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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": 322,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy import linalg\n",
"from IPython.display import Audio"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### A."
]
},
{
"cell_type": "code",
"execution_count": 323,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A matrix:\n",
" [[ 7. -4. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
" [-4. 6. -4. 1. 0. 0. 0. 0. 0. 0.]\n",
" [ 1. -4. 6. -4. 1. 0. 0. 0. 0. 0.]\n",
" [ 0. 1. -4. 6. -4. 1. 0. 0. 0. 0.]\n",
" [ 0. 0. 1. -4. 6. -4. 1. 0. 0. 0.]\n",
" [ 0. 0. 0. 1. -4. 6. -4. 1. 0. 0.]\n",
" [ 0. 0. 0. 0. 1. -4. 6. -4. 1. 0.]\n",
" [ 0. 0. 0. 0. 0. 1. -4. 6. -4. 1.]\n",
" [ 0. 0. 0. 0. 0. 0. 1. -4. 5. -2.]\n",
" [ 0. 0. 0. 0. 0. 0. 0. 1. -2. 1.]]\n",
"\n",
"b vector:\n",
" [ 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00\n",
" 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00\n",
" -2.8310059e-05 2.8310059e-05]\n",
"\n",
"w vector:\n",
" [1.41550295e-05 5.66201180e-05 1.27395266e-04 2.26480472e-04\n",
" 3.53875738e-04 5.09581062e-04 6.93596446e-04 9.05921888e-04\n",
" 1.14655739e-03 1.41550295e-03]\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#assign given values to variables\n",
"de = 0.401e-3\n",
"db = 0.708e-3\n",
"dg = 1.140e-3\n",
"dd = 2.333e-3\n",
"da = 4.466e-3\n",
"de2 = 6.790e-3 #all densities in kg/m\n",
"\n",
"Te = 7.28*9.81\n",
"Tb = 7.22*9.81\n",
"Tg = 7.32*9.81\n",
"Td = 8.41*9.81\n",
"Ta = 9.03*9.81\n",
"Te2 = 7.71*9.81\n",
"Tt = Te + Tb + Tg + Td + Ta + Te2 #all tensions in N\n",
"\n",
"\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 = 10\n",
"h = L/N #m\n",
"M = Tt*.004\n",
"\n",
"#create our A matrix\n",
"A=np.diag(np.ones(N)*6)\\\n",
"+np.diag(np.ones(N-1)*-4,-1)\\\n",
"+np.diag(np.ones(N-1)*-4,1)\\\n",
"+np.diag(np.ones(N-2),-2)\\\n",
"+np.diag(np.ones(N-2),2)\n",
"A[0,0] += 1\n",
"A[-1,-1] -= 5\n",
"A[-2,-2] -= 1\n",
"A[-2,-1] += 2\n",
"A[-1,-2] += 2\n",
"print (\"A matrix:\\n\",A)\n",
"\n",
"#create our b vector\n",
"b = np.zeros(N)\n",
"b[-2]+= (-M*h**2)/(E*I)\n",
"b[-1]+= (M*h**2)/(E*I)\n",
"print (\"\\nb vector:\\n\",b)\n",
"\n",
"#solve for w\n",
"w = np.linalg.solve(A,b)\n",
"print (\"\\nw vector:\\n\",w)\n",
"\n",
"#plot our results\n",
"x=np.linspace(0,L,N+1)\n",
"plt.plot(x,(M*x**2)/(2*E*I),label='Analytical Solution')\n",
"plt.plot(x,np.block([0,w]),'o',label='Numerical Soilution')\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### B."
]
},
{
"cell_type": "code",
"execution_count": 324,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The solution converges to a value of 0.0014155029501438582, or about 1.4 mm.\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# repeating part A for a larger value of N:\n",
"N = 100\n",
"h = L/N\n",
"\n",
