ0qdW4VHa53gaV8QhJqFiaTeA+gAFNHizP8B3wAX+VUuoQaQmgovPwDL9oD1897stBeAWAbOHuhX0aqbEV+M2OrYbn1+61prejFjxoy9CxYsaLpw4cKmK1eurFCE1927dzdYsGBBU2/rxcfHF9gVHoC8vLyAlStXuu0m3Lp1a+jWrVuJjo4ud2/a/v37gwAiIiKKvJXRFVURWkIQBL9xCsZl1hvW/qPA136TRqgBOLxxP5tbouywIgB27TQOloVaSXx8/PHRo0fvmz17duyECRNaV6SNK664Iktrvbqysnhq45xzzjlt5cqVkW+88ca2W2655bA37X744YeNAbp27VpuI2hPVEXwUEEQ/MokTDQVgGXACj/KIvidSZMgJhdG2tIeKRZv3HWAqVOnZjRs2LBo2bJlDXft2uV3Wx5vWbx4cdQnn3wSWVx8otlPVlZWwJ133tn6q6++ahQYGKjvu+8+nzhZLHcPj1KqKcaAeZvW+oAtPQ54AuiKMWyeorX+zRfCCYJQERy9PIuAB4Du/hVH8C87dsArlPbufIPRgVWtHc0RLJo2bVo0duzYvdOnT2+dl5dX6zowfv3117BHHnmkTdOmTQvj4+PzYmNjjx8+fDjozz//DDty5EhQcHCwfvbZZ9O6d++e54vjeTOk9SAwDugGHABQSoUA3wFtMYFYOgG9lFJnaq1rzTQ/Qah7PAE8j4k5IdRr2raFJ9MhBBgOPGJLF2o9Dz744L7XXnutRWZmZq0zvu7bt2/Wxo0b969ZsyYiPT09dO3atRFBQUE6Li6u4Morrzw0fvz4fWeeeWa+r47njcJzCaZ3Z60t7XogHmMkMAO4ErgHuBuZHiIIfqSZvwUQagrJycaGZ2QuTMHMtw0PN+lCjWf37t3rPOWHh4frjIyMtZ7K+JNffvllo7u8nj17HuvZs2e1dTV60wUWhwkeamcgZqr6bVrrr7XW/8T44LnMR/IJgiAIlWHYMJgzB+LjYacy6zlzSrx0C0J9wRuFpzHWUJaN84GNWuvttrTfgDaVFUwQBN+Rs/97fn/zKrIz6o+/FQGy9maR0juF7L5XQVoaFBebtSg7Qj3EG4XnGLZ+civURBzwvVO5AqDWWYsLQt2kGLiOiJhenHXzx6x/73l/CyRUGxvI+O029q3fyIppMlNPELxReP7AGCQ7lJ5hmOGsb5zKtQEqHfNCEITKkxz2OKvnlI5Et+rxClPVoySHif1GXSY5LJl1864lccD73LP1GfIOz2Wqmir3XajXeKPwvAWEA6uUUgswHs2ygIWOAkqpUOBsYIMPZRQEoYLcs+0eMtffRmG+8cvTtudO+l32Jfc2e8c4pBPqJP/c0Z/O1/8PgNBG+fy1pxldhnXh3u33+lkyQfAf3ig8czBKT1tgMJAHjNZa/2UrcyVGKZL+U0GoAUS1jKL4eGtWz0kqSes8fT2RuzaYmTui9NRJImJmoQJM6MMtSzqw87tW9SZAqCC4o9wKj9a6WGs9EkgAzgHitNbznYptAq4G3vSVgIIgVI6czByynotFHzP7DZP+Mn9ZcnPF226dZB3wfyV7jdo/R9KdSWKwLtR7vI6lpbXegfHk4Crvd+D3ygolCILvGLpgKATcAC8C91uJ0zCD0TvE227dY7JtexDNOlzGwNl+E0YQagwVdkWtlGqplOpuLS19KZQgCD6mbVt4EmN1B9AFuA7xtlvn+An42LY/3V+CCEKNw2uFRyl1m1JqI7AL+NladimlNiilbvW1gIIg+IDkZMgNh+dsadMUzJjmN5EEX6OBh2z7NwBn+kkWQah5eKXwKKVSMGHoEq2kPcBea/v/27vzuKrq9IHjnweQHXdD3EBTs9JGQ50W08rGSltsmsYmrWyxddQsza2xMUWtzDYbq2nBJqr5TTottllpZtmokI1LY7miIiDmEiAiXL6/P84BEbnIci/33sPzfr3u69yzfXnuia4P37Ur8JKIvO6x6JRSnlE62+7/tYND9rGuBm4qqfI2FUi+BJbb74OB6T6MRSn/U+2ER0T+BNwC5AD3AZHGmPbGmHZYI7PuBfYBt4jIjd4IVilVB8OHw/rd0HSGfWAQVtuWCnwVa3du5/jfpUopqFkNzyisWZQvNca8aIwpW8HUGFNojHkJGAgUAXd5NkyllOeMxZo54jMg8RTXqsBggLux5n0NA/7i23CU8kM1SXh6AiuMMT+6u8A+95V9rVLKL8UA/X0dhPKUlBRI6ARBo+AMgc8noMsZKnWymiQ8kcAv1bjuABBRu3CUUvWtbIFJnacl8KSkkDtqHMnpl5BnouDnXTB0nk4o6SBt27btISKJIpL4zjvvNHF3XZcuXc4WkcQlS5bE1Gd8FeXk5ASPHTu2TdeuXc+KiorqFRkZ2Ss+Pr770KFDO6alpYVXdo/L5WL27NmtunfvfmZkZGSvmJiYnomJiWe89NJLzT0ZW00Sngygr4iIuwvsc32wOjMrpQLAN7O/IO7cf/LdvPdPfbHyL1On8nVBX3bRgRUMsI7phJKONW3atLYul8vXYbi1cuXKyG7dunV/7rnn4vLy8oL79ev360UXXfRrZGRkyYcffth89erVkRXvKS4uZtCgQadPmTKlQ3p6eli/fv1+TUxMzNu4cWPUPffc03HkyJEeq66sycSDn2E1Ej8pIhONMSc8dREJAuYAnbBGciml/FhSRBIdB25i8Asf0zT+MKufO8B02UpIeAhTC/QfTH+XFJFEl8G/paBjBOarIFLpQyp9CKGIqbtm+To85WHh4eElW7ZsiXjxxReb33///Qd8HU9FO3fubHT11Vd3zcvLC54zZ86uCRMm5AQFBZ1wvqio6KQKkxkzZsQuW7as6emnn350+fLlP7Vv374YYMOGDWGXXHJJt4ULF5522WWX5Y4YMeJQxXtrqiY1PHOAw8A4YIuIzBCR20XkNhGZgbWsxENYg17n1DUwpZR3jdk+hoSL42kafxiA3vek8dsHWukCkwFizI6RXPPi+9y6fCF/+jCFJrEH6MF6xvKsTijpQLfffvs+gNmzZ7c9evSo25YWXxk9enS7w4cPB48ePTpz4sSJJyQ7AAkJCUVdunQ5Vv5YcXEx8+fPbw3w/PPPp5cmOwA9evQofPTRR/cAPP744x6Z3Lgma2ntAq7EatpKwBoD+XfgFft9J6zJCAcbY3Z7IjillPfExMVwYNsF7PrGqjEODnURlphETFwMIkLr1q19HKGqSkzrBYS3sgbLxvbIJv9QNGEUEh1ZYk00qRxl2LBhB3v06JGfkZEROnfu3Fa+jqe8Xbt2hXzyySfNQkNDzdSpU7Ore9+XX34ZfeDAgZDY2NiiK6+88qROhCNHjjwYEhJiNm7cGLljx45GdY2zRhMPGmNWY03ucAvwGlYz11L7/S1AV/sapVQAyM8+wnMT25btD7hpL+fYk/NmZ1f7e0vVuwxgXtmeebIpPQt/IC+ilTXB5PDhvgtNeU1SUlIGwNNPPx13+PDhWi8N5WmffPJJY5fLJT169Mhv2bKla9GiRY3vvvvudjfddFOHSZMmtV67dm2lnZVTU1MjAc4555z8ys7HxMSUdO7c+ShAZf1/aqo2i4cWAm/aL6VUABu2eBg3yo30/wCuuQaCgmDOHBg82NeRqapNAwrs971oOj+VIfP95t8/5SVXX3117oUXXvjrt99+2/ixxx6LfeqppzJPfZd7S5Ysibn66qu71vS+cePGZc6bN69scNKGDRsiANq0aXOsX79+Xb799tvG5a9/4okn2o4YMSLn9ddf3xUcHFx2fMeOHaEA7du3P6Gpq7w2bdoUbt68OWL79u2hNY2zohonPEop55kyBa66ykp4rrwSfvc7+PxzX0elKrcBSC63/yR1WAc6ADzYBp6uZh+OG/fD2+knHvtTPLzTsnr3j8uEeRVGGV/aGZa7HQ5+oifTYfz+6l1bO3PmzMno379/45deeqn1Qw89lNOmTZviU99VubZt2xb9/ve/r850Myfo1avXkfL7Bw4cCAb4+OOPm4kIU6dO3TNy5MgDUVFRZtGiRU2mTJnS/h//+Eer0047rWju3LllSVp+fn4wQFRUlNuhZ1FRUSUAubm5we6uqa4aJzwiEgpcD1wMtMOa4nMv1oSDi8rPwKyUCgybNsFrr8Gd9vK/S56CkJ5AQoLVH0SbSPzIJKB0DbQrsCa4Vw1Fv379jgwePPjgRx991OyRRx6Je+2112rdZ7ZXr15HFy1atLOuMRljBMDlcsnDDz+cMXPmzLL28D//+c+/REdHu2677bbTFyxY0HratGnZjRs3LrHvA6CK2W48qqaLh16ANRrrTaylJq4EBgN3Av8AfhaRfp4OUinlfX/5Cxy1uw2G9oCgO4D0dLjrLp3Izm8sAz623wvwuA9jUb4yZ86cjODgYJOSktLq559/rnNTT11FR0eX1dCMGTPmpBqukSNHHmratGnxkSNHgr766quoivfl5eW5rb3Jz88PAoiJianzBETVruERkbOxOihHAtuBt4Gd9ukEYBjQGfhURH5rjNlU1+CUUt4XGxtLdnY2WVlQMAfCZ9onZgDvALn2RHZay+NjJcCEcvsjgXN8E0q9mrf35Gammng7/eRmrppYtrX293pH9+7dC4cNG7b/rbfeajVp0qQ2ixcv3lmbctatWxc+c+bMGg/HHDp06KGbb765bF6chISEY2DNFdS2bdtKm9jatWt37NChQyF79+5tVPG+3bt3u03aMjMzQwE6duzotp9PddWkSesxrGRnNvAXY0xJ+ZMi8qh9zRRgOvCHuganlPK+rKys4ztRYk0v2hiYC5Q2UO/aVf+BqQreBL6334djfd2qhmrWrFmZixcvbvH++++3WLt2bdap7zhZRkZGo8WLF7eo6X3x8fHHyic8ffv2zQcoLCwMysvLk+joaFPxnoMHD4bAiTU1ffr0OQKwfv36qIrXA+Tm5gZt2bIlAuC88847Utk1NVGTJq0BwE/GmKkVkx0AY0yJMeYR4Ces/j1KqUDTKh5uADpD7txoko+NJI9oncjOD+Rl92bHsj723oNYXShVQxUfH190xx137CspKWHixIm1+mW46qqrco0xaTV9lR+hBXDppZfmt2rVqsgYw5IlSxpX/DkbN24MK62pufDCC8sSl4EDB+Y1b968ODs7u9Enn3wSXfG+5OTkZsXFxdK9e/cjHTt2LKrNZyyvJglPBMf/vKjK91h/fiilAk1SEmyIhP3wNQOsNZqCB+pEdn5gxfQd/ON3V7HqqTnAZF+Ho/zA9OnTs5o0aeJavnx5kz179visL09wcDBjx47NApg8eXK7zZs3l8WSk5MTfMcdd8SXlJQwaNCgQwkJCWWJS0hICPfff38WwOjRo+MzMjLKWp02bNgQ9thjj7UFmDhxYp2G35f9vBpc+xNQnaGBccCW2oWjlPKp4cNJum0bxRyvkU519SJ1xFZC7kzSNbZ8ICkiieKjx7tFfD7+KJ+Pf0rXPFO0aNHCNXr06MyZM2e2O3r0qE/nJpg0adK+VatWRX/88cfNzj333LN79uyZHx4eXrJu3bqoQ4cOhZx++ulHk5OTT+pLNW3atOxvvvkmZvny5U26devW/fzzz88tLi6WVatWNS4sLJRbb711nyfW0YKa1fC8CPQXkQvdXWCf6w+8VNfAlFK+MSZ9HN1v6k5IpPX3UFzvX7jp41TG7hjt48gapjHbx5zw3yMkMoQew3vommcKgMmTJ++LjY2tc3NPXQUHB/Phhx9unzdvXnqXLl0K1q9fH7Vq1arGrVq1KnrwwQf3pqWl/S8uLu6kDs0hISF8/vnnW5OSknZ16NChcOXKlY3XrFkTc/bZZ+cvWLBgR3JysseWqqp2DY8x5mUR6YY1CutvQAqwwz6dAAwH7gOeNcboaulKBaiYuBjCGofhOuriyvmf0fue/xAUbIB3gdt9HV4D8zkxcV8QdVoirqMuQsJDcB11EdY4jOjWJ3V5UA6UkZGxoarzkZGRJisra319xVOVoKAgxo0bt3/cuHE1mnwxODiYKVOm5EyZMiXHW7FBzYallx8DP95+VeYBEXmgwjFjjNFZnZUKEPnZ+STek8hZf/iFoODv7KMTgaFAcx9G1oC8tRD6jIIuRQyYGEFjcwedbptK2stp5GWetM6iUuoUapKE1GUqRL9byl4p5d6wxcPsdxcD7wG7gP3AI8DffBRVA5KSAj+MgpusloqIyAIu+OBV6HMeQ17Q+ZCUqo1q9+ExxgTV5eXND6GU8pYo4Jly+y8CaT6KpQGZNwmmluuWMQPYUWBNAKmUqhVNRJRSpzAUa80msJbOu4/jazkpr3hgDzS13/8MPGu/1wkglao1TXiUUqcgwHNA6dQaa4DXfBeO430BN5fbHQOUVvboBJBK1VqdEh4ReVJEtnkqGKWUv+oCPFxufxLwi49icbIC4N7ju28Dn9nvIyN1Akil6qCuNTwtsYakK6UcbzIQb7//hZ8+uJ68LB0t5EmFuY8C9lqVxyJhXjsQgfh4ePllXcBVqTrQJi2lVDVFcrwzCZx++Tesfm6R78JxnB9pFPH08d3QebB2N5SUwM6dTk12jDEnrTOpVK2c6ndJEx6lVLUlRWxg8/tnkLG2DX/vfRffzN7JdJlOUqiu3F0XSRFJrH72doJCrIlod33bnulBe0mKcHYTlojsP3r0qM/WgFLOcuzYsUYictDdeU14lFLVNmb7WH5+YQQLz7+VfRtjCeEYPVjP2JD51twxqlbGbB/DnrUP8dH915KXHcWnDwylx02/cfzyES6X682cnJwYreVRnnDo0KGYkpKST9ydr2vC8wvWjGRKqQYgJi6GoO82UexqRAhFuAghjEKiC3J0jpg6iImLISwmgrQXz2X+GePJ+r5lg1g+oqSkZOHBgwfX79y5s/nhw4eji4uLgzX5UTVhjKGwsLBRdnZ28+zs7EMul+tld9fWabkHY0xVS0wopRwoP6+ERFJJJI00EskjGjoAmScthKxqoHQ5j8S7EhvM8hGJiYmH0tLSbjhw4MCNubm5g4FzjDGRvo5LBRYROVhSUvKOy+V6OTExcafb66qbTYtIN2PMZk8FGAh69+5tUlNTfR2GUv4lIQHS7eRGsOYhnAO80gQeOOS7uAJSKtADCPN1IB4jImnGmN6+jkOpimrSpLVJRL4QketERPv+KNVQJSVZc8IA/BGYD0QDY/KAKhd2VidIBy4F+gL/9XEsSjlfTRKXfVj/d74LpIvIIyIS652wlFJ+a/hwa06Y+Hj4F5Bq104EuYBbgUIfBhcoSoDbgFxgPTAcXa5DKe+qScLTHrgJ+BZoC0wHdonI2yLSzxvBKaX81PDh1twwLgO9f+B4k8w6juVNIHlAsk5K6Ebu/IWsfugiYLl1oESAV9BBs0p5V01WSy82xrxjjOmP1ej8MtafcsOAFSKyXkTuFpEoL8WqlPJL3YDHy/ZCo58nJGIZKx5b4buQ/FVKCmkL3uDcmWuOH5sbDCm6Qo9S3lbtTsuV3iwSDYzEWvzlTKyllHOBhcCCQO/krJ2Wlaouw9ZPu9H5ip8ByMuKYsE593IkJ5qQ8BCmFuiQ9aSIJEqKC7n921dp23cvAFk/xPJ639uY3OZtq8bMAbTTsvJXdUp4ygoREWAWMLHcYQN8Akwyxmys8w/xAU14lKq+vOzthIQlEt7UGqm19dOurH9zFoPmXu74+WSqIzczl8yURLqO3wKA61gQy3tfwnkbVhMt+dYSEg6gCY/yV3VdLb2piDwI/MTxpZR/Al4AcoDBQKqIXF6nKJVSfi86thM/vDGubL/zFT9zxjVLNdmxxcR9UZbsACx/5BIKN4QTTR506ODDyJRqGGqV8IhIbxF5DcgAngQ6AR8DVxhjzjTGjMbq5PwQ1uSGMz0Ur1LKj6V/dQbbv7iubP+MaxZi/e3T0G3Dav23HP0wlMK5oeQRZQ3