"A=np.diag(np.ones(N)*6)\\\n",
"+np.diag(np.ones(N-1)*-4,-1)\\\n",
"+np.diag(np.ones(N-1)*-4,1)\\\n",
"+np.diag(np.ones(N-2),-2)\\\n",
"+np.diag(np.ones(N-2),2)\n",
"A[0,0] += 1\n",
"A[-1,-1] -= 5\n",
"A[-2,-2] -= 1\n",
"A[-2,-1] += 2\n",
"A[-1,-2] += 2\n",
"\n",
"b = np.zeros(N)\n",
"b[-2]+= (-M*h**2)/(E*I)\n",
"b[-1]+= (M*h**2)/(E*I)\n",
"\n",
"w = np.linalg.solve(A,b)\n",
"\n",
"x=np.linspace(0,L,N+1)\n",
"plt.plot(x,np.block([0,w]),'o',label='Numerical Solution')\n",
"plt.plot(x,(M*x**2)/(2*E*I),label='Analytical Solution', lw = 2.5) #rearranged and adjusted line width for better visuals\n",
"plt.legend();\n",
"\n",
"print (\"The solution converges to a value of {}, or about 1.4 mm.\".format(w[-1]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2. Here we will record the first three frequencies of the 6-string guitar. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"a. Consider the G-string on the guitar, L=0.64 m, $\\mu=1.14~g/m,$ and T=71.81 N [1]. \n",
"\n",
"__Guitar string equation:__ $\\mu\\frac{\\partial^2 y}{\\partial t^2}=T\\frac{\\partial ^2 y}{\\partial x^2}$\n",
"\n",
"a. Calculate the first, second, and third natural frequencies using 6, 30, 45, and 60 nodes. Plot the mode shapes and determine the number of nodes needed to converge for the first three modes. "
]
},
{
"cell_type": "code",
"execution_count": 325,
"metadata": {},
"outputs": [],
"source": [
"def find_nat_freq(N, mu = 1.14e-3, T = 71.81, L = 0.64):\n",
" #mostly taken from notebook 3, \"Good_Vibrations\"\n",
" x = np.linspace(0,L,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[isort]\n",
" v = v[:,isort]\n",
" freq = e.real**0.5/2/np.pi\n",
" print('Natural frequencies of {}-element G string (Hz)'.format(N))\n",
" print('1st natural frequency =',freq[0],'\\n2nd natural frequency =',freq[1],'\\n3rd natural frequency =',freq[2],'\\n')\n",
" plt.plot(x,v[:,0])\n",
" plt.plot(x,v[:,1])\n",
" plt.plot(x,v[:,2]);"
]
},
{
"cell_type": "code",
"execution_count": 326,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 6-element G string (Hz)\n",
"1st natural frequency = 194.43708661091495 \n",
"2nd natural frequency = 379.1242858005909 \n",
"3rd natural frequency = 544.8006102150756 \n",
"\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"find_nat_freq(6)"
]
},
{
"cell_type": "code",
"execution_count": 327,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 30-element G string (Hz)\n",
"1st natural frequency = 195.994645953565 \n",
"2nd natural frequency = 391.48617646194407 \n",
"3rd natural frequency = 585.9727675700807 \n",
"\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"find_nat_freq(30)"
]
},
{
"cell_type": "code",
"execution_count": 328,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 45-element G string (Hz)\n",
"1st natural frequency = 196.04043698528574 \n",
"2nd natural frequency = 391.8522995904132 \n",
"3rd natural frequency = 587.2072799426845 \n",
"\n"
]
},
{
"data": {
"image/png": 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48wb1kHe2VfPOsDDinutOqLcjb60+xdDZe0lMN5ILogM/BP/usPZZyD4idxq9Ugq+4o6ullbx0rLjTPzhAFU1Gn54LJyfp3TS7SYbWiKKIrOPzMbLzosxIWPkjlNnj7R6BFdrV2Yfna3dFy4rhMUTwNoRxv0Gau2sngrxdmTx1Ai+ntieq2VVjJ6TwL9WnaS4olorr68zFmrpYrWDFyyZBCU5cifSG6XgK/5CFEXWHb9E/y92seZYNrN6B7H5hR70a+Vl0NM3t9p1cRcn8k/w9ENP67VXTUPZq+15ss2TJFxO4NCVQ9p50doaqX1wyWXpoqWWG4oJgsCQtk3Y9lJPnowKYPHBTAZ8vvuPDp0Gy74RTFgEFddg2aNQUyl3Ir1QCr7iD5eLypn6ayLPLj5KExdb1j4TxSsDQxu2gYaeaUQNs4/Oxs/Rj2HNh8kdp97GhYzD09aTr458hVaWTG95C9J2S83Qmt53C4oHZmdlyVtDWrFyZjdc7NRM/TWRWYuO/LGxvEHybiPtlpV1AOJeljZVMXFKwVeg0YgsSEin/+e72Zucz5uDW7Ly6a60auIkd7R625y+mQtXLzCz3cwG7SErFxtLG6Y/NJ1jecfYk72nYS92dCHs/xa6PA3t9HPhup2vC2ufieLlAS3YcjqHfp/vYllilnZ+eOlC2MPQ/WU48isc+kHuNDqn3Hhl5jILynj59+McTC8kqrk7Hz7cBr9Ghn+R805qNDU8vOZhLFWWrBi2wiDX3ddFdW01Q1cPxcnKiSVDljzY3+PSUfhxAPhFwCOrwEL/F9mTc6/z+soTHEq/Svdgdz4d3ZbGztrZi1irNBpYMhGSt0iN1vz038xOm5QbrxR/I4oiSw5mEvO/3Zy9XMyno9uy4MnORlvsQdpRKr04nWfaP2O0xR5AbaFmZruZnC08y9aMrfV/gaoyWDEV7Nyli5MyFHuA5p4OLJ0WyXvDw0hMv8qAL3az+mi24Y32VSoYOVfa1WvlVKnthIky3u8KxQPLLangqfmJvLbyJG2burDxhR6MDfc1mouyd1JVW8Wc43No3ag1fXz7yB2nwQYHDCbQOZBvjn1Draa2fk/e8m8oSIKHvwM7N90ErCOVSuDRSH82/KM7wZ4OPL/0GM8sOmp4N2zZOMHIeVB0ETa+JncanVEKvpnZeOoyA7/YzZ7kfN4a0oqFT3XBx8UA32bX0/ILy7lUeoln2z9r1D+4brJQWTCr3SxSi1KJTYut+xOTtsCheRAxCwJ76Spevfm727NseiSvDAxh85krDPhyNzvO58od6698O0vz+ccWShu4myCl4JuJ4opqXlx6jBm/HaGpqx2xz0bxZFTAvTezNhLlNeXMOzmPjl4diWwSKXccrenXrB8t3Vry7bFvqa6tw9r20gJYMws8W0Hff+s+YD1ZWqiY1bs5q2d1k7ZX/PkQb6w6SWmlAfW16flPaNIB1v0Dii/LnUbrlIJvBo5kXiXmyz2sOX6J5/o0Z+XMrgR7ybfzlLYtv7Cc/PJ8nmv/nEmM7m9SCSqebf8s2dezWZuy9t4HiyKse07a0GTkXK3dXKULYU2cWftMFNN6BLL4YCZDZu81nGZsFmrp36+6AtbMlC7omhCl4JswjUbku50pjJmTgCDA7zMieXFAiF43Dde1Wk0ti84uooNnBzp4dZA7jtZF+UQR4hrCwnML732x89hCOLce+rwlrS83cDZqC94Y1JJFT0VQVlXDyG/j+WVfmmFc0HUPlprLpWyXpsdMiOl85yv+Iq+kksk/H+STjeeIDvMm9rnudPBzlTuW1u3J3sPF6xeZ1HKS3FF0QhAEJrWcRNLVJBJz7rJEuTANNrwq9YeJfEa/ARsoMqgRG/7Rg6hgd95Zd4ZpCw5zrcwALuiGPwHBA6UL4Lnn5E6jNUrBN0F7k6SGZwfTCvng4dZ8PbE9zrbGdxNSXSw8uxAvOy/6+Bn/ypy7iQmIwcXahYVnF/79wdoaWDUdBAsY8Z20xNDIuNlb8ePkcN4c3JKd53MZ9L89HJK7EZsgwLDZYGUPK5+CGgP4IaQFxvfVobirmloN/7fpHI/+dAAXOzVrnunGpC7NTGpe+1Yp11LYf3k/40PHY6ky7O6dDWFjacOo4FHsyNpB9vXsvz649wupNcDgz8DFV56AWiAIAk91D2TF011RW6oYP3c/X29PkrftsqOXVPSvnISdH8qXQ4uUgm8icosrmDjvAN/sSGFsR1/WPtONUG/ja41QH4vOLsJKZcWo4FFyR9G5cSHjEBBYeu6WHu6XT0gbmrQeBW2NpyvovbRt6sL6Z6MY1KYx/918gSk/H6RQzjX7oYOlHvp7v4TMA/Ll0BKl4JuAg2mFDJ69l5PZRXw5rh2fjG6LnZXpjngBiiqLWJe6jsGBg3G1Mb1rE7dr7NCYPn59WJG0gvKactDUSksHbV1h0H/ljqdVjjZqvhrfjo9GtuFAWiFDZ+/leNY1+QIN/AicfGD981CX5bEGTCn4RkwURX7Yk8qEeftxsLZk9axujGjvI3csvVidvJrymnImtjT83ay0ZVLLSRRXFRObGis1+rp0BKI/lv1uWl0QBIEJnf1YMaMrAGPmJLDwQIY8q3isHWDwfyH3DMR/pf/za5FS8I3U9coanll0lPdjz9KvpSdrnulGiLfprK2/