xT3L2mllK+YNqJzwiEiYiI0VkDbAa6//eY8AzQFdjzNXGmKWl1xtjiowxTwOfAWd7NmyllD8atngYnS57BzgXaE/I1xMgoQ8EBVkTFjbY9baeBX613ua1IvyR0xjCpwyLX20N8XfmSuhK+ZWaLC2RATTDmlv1R6zpxt4wxhw5xX2ZOGkaUaXUKYQCi+BfS2HkODhif0Wkp8Ndd1nvG8g/8K1btyY7O5ugIHj0UZgwAS66OIc92bFkOaTPjlKBoiZLS7iAD4DnjTHLqv0DRLoCccaYgBujqp2WlaqD8ktQlBcf75gRSadijec4Li4OMjOt905dJFM7LSt/VZM+PJ2MMdfVJNkBMMb8HIjJjlKqjnbtOmE3r3Mky669hLz0X3wUUP3KzcxlJCOJ5nin7dJkRylV/2oy8aAuhayUqr7yI48ug7A1x+j/ztf8MOA838VUb7aRs+kWEkLaMoABvg5GKYXOZa6U8hZ7kdFZQZPJejKWRs2KCQl38Zu3/sNTbR4iKcKZI5PmtZvCLz/3pdNl7zH8w3e4MPoc/spfmYpOvqiUL9Wk07JSSlWf3TF59MSZfHv9b+i/ZiWRLQqIaZPHHav+TUjE1z4O0MNSUuCxyYz9vwyCu1odkuMHpNOkWyZfpv7KUpaeogCllDdpDY9SynuGDydmz/8oHjSaRTf+kZJi6yunacIOomP/CDhkgdGUFLhnFMzaTfAFVrJjSmDxiGvJTu1AIYXklfussbGxvopUqQZLEx6llNflZ+fTvOsN5O59qtzR74BrgAIfReVBU6fAjAK4/vihHx88kwHfbaPvfX25+bqbMcaUvbKysnwXq1INlEfW0nIqHZaulDc8D4wptz8EWIw1f08gMvB0EIwrd+hp4EFAxDFrZFWXDktX/kpreJRS9Ww0MLvc/kcUFdzIwktfJS8rsJq4cjMPs/n9gScmO+9iLaoDukaWUn5EEx6llA9MgnKjlhpF/Jvg4K9YEXdjAC1BUczh9N/T7drlxw8tAm4CDLpGllJ+RhMepZSPzGDNC+cDsDLpIrZ90ZlU+jA9/TaSRmz266QnKSKJJ1pMJbzpf8uOrU/pwawbp0CxWLNJ6xpZSvkV7cNTBe3Do5R35WYeZvO0wSx9dQDFJowQjnEmmxnEUqLjW/jtEhS5mbksHb+UjDWrufmzv7NzxensWDaRQU9eSXTr6FMX4GDah0f5K52HRynlMzFxTch+pRkuGhFCES5CCKOQ6Jg8OM1/+/PExMUQ1jiMQ9ujSR5wL7mZoSTeFdngkx2l/Jk2aSmlfCo/ohWJpHIHr5BIKvnBEfBPYCXAa+Rm/krygGTfdWhOSSG33ZmsvPUiCmecVtbUlp+dT+I9ifxpyRgS7+4TcB2ulWpotEmrCtqkpVQ9SEmBu+6CI0es/ceBh4+fzt7Qh5Qr+3PGNZcw5G9D6j+20aPY9XhLOozajXGBXBUGI17V/jluaJOW8leOquERkSgRGS4iz4jItyJyRESMiCzxdWxKKTeGD7c6+MbHW/PWfNgGDrcpOx3bYy33bniBY7mvMl3+Wq9rcL356qdkr4ihw6jdAEgw7JgQR9LN/6u3GJRSnuGoGh4R6Qmsq+TUR8aYq2pantbwKOUr+RzLH09o1IsnHM385iwaTzhK1Ood1hw3SUleqmnZCkwA3jvh6MaUs9l29+kMzF9GtMn1ws8NfFrDo/yVo2p4gFzgNeA+4LfAPb4NRylVO1GERi1g1bxZHNjWrOxoXL8fiVq5Hd4w5MfsI/mWZeS9sNAjPzE3M5eUwX/jWN4DwFmUT3aO5Tfi0/suZ/GI3xOS77JGkCmlAoqjEh5jzDZjzB3GmAXGmDVAoa9jUkrV3u5vOrHmhZfJ33/b8YMhwAgI/bqIvaGxrJj0Se0KT0mxJjkMCoKEBPZ/N4Qb/vUAodHPAkVll+14I4Gvu15EzwU/kEgaeUGNdUJBpQKQoxIepZSzDFs8jCvm/YGolq9Bf+DL4+dWv3geRUfDSM07k+ky3e7bsxbYRe78hSSH30uexJwwc3NuZi7JA14n75UXrI7S6ekkmSlMT7+NnIxCQqOOJzq7v+sArKZj8Ewua7SN1rKPIfGbGPbGEO2wrFQAclQfnopEZCTwOtqHR6nAl5AA6enk94ng4PjmvDvmeg5nNyeYY6xjMwszFxLduh/wX47sjODgvmaE5RbS8tdfoCAYzv8th4JyiGieTsmhECI6WKPCcolmKYM43Lsxt69NZt+Pp7Fz2XDO+sN0olvH+PQjByLtw6P8lU48qJQKDElJ5I/hflVOAAAMpklEQVQYQdTaApYP68mvNCWYIooJoZBColsXANZSD5EJBUQmFJS72QWsomnpbswxZkVNxuQHMZUkwihkT2p7/n7OnWRuakfi3b012VHKYbRJqwIRuUtEUkUkNScnx9fhKKVKDR/OKGAnkEcUXUllG6+wllSiiAIOUFx4Ca6CU3+tFRwMp3e7VMbyLAD5RJFIGlfvTyXxnt46iaBSDuQ3TVoi8gRwTS1uHWiMyXBT5ki0SUspxxARt+dKv8s+bvlHdp7WkojGBTSKKeLMmP+R2Ph7/hvVhx9+7M7B7bH8ujuMxKAfGOJ6/3gBkZG64KcHaJOW8lf+1KTVBjijFvc18nQgSqnAlduxL/HrVpLoWk0aiWylM4mRm9l81h9p2fdMLn8mkbSX08hbEw05P8CuXV6e00cp5Q/8pobHG7SGRylnad26NdnZ2Scdj42NJSsr6/iBlBSYOlWTGR/QGh7lr/yphkcppap0QlJTleHDNcFRSp1AOy0rpZRSyvE04VFKKaWU4zmuSUtE/g3E2but7O2FIvKfcpfNMMZ8VL+RKaWUUspXHJfwAL2A+ArHmmItJlqqFUoppZRqMByX8BhjEnwdg1JKKaX8i6OHpdeViOQA6bW8vSWw34PhqOrTZ+87+ux9x1+efbwxRmvRld/RhMdLRCRV56LwDX32vqPP3nf02StVNR2lpZRSSinH04RHKaWUUo6nCY/3vOzrABowffa+o8/ed/TZK1UF7cOjlFJKKcfTGh6llFJKOZ4mPEoppZRyPE14qkFEbhKRlSJyWETyRCRVRO4XkVo9P0+X52SeeFYi0khEBorIUyLyHxHJFJFjIpIhIu+KyMVe/AgBy5u/pyIyS0SM/RrviXidxAvfOREi8rCIrBWRQyJyRER2iMi/RORCT8evlD/SPjynICIvAPcBR4EvgSJgIBAD/Bu4wRjj8lV5TuapZyUilwGf27tZQBqQD5wFdLePzzDGTPPoBwhg3vw9FZE+wHdYf3AJMMEYM9cTcTuBF75zOgJLgc7APuA/QCGQAPQEHjPGzPTgR1DKPxlj9OXmBVwPGCAT6FLueCzwo31urK/Kc/LLk88KuBR4F7ioknPDgGK7vEt8/bn94eXN31MgDNgEZGD9422A8b7+zP7y8sJ3ThSw1b7vMaBRhfMtgK6+/tz60ld9vHwegD+/gFT7i+KWSs4NKPfFFOSL8pz8qs9nBbxil/eqrz+3P7y8+eyBx+37rwaSNeHx7rMHZtv3LPT1Z9OXvnz90j4jbohIOyAROAb8q+J5Y8wKrL9SWwPn1Xd5TuaDZ7XO3rbzQFkBzZvPXkR+CzwEvGWM+bDu0TqLF75zQoFR9u4cz0WqVGDShMe9XvZ2kzGmwM01aytcW5/lOVl9P6su9jbTA2UFOq88exEJBxYCB4CxtQ/P0Tz97BOxmqx2G2P+JyIX2J3FXxKR6SJyfl0DViqQhPg6AD/W0d5WtVr6rgrX1md5TlZvz0pEWgMj7d1FdSnLIbz17JOAM4AbjTH+sKK3P/L0s+9hb7eISDJwa4Xz00RkEXBzFQmWUo6hNTzuRdvb/CquybO3MT4oz8nq5VmJSAjwJtAE+FKbWQAvPHsRuQB4AHjPGPPPOsTmdJ5+9s3tbX/gFmAu1kitZsC1WM1j1wMv1DhSpQKQJjzuib311Lh9T5fnZPX1rF7EGu67Gxjh5Z8VKDz67EUkAngd+BVrqLVyz9O/96Xf7yFYHfInGGO2GWMOGWM+AIbaP+tWEenkoZ+plN/ShMe9XHsbXcU1pedyq7jGW+U5mdeflYg8C9yBNS/PQGNMVm3KcSBPP/tZQFfgQWOM9pGqmre+cwD+XvGkMSYVa06qIODiapSnVEDTPjzu7bS38VVc077CtfVZnpPttLdeeVYi8hQwBsjBSna21LQMB9tpbz317K8DSrBqESr2Ielmb+8VkauArcaYO6sZpxPttLee/s4B2OHmmh1Ab6yRX0o5miY87pUOVT5bRCLcdOrrU+Ha+izPybz2rETkCeBB4Bfgd8aYH2sfpiN549kHYc0h404n+9W0muU5laef/ffl3rfASvAramlv8yo5p5SjaJOWG8aY3VhfGKHADRXPi8gArHlbsrCmya/X8pzMW89KROYAE4CDWMnOfz0SsIN44fc+wRgjlb2whqmDtbSEGGN6eu6TBB4vPPsMYLW9O7CS8poB59q7qbWLWqnAoQlP1Wbb28dFpHPpQRE5DfibvTvHGFNS7txsEdksIrM5WY3La8A8+uxFZAYwETiElew09Fq0qnj6915Vn6effZK9nSYiPcvdEw4swBqhmEYD/yNLNQzapFUFY8y7IrIAuBfYICJfcHwhv8bAe8D8CrfFYc03Eueh8hokTz57EbkGeMTe3QqMFhEqsdkY0+BnpPX0772qPi9853woInOB8cBqEVmN1ZzbF2iDNTT9T8YYHT2qHE8TnlMwxtwnIt8A92P1QwgGNgOvAQtqWhvj6fKczIPPqnm5973tV2VWoFPwA/p76kte+M6ZICKrgNFYMzRHYk1gOA+rtqiyvj1KOY5oYq+UUkopp9M+PEoppZRyPE14lFJKKeV4mvAopZRSyvE04VFKKaWU42nCo5RSSinH04RHKaWUUo6nCY9SSimlHE8THtXgiYipxSvZvvdie/8r336KuhORifZnuaIOZZwrIiX27L5KKeU3dKZlpY4vYllea+ByIB94t5Lz33g1onomInHAVOBrY8yntS3HGPO9iCwGxojIS8aYLR4LUiml6kBnWlaqEiJyMbAcSDfGJFRxXSTQAThijNlVP9F5noi8DIwCBhpjltWxrB7AemCRMeYPnohPKaXqShMepSpR3YTHCUSkBbAH2At09sRCkiKyFmvdpk6BnAgqpZxD+/AoVQfu+vCISIJ9fKeIBInIgyKySUQKRGSPiMyza4cQkWYi8ox9baGIbBGRB6v4mSIiN4rIUhHZb9+zS0T+LiIJtfgYtwPhwBuVJTsi0lREZtnxHyn3Gb4SkcluylyItejl3bWIRymlPE4THqW87y3gMWAHsBSIAsYBi0SkObAaGAasxeoblAA8JSJTKhYkIo2w+hS9DfQDfgQ+wOprdCfwvYi4Ww3enaH29otKfl4k8C0wGWhpX/MesBU4C3jUTZmlZV1bw1iUUsortNOyUt4VDxwFuhpj9gKISHtgHXAFsAL4L3CzMeaofX4IsASYJCLPGGOOlCtvBvB74GtguDFmT+kJEfkz8Dzwjoh0M8YUnyo4O6HpAxQBaZVc8gesxOYjYGj5MkUkGBjgpuifgIPA2SISa4zJPlUsSinlTVrDo5T3jSlNdgCMMbuBN+3deODe0mTHPv8RVqffGKCstsauDRoD5AE3lE927PvmYyUmpwNXVjO2s4FGwI7yMZQTa2+/qJhAGWNc7jo4201j/7N3e1YzFqWU8hpNeJTyriKgsqRgq71NNcbsr+R86XDuNuWOXQJEACuMMfvc/LwV9vb8asZ3mr39xc35NfZ2ooiMEJGm1SwX4IC9ja3yKqWUqgfapKWUd2W5aVrKs7d7KjlX/nx4uWOd7O0QETnVSKpW1Yyvib39tbKTxpgVIvIEMB74B2BEZDNWX6NFxpjPqii7tMyaJElKKeUVmvAo5V0ldTxfXrC9/Qn4zymuXV3NMg/Z28buLjDGTBSRF7E6IPcDLsSas2eUiCwFhrhJ6krLPFjNWJRSyms04VEqcOy2txuMMSM9VGZp01iLqi4yxuwAnrFfiEg/rJFig7CGtb9cyW2lZbprflNKqXqjfXiUChxfYPUJuqyGfWmqsgkoBDqKSER1bzLGfAMk27u/qXheRAToZu+uq2OMSilVZ5rwKBUg7KHdL2D1iflARLpVvMaexPBOEalWR2FjTAFW81cjILGS8q4Tkf4iElTheARwmb2bXknR3YBmwKYqOlgrpVS90SYtpQLLw1gjt/4IbBSRH7AmNAwH2gNnAqH2trpz37wH9MdKYCouijoAGAvkiMg6IAero/MFQHNgM/BSJWWWJkPvVzMGpZTyKq3hUSqAGGOKjDHDsDoQL8FKfq7FSkBCsGZ1vg7YVoNik4EC4Ba7KariuceBn4HuwA1AX6xh9eOAvsaYw5WUeSvgovJkSCml6p0uHqqUwh6FdTe6WrpSyqE04VFKISKtsWpx1hlj3C0XUd2y3gWuAc42xmw51fVKKVUftElLKYUxJguYCfQXkStqW46InIu11tfzmuwopfyJ1vAopZRSyvG0hkcppZRSjqcJj1JKKaUcTxMepZRSSjmeJjxKKaWUcjxNeJRSSinleJrwKKWUUsrx/h/lN6KbiLvVpAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N = np.array([6,30,45,60])\n",
"\n",
"for i in range(len(N)):\n",
" dx = L/(N[i]+1)\n",
" k = T_g/(dx**2*mu_g)\n",
" A = k*(np.diag(np.ones(N[i])*2)\\\n",
" -np.diag(np.ones(N[i]-1),-1)\\\n",
" -np.diag(np.ones(N[i]-1),1))\n",
" e,v = linalg.eig(A)\n",
" isort = np.argsort(e.real)\n",
" e = e.real[isort]\n",
" v = v.real[:,isort]\n",
" x = np.linspace(0,L,N[i]+2)\n",
" v = np.pad(v,((1,1),(0,0)))\n",
" print('Natural frequencies of {}-element string (Hz)'.format(N[i]))\n",
" print('f1:', (e[0]**0.5/(2*np.pi)))\n",
" print('f2:', (e[1]**0.5/(2*np.pi)))\n",
" print('f3:', (e[2]**0.5/(2*np.pi)))\n",
" \n",
" colors = ['black', 'red', 'purple', 'yellow']\n",
" shapes = ['s', 'o', '*', '--']\n",
" plt.figure(1);\n",
" plt.xlabel('Time (s)')\n",
" plt.ylabel('y-position (m)')\n",
" plt.title('Convergence of First Mode')\n",
" if N[i] == 45:\n",
" plt.plot(x,v[:,0]/np.max(v[:,0]),shapes[i] ,color = colors[i] , label = 'N ='+ str(N[i]))\n",
" else:\n",
" plt.plot(x,-v[:,0]/np.max(-v[:,0]),shapes[i] ,color = colors[i] , label = 'N ='+ str(N[i]))\n",
" plt.legend(bbox_to_anchor=(1,0.5),loc='center left');\n",
" \n",
" plt.figure(2);\n",
" plt.xlabel('Time (s)')\n",
" plt.ylabel('y-position (m)')\n",
" plt.title('Convergence of Second Mode')\n",
" if N[i] == 45:\n",
" plt.plot(x,-v[:,1]/np.max(v[:,1]),shapes[i] ,color = colors[i] , label = 'N ='+ str(N[i]))\n",
" else:\n",
" plt.plot(x,v[:,1]/np.max(v[:,1]),shapes[i] ,color = colors[i] , label = 'N ='+ str(N[i]))\n",
" plt.legend(bbox_to_anchor=(1,0.5),loc='center left');\n",
" \n",
" plt.figure(3);\n",
" plt.xlabel('Time (s)')\n",
" plt.ylabel('y-position (m)')\n",
" plt.title('Convergence of Third Mode')\n",
" if N[i] == 45 or N[i] == 6:\n",
" plt.plot(x,-v[:,2]/np.max(-v[:,2]),shapes[i] ,color = colors[i] , label = 'N ='+ str(N[i]))\n",
" else:\n",
" plt.plot(x, v[:,2]/np.max(v[:,2]),shapes[i] ,color = colors[i] , label = 'N =' + str(N[i]))\n",
" plt.legend(bbox_to_anchor=(1,0.5),loc='center left');"
]
},
{
"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": 7,
"metadata": {},
"outputs": [],
"source": [
"N = 60\n",
"dx = L/(N+1)\n",
"x = np.linspace(0,L,N)\n",
"\n",
"k_e = T_e/(dx**2*mu_e)\n",
"k_b = T_b/(dx**2*mu_b)\n",
"k_d = T_d/(dx**2*mu_d)\n",
"k_a = T_a/(dx**2*mu_a)\n",
"k_E = T_E/(dx**2*mu_E)\n",
"\n",
"A_e = k_e*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"e_e,v_e = linalg.eig(A_e)\n",
"isort_e = np.argsort(e_e.real)\n",
"e_e = e_e.real[isort_e]\n",
"v_e = v_e.real[:,isort_e]\n",
"\n",
"A_b = k_b*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"e_b,v_b = linalg.eig(A_b)\n",
"isort_b = np.argsort(e_b.real)\n",
"e_b = e_b.real[isort_b]\n",
"v_b = v_b.real[:,isort_b]\n",
"\n",
"A_d = k_d*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"e_d,v_d = linalg.eig(A_d)\n",
"isort_d = np.argsort(e_d.real)\n",
"e_d = e_d.real[isort_d]\n",
"v_d = v_d.real[:,isort_d]\n",
"\n",
"A_a = k_a*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"e_a,v_a = linalg.eig(A_a)\n",
"isort_a = np.argsort(e_a.real)\n",
"e_a = e_a.real[isort_a]\n",
"v_a = v_a.real[:,isort_a]\n",
"\n",
"A_E = k_E*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"e_E,v_E = linalg.eig(A_E)\n",
"isort_E = np.argsort(e_E.real)\n",
"e_E = e_E.real[isort_E]\n",
"v_E = v_E.real[:,isort_E]"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 60-element top E - string (Hz)\n",
"f1: 329.66287320010764\n",
"f2: 659.1071584966114\n",
"f3: 988.114412923938\n",
"Natural frequencies of 60-element B string (Hz)\n",
"f1: 247.0748304582595\n",
"f2: 493.98583425108916\n",
"f3: 740.5692933408752\n",
"Natural frequencies of 60-element D string (Hz)\n",
"f1: 146.89843350538408\n",
"f2: 293.69946380512823\n",
"f3: 440.30575227830343\n",
"Natural frequencies of 60-element A string (Hz)\n",
"f1: 110.01731758315341\n",
"f2: 219.96168653677248\n",
"f3: 329.76020660099965\n",
"Natural frequencies of 60-element bottom E string (Hz)\n",
"f1: 82.44585723617439\n",
"f2: 164.8370475123807\n",
"f3: 247.11894011639782\n"
]
}
],
"source": [
"print('Natural frequencies of {}-element top E - string (Hz)'.format(N))\n",
"f_e = np.array([e_e[0],e_e[1],e_e[2]])**0.5/ (2*np.pi)\n",
"print('f1:', f_e[0])\n",
"print('f2:', f_e[1])\n",
"print('f3:', f_e[2])\n",
"\n",
"print('Natural frequencies of {}-element B string (Hz)'.format(N))\n",
"f_b = np.array([e_b[0],e_b[1],e_b[2]])**0.5/ (2*np.pi)\n",
"print('f1:', f_b[0])\n",
"print('f2:', f_b[1])\n",
"print('f3:', f_b[2])\n",
"\n",
"print('Natural frequencies of {}-element D string (Hz)'.format(N))\n",
"f_d = np.array([e_d[0],e_d[1],e_d[2]])**0.5/ (2*np.pi)\n",
"print('f1:', f_d[0])\n",
"print('f2:', f_d[1])\n",
"print('f3:', f_d[2])\n",
"\n",
"print('Natural frequencies of {}-element A string (Hz)'.format(N))\n",
"f_a = np.array([e_a[0],e_a[1],e_a[2]])**0.5/ (2*np.pi)\n",
"print('f1:', f_a[0])\n",
"print('f2:', f_a[1])\n",
"print('f3:', f_a[2])\n",
"\n",
"print('Natural frequencies of {}-element bottom E string (Hz)'.format(N))\n",
"f_E = np.array([e_E[0],e_E[1],e_E[2]])**0.5/ (2*np.pi)\n",
"print('f1:', f_E[0])\n",
"print('f2:', f_E[1])\n",
"print('f3:', f_E[2])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"c. Create an audio signal that has the 18 frequencies (6 strings $\\times$ 3 modes) in an array and display it using the `from IPython.display import Audio` library. \n",
"\n",
"_Hint: you don't need to solve the differential equations here. You can use the calculated frequencies to add sine-waves together:_ $\\sin(f_12\\pi t)+\\sin(f_22\\pi t)+...$"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"dx = L/(60+1)\n",
"k = T_g/(dx**2*mu_g)\n",
"A = k*(np.diag(np.ones(60)*2)\\\n",
" -np.diag(np.ones(60-1),-1)\\\n",
" -np.diag(np.ones(60-1),1))\n",
"e,v = linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e = e.real[isort]\n",
"\n",
"f_g = np.array([e[0],e[1],e[2]])**0.5/(2*np.pi)\n",
"frequencies = np.array([f_e[0],f_e[1],f_e[2],\n",
" f_b[0],f_b[1],f_b[2],\n",
" f_g[0],f_g[1],f_g[2],\n",
" f_d[0],f_d[1],f_d[2],\n",
" f_a[0],f_a[1],f_a[2],\n",
" f_E[0],f_E[1],f_E[2]])"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
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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": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"N = 10000\n",
"dt = 3/N\n",
"t = np.linspace(0,3,N)\n",
"data = np.sin(2*np.pi*frequencies[0]*t)\n",
"for i in range(18):\n",
" data += np.sin(2*np.pi*frequencies[i]*t)\n",
"r = int(1/dt)\n",
"Audio(data = data, rate = r)"
]
}
],
"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": 2
}