l1pNLYvPLaajV0dC3ULljqM3HTw7EOoWysLT8xG3vQdBfaTpHBPWpqkz65+NIjKoEf9adYqXfz9BRXU9W01oQ0gMtBwKuz6FwlT9n19LlIJvhJJzSxj+9V42nLrMazGhzHmkI042prkK5052X9xN9vVsk12KeTeCIDAxdCLJxekcUtPgrQqNhau9FT9N6cQ/+gaz8uhFRn4bT2ZBmf6DxHwKKjXEvmS0vfOVgm9kNpy8zPCv93GtrJrfnuzCjJ5BJrsK524WnluIt703vX17yx1F7wZVC7jW1rLQ/yFwC5A7jt5YqARe6N+CnyZ3IvtaOUNm72HHOT334nFqIrWsSNkOJ5fr99xaohR8I6HRiHy++TxPLzxCC29H1j8XRdfm7nLH0rvkq8kcuHyAcSHjTHop5h1VlmC98Q1G1dqws/zi35domoHeoZ6sfzaKpq52PDH/EN/tTNHvvH6nJ8GnI2x6Xdor2MgoBd8IXK+sYcZvh/lqezJjOjZlybQIw9xIQg8WnVuEtYW1WSzF/JvtH0DxJcb1+vDvSzTNiK+bHSue7srgNo35ZOM5nl96TH/z+ioLabvIskLY+rZ+zqlFSsE3cJkFZYz6Np5t53L595BWfDq6LdaWxrPHrDYVVRaxLsV8lmL+RfYROPg9hD+Bd3A0ff36sjxpOWXVMsxlGwBbKwtmT2jPKwNDWHv8EmO/T+ByUbl+Tu7dBiJnSdsiZsTr55xaohR8AxafnM+wb/ZypbiC+Y935omoALObr7/VqqRVVNRWMDHUfJZiAlL7hHX/AHuPP9oeT2o5iZKqkvr1yjcxgiAwq3dz5j0aTkrudYbO3sfhjKv6OXmv18DZD9Y9DzUGvFH7bZSCb4BEUWR+fDqP/nQQDwdr1szqRlSw+c3X3+rmUsxwr3BC3ELkjqNfB7+HKycg5hOwdQGgvWd7Wrq1ZNHZRYbRYVJG/Vp5sWpWN+ytLZgwdz/LErN0f1IrexjyOeSfh33GszZfKfgGprpWwxurTvH22tP0DvFg5cyu+Lvbyx1Ldrsv7uZS6SWzW4pJUbY0dx88AFqN+OPTgiAwseVEkq8lc+jKIRkDGoYWXo6smdWNzgFu/HP5Cd5ff0b3fXiC+0PYw7D7/4xmbb5S8A1IUXk1j/98iMUHM3m6VxBzHw3H0YzW19/LyuSVuNu608u3l9xR9GvrO6CpkdaA3zadF+0fjaPakVXJq+TJZmBc7Kz45fFOTI5sxg9705i+4LDud9Ma+BGoLGHzW7o9j5ZopeALghAtCMJ5QRCSBUH42w7AgiCECoKQIAhCpSAIL2vjnKYms6CMUd/FcyCtgE9Ht+XV6FCT2H5QG/LL89lzcQ9DA4ea11LMrINwchl0feaOa+5tLG2IDohma8ZWSqpKZAhoeCwtVLw7vDXvDgtj+7kcxszR8cVcp8bQ4yVp85nUnbo7j5Y0uOALgmABfAPEAK2ACYIgtLrtsELgOcC0ujxpyeGMQh7+dh95JZX8+kQXxoYbb5tbXYhNjaVWrGVE8xH3P9hUaDTSpiYO3hD14l0PG9F8BBW1FWxK36THcIZvcld/fpzciYyCUkZ8s0+3WyhGzAKXZrDxdekCuwHTxgi/M5AsimKqKIpVwBJg+K0HiKKYK4riIcC4W83pwJpj2UyYdwBHG0tWzexKZFAjuSMZFFEUWZ28mrbubQl0CZQ7jv6cWCI1R+v3jtS86y7auLch0DmQNclr9BbNWPQO9WT5012xEATGzElgy5kc3ZxIbQMD3peaqx3+WTfn0BJtFHwf4NbL4hdvfO6BCIIwTRCEREEQEvPy8hoczlCJosj/tibxjyXHaNfUhZUzuxHocfdvbHN1puAMydeSGd58+P0PNhWVJbD1XemOzrbj7nmoIAiMaD6CY3nHSCtK01NA49GysROrZ3WjhZcD0xYk8sOeVN2samo5VNpicscHBn0HrjYK/p0mmh/4X1QUxbmiKIaLohju4eHRgFiGq6pGw8u/n+CLrRcY2cGHBU91xs3eSu5YBmlV8iqsLayJCYiRO4r+7Pkcrl+B6E/qtGXh0KChWAgWyij/LjydbFgyLZLoMG/ejz3Lv9ec1v4KHkGQWlVXFMGuT7T72lqkjYJ/Ebh10rkpcEkLr2uSSiqqeXL+IVYcucgL/Vrw2ZiHzPbO2fuprK0kLi2Ovn59cbQyj9bPFKZBwtfSyN63U52e4m7rTpRPFOtS1lGrkaF1sBGwtbLgm4kdmN4jkAX7M5jx22HKq7T8b+XdGjpOgYPzDHbjc20U/ENAsCAIAYIgWAHjgbVaeF2Tc6WogrHf7ychpYD/G92Wf/QLNus7Z+9nR+YOSqpKzGs6Z8tb0jK/fu/U62nDmw8ntzyX+EvGdau/PqlUAq8Pasm7w8LYejaHCfP2U3Bdy3fJ9v6XdM1l0+sG2UK5wQVfFMUa4BlgE3AWWCaK4mlBEGYIgjADQBAEb0EQLgIvAm8KgnBREATT3nD1NhdyShj57T4yC0r5cUonxigrce5rdfJqvO296eLdRe4o+pG2G86ug+4vSq1466FX0164WLuwOnm1jsKZjsld/fluUkfOXi5m1HfxpOeXau/F7d2h1+tSC+ULhrdySivr8EVRjBNFsYUoikGiKH5w43NzRFGcc+P3V0RRbCqKopMoii43fl+sjXMbg4SUAkZ9F0+NRmTp9Eh6tjDNaxPadKX0CvGX4hkWNAwLlRlMedXWSMv6nP0g8pl6P11toWZw4GB2ZO2gqFKHSxBNRHRrbxZNjaCovJqR38VzNFOLPXg6PQXuLaRRfo2MG7DfgXKnrY6tPX6JyT8dxMvJhpUzu9Lax1nuSEZhXco6RERGBJnJ2vsj8yHnFAx4D9QP1vp6RPMRVGuqpT1vFffVsZkrK57uioO1JRPm7dfesk0LtXQHbmEqHJijndfUEqXg69APe1J5bvFR2vm5sGJGV5q62skdySjcXHvf0asjvk5mMPVVUQTb34dmUdDqwa9XhLqFEuoWqkzr1EOghwMrZ3YlxMuR6QsSWXQgUzsvHNwPggdKe+CW5mvnNbVAKfg6IIoiH8Wd5f3Yswxq482vT3TG2U7piVNXx/KOkVmSaT531u79EsoLYeAHDd6jdkTzEZwtPMv5wvNaCmf63B2sWTwtgp4tPHhj1Um+2paknbX6A96H6jKp6BsIpeBrWXWttMb++92pPBrRjNkTOmCjNoM5aC1anbwaW0tbBjQbIHcU3SvKhv3fQpsx0KRdg19uUMAgLFWWrElR1uTXh52VJXMfC2dkBx8+33KBt9dqYa2+Rwvo8Cgk/ggFKdoJ2kBKwdei8qpapi84/Mca+/8MD8NCaYBWL2XVZWxM28iAZgOwU5vBFNjOD0HUQJ83tfJyrjau9Grai9jUWKo1SieT+lBbqPhszENM7xHIrwkZPLfkKJU1DVyr3+t1sLCC7e9pJ2QDKQVfS66VVQIrBUUAACAASURBVDHph/3sPJ/LBw+3VtbYP6CtmVspqykzj+mc3LNwbBF0mgqu/lp72RHNR1BYUcjui7u19prmQhCktfpvDAol9sRlHv/5ECUVDfjB6egtrbo6vQqyD2sv6ANSCr4WXC4qZ8ycBE5lF/PtpA5M6tJM7khGa3Xyanwdfeno1VHuKLq39R2wcoQe2u0Y3s2nG+627srF2waY1iOIz8c+xMG0QibM209eSQNu0Or2HNi5w5a3Zb8ZSyn4DZSce51R38ZzpaiC+U90Jrp1Y7kjGa2LJRc5dOUQw4OGm/67o/R9cGEjRD0Pdm5afWlLlSVDA4ey5+Ie8ssNZ4WIsRnZoSnzJoeTklvKmDnxZBU+4Ibx1o7Q81VI3wNJW7Qbsp6Ugt8AJy8WMfb7BKpqRZZMj1BaGzfQzfXjQ4OGypxEx0QRtvwbHJtAxNM6OcWwoGHUirVKn/wG6h3iycKpXbhWXs2o7+K5kPOAG810nAKuAbD1bZCx35FS8B9QQkoBE+btx87KguUzIglrotxQ1RCiKBKbFksHzw40cahfWwGjc2YNZCdC7zce+Car+2nu2pwQ1xDiUuN08vrmpIOfK0unRQIw9vuEB7sr19IK+v5b6pl/fImWE9adUvAfwNYzOUz++SDezjYsn6FsMq4N56+eJ60ojcGBg+WOolu11bDtXfBoCe0m6vRUgwIHcSL/BFnFWfc/WHFPId6OLJ/RFScbNZN+OMC+5AeYKgt7GJp0kHrmV+tw28V7UAp+Pa06epHpvx2mpbcjy6ZH4u1sI3ckkxCXGoelYEn/Zv3ljqJbh3+Rbrnv/y7ouEdQjL+0h0BcmjLK1wa/RnYsnxGJr6sdj/98iI2nrtTvBQQB+v8HirNla7mgFPx6mB+fzgtLj9PZ342FUyOUTUu0RCNqiEuLo6tPV1xtXOWOozuVJbDzY6mFQrDubypr7NCYDp4diE2L1c0uT2bI08mGpdMjCPNxYubCw/yeWM93TwHdpZYLe76QZWcspeDXgSiKzN6WxNtrT9O/lRc/P94JB2tLuWOZjCM5R8gpy2FQwCC5o+hW/Gwoy5dGeXpahTQ4cDBpRWmcv6q0WtAWFzsrfnuyC92au/PK8hP8uLeeW0v2eweqSmDPZ7qId09Kwb8PURT5MO4sn22RtiP8bpLSKkHb4tLisLW0pbdvb7mj6M71XIj/GlqNgKb6u8egf7P+WAqWysVbLbO3tuSHyeHEtPbmvfVn+HLrhbq/i/JqBQ9NhINz4Zp+r68oBf8eajUib6w6xbw9aUyObMZ/Rz+EpYXyT6ZN1bXVbM7YTC/fXqbdSmHP51BTAX3e0utpXW1c6erTlbi0ODSiRq/nNnXWlhbMntCe0R2b8uXWJD6MO1v3ot/rNemjnve/VarXXVTXanhx2TEWH8xkZq8g3hkWhkrpi6N18ZfiKaosYkjgELmj6M61LKmBVruJ4N5c76cfHDCYnLIcjuQc0fu5TZ2lhYpPR7VlcmQz5u1J441Vp+rWdM3FF8KflFpr5CfpPugNSsG/g8qaWmYuPMKaY5d4ZWAI/4wONf07P2USmxaLi7ULkU0i5Y6iOzdHcT1fleX0vXx7YWtpq6zW0RGVSuCdYWHM7BXE4oOZvLjsGNW1dXg31f1FsLSBHR/qPuQNSsG/TVlVDU/NT2TLmRzeGdqKWb31PyIzF2XVZezM2smAZgNQq0x0v4D8JGkUF/6kNKqTgZ3ajt6+vdmcsZnqWqWDpi4IgsA/o0N5ZWAIa45dYubCI/fvtOngKd1pfXolXD6hl5xKwb9FcUU1k386yL7kfD4d3ZYp3QLkjmTSdmTtoLymnEGBJrw6Z8eH0iiu+4uyxhgcOJiiyiLiL8XLmsPUzerdnHeGtmLLmRyemp9IWVXNvZ/Q9VmwcZZuxtIDpeDfcLW0iknzDnA08xqzJ3RgbLgZbK0ns7i0OLztvWnv2V7uKLpx+YQ0eot4WhrNySiySSQu1i7Epin73eralG4BfDq6LfuS85n800GK79Ve2dYFuj0vNdLLPKDzbErBB/JKKhk/dz/nc0qY+1hHBrdVOl7q2tWKq8RnxxMTEINKMNEvw+3vS6O3rs/KnQS1Ss2AZgPYmbWTsuoH7PqoqLOx4b7MntCBo5nXePSHA1wrq7r7wV2mg70nbPuPztsnm+h3Wt1dLipn3PcJZBaW8fOUTvQJ9ZI7klnYkrGFGrGGwQEm2jsncz8kbZJGb7YucqcBpN465TXl7MjaIXcUszC4bWPmPNKRs5dLGD93P/nX79JT38oeerwCGXshVbf/N2Zd8LMKyxj7fQK5JZX8+mRnujV3lzuS2YhNjSXIOYgWri3kjqJ9ogjb3pNGbV2my53mD+092+Nt762s1tGjfq28+HFKOOkFpYyfu5+c4oo7H9hxMjj76XyUb7YFPy2/lLHfJ1BcXsPCp7rQyV+7m1Ao7u7y9cscyT3CoMBBprncNXWHNFrr8Yo0ejMQKkFFTEAM8dnxXK14gBa/igfSPdiDXx7vzOVr5Yz9PoGLV+8wpWZpDb1ehUtH4dx6nWUxy4J/IaeEsd8nUFmjYfHUCB7yNYy33Obi5ggzJiBG5iQ6IIrSKM3ZTxq1GZjBAYOpEWvYnL5Z7ihmJSKwEQue6kJhaRXjvt9PRkHp3w9qOx4aBUvXfnS0SYrZFfxT2UWMn7sfAVg6LYJWTZzkjmR24tLiaOvRFl9HE1wJdW69NErr9Zo0ajMwLVxbEOQcpEzryKCDnyuLp0ZQVlXDmDkJJOfetnuWhSX0+RfknYOTv+skg1kV/GNZ15g4bz+2aguWTY8k2MtR7khmJ/lqMheuXjDNzpiaWml05t4C2o6TO80dCYLAoMBBHMk9wuXrl+WOY3Za+zizZFokGhHGfb+fs5eL/3pAy+Hg3RZ2fgQ191jZ84DMpuAnphfyyA8HcLGzYsm0CGWXKplsTN+ISlAx0H+g3FG079QKaXTW63VptGagbm6Moux3K48Qb0eWTY9AbaFiwrz9nMou+vNBlQoGfgDdXwIdLFc2i4KfkFLAYz8dxNPRmqXTI/B1M+GujAZMFEU2pm+kk1cn3G1NbEVUbY20uYlXa6kFsgHzdfIlrFEYG9I3yB3FbAV6OLB0egT2VpZMnLf/r/vkBvSADo/pZNBg8gV/T1Iej/9yEB8XW5ZMi6Cxs242jVbc37nCc2QUZxAdEC13FO07sQQKU6SNyVWG/20VExDDmYIzZBZnyh3FbDVrZM/S6RG42Fnx6I8HOZSu+x2wDP8rswF2nMvlyfmJ+DeyZ8m0CDydlP1n5bQhfQOWgiX9/PrJHUW7aqpg5yfQpD2EGMe1iZtTahvTN8qcxLw1dbVj2fRIPB2tmfzTQeJTHmBz9How2YK/6fQVpi1IJMTLkcVTI2jkYHgrJsyJKIpsSttERJMIXGxMbBns0QVQlAm939Tb1oUNdbOH0YY0ZVpHbt7ONiyZHoGPiy2P/3yIXRfydHYukyz4609I7Ulb+zjz21NdcFU2G5fdifwTXCq9ZHpr76srYPd/wbcLNO8rd5p6ifaPJvlaMslXk+WOYvY8HW1YMi2CQA8Hps5PZNvZHJ2cx+QK/tXSKl5bcZKOfq4seLILzrYm2mfdyGxM24hapTa9fWsP/wwll6CP8YzubxrgPwCVoFKmdQxEIwdrFk/tQoi3I68sP8H1yvu0Vn4Ahrt27AG52lvx21NdaOHlgJ2Vyf31jFKtppZN6Zvo7tMdRysTuvehqhT2fAb+3aWVFUbG3dadTl6d2JS+iVntZplmmwsj42JnxcKpXcgsKMPBWlmlUyftfF2UYm9AjuQeIa88z/RW5xycB6V50ujeSA0MGEh6cTrnCs/JHUVxg5ONmtY+zjp5bZMs+ArDsil9E7aWtvRs2lPuKNpTUQz7/gfN+4FfhNxpHlg/v35YCpbKtI6Z0ErBFwQhWhCE84IgJAuC8NodHhcEQfjqxuMnBEHooI3zKgxfjaaGLRlb6Nm0J3ZqE7rh7cAcKC+U1t0bMVcbVyKaRLApfROijjffUMivwQVfEAQL4BsgBmgFTBAEodVth8UAwTd+TQO+a+h5Fcbh4JWDFFYUEu1vQtM55Vch/msIGQw+HeVO02DR/tFkX8/mZP5JuaModEwbI/zOQLIoiqmiKFYBS4Dhtx0zHPhVlOwHXARBUPYRNAMb0zZir7YnqmmU3FG0J/5rqCwy+tH9TX38+qBWqZU1+WZAGwXfB8i65c8Xb3yuvscAIAjCNEEQEgVBSMzL090NCArdq66tZmvmVvr49sHawkRufCstkKZzwh4G79Zyp9EKRytHonyi2Jy+GY2okTuOQoe0UfDvtJbr9snAuhwjfVIU54qiGC6KYriHh0eDwynkE38pnpKqEtNanbPvS6gukzpimpCYgBhyy3M5knNE7igKHdJGwb8I3LqTRVPg0gMcozAxG9I34GTlRGTjSLmjaEdJjrQUs80Y8AiRO41W9WzaExsLG2W1jonTRsE/BAQLghAgCIIVMB5Ye9sxa4HHbqzWiQCKRFFUdl8wYRU1FezI3EH/Zv1RW5jI3c57P4faKuj5qtxJtM5ObUdP355sydhCjUb7d3gqDEODC74oijXAM8Am4CywTBTF04IgzBAEYcaNw+KAVCAZmAfMbOh5FYZtT/YeymrKTGc6p+giJP4E7SZCoyC50+hEjH8MhRWFHLxyUO4oCh3Ryu2ooijGIRX1Wz8355bfi8AsbZxLYRw2pm3EzcaNcK9wuaNox+7/ShuU9/yn3El0JqppFPZqezalb6Jrk65yx1HogHKnrULryqrL2H1xNwOaDcBSZQItLgrTpBbIHSeDi5/caXTG2sKaPr592JKxheraarnjKHRAKfgKrduetZ2K2grTmc7Z/X+gsoTuL8udROeiA6IpqSph36V9ckdR6IBS8BVatzFtI152XrT3bC93lIbLT4LjiyH8SXAy/XsFIxtH4mztrNyEZaKUgq/QqqLKIvZd2kdMQAwqwQS+vHZ+DJY2EPWC3En0Qm2hpn+z/uzI2kF5TbnccRRaZgLfkQpDcnNZn0nsbJVzBk6tgC7TwcF8bgIcFDCI8ppydmXtkjuKQsuUgq/Qqg1pG/B38qelW0u5ozTczg/B2hG6Pid3Er3q4NkBT1tP4tLi7n+wwqiYZsEvzZc6Gir0Krcsl0NXDhEdEG38uyddOgZn10HETLBzkzuNXlmoLBjgP4C92XspriqWO45Ci0yv4Jdfg686SOumFXq1OX0zIqJpTOfs+BBsXCDSPO8RHBQwiGpNNdsytskdRaFFplfwbV2g5RCp50lRttxpzMqGtA2EuoUS6Bwod5SGydwPSZug23Ngo5ut5gxda/fW+Dr6Kqt1TIzpFXyQep2IGmn9tEIvskqyOJF/wvhH96II2/4D9p7QZcb9jzdRgiAQ7R/NgSsHyC/PlzuOQktMs+C7NoPwx6W7IwtS5E5jFjamSV0WjX5nq5TtkLEPerwCVvZyp5FVTEAMGlHD5vTNckdRaIlpFnyQ7opUqaV11Aqd25C+gXYe7Wji0ETuKA/u5uje2U9qo2Dmgl2Dae7SXGmZbEJMt+A7ekHEDDj5O+ScljuNSUu+mkzS1STjn845uw4uH4Ner4GliezQ1UCDAgZxNPcol68r3cxNgckV/OraatamrOV43nFp/bS1I2z/QO5YJi0uLQ6VoGKA/wC5ozw4TS1sfx/cW0DbcXKnMRg3+yFtSFcu3urLoSuHiEuN08m+BCZX8AH+79D/sfDMQmn9dNfn4HwsXEyUO5ZJEkWRDWkb6OzdGXdbd7njPLgTyyD/PPT+F1iYQIdPLfF19KWNextltY4e/XzqZz4//LlOWpOYXMFXW6gZ6D+QHVk7KK0ulaZ17NyluVmF1p3KP8XF6xcZFDBI7igPrqZKuqu28UPQcpjcaQxOTEAM5wrPkVqUKncUk1dYUUj8pXgGBw5WCn5dDQkcQkVtBdsyt0lTOt1fgrRdkLpT7mgmZ0P6BtQqNX2b9ZU7yoM7Mh+uZUKff4PKJL8lGmSg/0AEhD9WYil0Z2PaRmrFWgYHDtbJ65vkV/dDHg/h4+DD+pT10ifCnwAnH9j2nrQSQ6EVtZpaNqVtIsonCicrJ7njPJiqMumubL+u0NyIf2jpkKedJ528O7EhbQOi8v2jU7GpsbRwbUEL1xY6eX2TLPiCIDAkcAgHrhwgtywX1DbSzVjZiXBemYvUliO5R8gtzzXu1TmH5sH1K9D3LTD2/j86FB0QTXpxOmcLz8odxWRlFGdwIv8EQwKH6OwcJlnwAQYHDkYjav682NRuIrgFSSsxNBp5w5mIuLQ4bC1t6dm0p9xRHkxFEez9Apr3h2bKHq730t+vP5aCpXLxVofiUuMQEHQ6gDLZgh/gHEBYozBiU2OlT1ioofcbkHsaTi2XN5wJqK6tZkvGFnr59sJObSd3nAcT/7XUVbXPm3InMXguNi509enKhrQNaERlwKRtoiiyPnU9nb07423vrbPzmGzBB+ni7dnCs6Rcu9FeIWwkeLWB7e9BTaW84Yzc3uy9FFUWMThANxeXdK7kCiR8Da1GQJN2cqcxCoMDBpNTlsPhnMNyRzE5J/NPklmSqbOLtTeZdMGPDojGQrD4c5SvUkH/d6UVGYd+lDeckVuXug43Gze6+hjpVMjOj6G2Cvr+W+4kRqO3X2/s1fasTVkrdxSTsz51PVYqK/o166fT85h0wXe3dSeiSQSxqbF/vg1t3hcCe0mdNCuK5IxntIoqi9iZtZNBAYNQq9Ryx6m//CQ48qu0eqtRkNxpjIatpS0Dmg1gc/pmZb9bLarWVLMpfRO9fHvhaOWo03OZdMEH6W3opdJLHM09+ucn+70L5YWw90v5ghmxjWkbqdZUMyzISG9S2voOqG2hxz/lTmJ0hgYNpaymTLrHRaEVCZcSKKwo1OnqnJtMvuD39euLraXtn9M6IM3ZthkD+79VNkl5AGtT19LcpTmhbqFyR6m/zANwbj10+4dZbUyuLR29OtLEvgnrUtbJHcVkrE9dj7O1M1E+UTo/l8kXfDu1HX38+rApfRNVtVV/PtDnTWmTlJ0fyhfOCKUXpXMi7wTDgoYZ3761oghb/g0OXhA5S+40RkklqBgSNIT9l/eTU5ojdxyjV1pdyo7MHUT7R6O20P30qMkXfJBW6xRXFbMne8+fn3T1h05T4dgiyFVuJqmrdanrUAkqna8m0InzcZC1X2p/bOabmzTE0MChaEQNcWlxckcxetszt1NRW6G37yezKPgRjSNws3H767QOQI+XwcpRmtNV3JdG1LA+ZT0RjSPwtPOUO0791NZI/8+NgqH9Y3KnMWr+zv609WjL2pS1SquFBlqfuh4fBx/aeehnabBZFHxLlSUxATHszNpJcVXxnw/YuUHU83BhI6Tvky+gkTicc5hLpZcYGjRU7ij1d+w3yL8A/d5W2h9rwbDAYSRfS+Zc4Tm5oxitvLI89l/ez+DAwXqbHjWLgg/StE61ppqtGVv/+kDE0+DYRJrbVUYr97QuZR12lnb09TOyJmNVpbDjI/DtAqG6XwlhDqIDolGr1Mqa/Aa4edeyPqdHzabghzUKw9/Jn/Wp6//6gNpWarmQnQhn1sgTzgiU15SzOWMzA/wHYGtpK3ec+kn4VmqQ1v8/SoM0LXG2dqaXby/i0uKo1lTLHccoxabFEtYojEDnQL2d02wKviAIDAocxKErh/6+P2e7ieDREra9C7XKF++d7MiUNpQxurX3pfmw73/SyN4vQu40JmVo4FAKKwpJuJQgdxSjk3otlTMFZ/S++MFsCj7AkADp7Xxs2m0Xb1UWUsuFwlRI/EmGZIZvbepaGts3pqNXR7mj1M/Oj6G6DPq+LXcSkxPlE4WrtasyrfMAbq5203drcbMq+L5OvnT06sjKpJV/7/gXPAACesKOD6GsUJ6ABiqvLI+ESwkMCRyik23XdCbnjPQDPPxx8NDNhhLmTG2hJiYghh2ZO/66GEJxTzWaGtYkr6G7T3e97wNtRN+92jEqeBRZJVkkXrltU3NBgOiPobJYKvqKP8SlxaERNca1OkcUYeNr0haXvf8ldxqTNSxoGFWaKjanb5Y7itHYc3EPeeV5jAoepfdzm13B79+sP45qR1Ykrfj7g16tIPxJSPxRGh0qAFibspa27m0JcA6QO0rdnY+T9jHu/Ya0/FahE60atSLQOVBptVAPK5NW4mHrQfem3fV+brMr+DaWNgwOHMzWjK0UVd6hW2bvN8DaSRodKss0OV94ngtXLxjX6L6mEjb9CzxCpY6YCp0RBIGhQUM5knuErOIsueMYvJzSHHZn72Z48+FYqvR/P0iDCr4gCG6CIGwRBCHpxkfXuxz3kyAIuYIgnGrI+bRldIvRVGmq/r5EE6TRYO83pNHheeXW8bUpa7FUWRLtHy13lLrb/x1cTYOBH0o7nSl0akjgEASEO38/Kf5iTcoaNKKGkc1HynL+ho7wXwO2iaIYDGy78ec7+QUwmIoR4hZCWKMwll9Yfudbw8OfkEaHm/5l1jtjVWuqiU2NpYdPD1xsXOSOUzclOdJeBy1ipL0PFDrnbe9N58ad/yhmijvTiBpWJq2ki3cXfJ18ZcnQ0II/HJh/4/fzgRF3OkgUxd2AQS19GdViFMnXkjmZf/LvD1qoIfojaZS4/zv9hzMQ2zO3U1BRwKgW+r+49MC2/0f6IT3wA7mTmJWRzUeSfT1bWZN/DwcuHyD7eras308NLfheoiheBrjx0Wg6asX4x2BracvKpJV3PiCojzRK3P1/0qjRDP1+/nea2DehW5Nuckepm+wjcHQhRMxQdrLSs37N+uFm48ay88vkjmKwViatxNnamT5+fWTLcN+CLwjCVkEQTt3h13BdBBIEYZogCImCICTm5eXp4hQAOFg5EO0fTVxaHKXVpXc+aOAH0mhx2390lsNQpRWlceDKAcaEjMFCZSF3nPsTRdj4Oti7Q49X5E5jdqwsrHi4+cPsvLiTK6VX5I5jcK5WXGVb5jaGBg7F2sJathz3LfiiKPYTRbH1HX6tAXIEQWgMcONjbkMDiaI4VxTFcFEUwz08dLsj0cjgkZTXlLMxbeOdD2gUJDVXO7ZQGj2akWXnl2GpsmRE8zvO0hmeUyukXvd9/w02znKnMUujW4xGFMU7L3k2c+tS1lGtqWZksDwXa29q6JTOWmDyjd9PBoyq+9hDHg8R5Bx092kdkEaL9u5mtUyzoqaCNSlr6OfXT+93Aj6QqjKp26l3W2g3Se40ZqupY1O6+XRjxYUVSkO1W4iiyMqklbT1aEuwa7CsWRpa8D8G+guCkAT0v/FnBEFoIgjCH2saBUFYDCQAIYIgXBQE4ckGnlcrBEFgVItRnMg/wYWrF+58kI2TNGrMOgAnluo3oEw2pm+kpKqEsSFj5Y5SN3s+g+JsiPlE6oukkM3YFmPJK89jV9YuuaMYjON5x0kpSmF08Gi5ozSs4IuiWCCKYl9RFINvfCy88flLoigOuuW4CaIoNhZFUS2KYlNRFH9saHBtGRI4BLVKfe9RfrtHoGkn2PSGWfTZWXZ+GYHOgYR7hcsd5f5yz0ndMNuOh2Zd5U5j9no07YG3vTdLz5vH4KguViStwM7SjoH+A+WOYn532t7O1caVfn79WJeyjsrau6y5V6lg6P+gogi2vKXfgHp2puAMJ/NPMjZkrOFvUq7RwPrnwdpBWYZpICxUFowOHs3+y/vJKM6QO47srlddZ1P6JgYFDsJObSd3HKXgA4xsMZLiquK/74Z1K68wiHwGjv4G6Xv1F07Plp1fho2FjXG0Ujj6K2QmwID3pessCoMwMngkloIlv5//Xe4osotLi6O8plyWRml3ohR8oLN3Z3wcfO49rQPQ81VwaQbrnjfJO3BLqkqIS4sjJiAGJysnuePcW0mOdKG2WZRyodbAeNh50NuvN6tTVlNRUyF3HFmtTFpJC9cWhDUKkzsKoBR8AFSCilHBozh45SCZxZl3P9DKDgZ/DgVJsPcL/QXUk/Wp6ymvKTeOi7Wb3oDqchj6pbJtoQEaGzKWosoitmRskTuKbM4VnuN0wWlGBY8ymOlRpeDfMLz5cCwFSxafW3zvA4P7QetR0sqQ/CT9hNMDURRZdn4ZrRq1orV7a7nj3FvSVji1HLq/BO7yLnNT3FkX7y74O/mb9cXbxecWY2Nho/dtDO9FKfg3eNp5EhMQw4qkFXdum3yrgR9Jm5+vf8Fk1uYfzT1K8rVkxoWMkzvKvVWVQeyL0CgYol6QO43iLgRBYEyLMRzPO875wvNyx9G7/PJ81qWsY0TzEThbG86NgErBv8XksMmU15Sz/MLyex/o6AX93oX0PXBskX7C6djS80txVDsafhvkXZ/AtQxpKsdSvlvUFfc3vPlwrC2szbK/zqKzi6jR1PBYq8fkjvIXSsG/RYhbCJGNI1l4diFVtVX3PrjDZPCNgM3/gtJ8/QTUkcKKQrZkbGFo0FCDWDp2V1dOQfxs6b4I/yi50yjuw9namYH+A1mfuv7u/apMUFl1GUvPL6Vfs36ytUG+G6Xg32ZK2BTyyvOIS7vP5icqlTTKrLwOm9/UTzgdWZ28mmpNtWFfrNVoYN0/wNYFBrwndxpFHY0LGUdZTRmxqbFyR9GbVcmrKK4qZnLY5PsfrGdKwb9NZJNIgl2DmX96/p03R7mVZ0vo9g84vli6kGiEqjXVLDu/jI5eHQlyMeCWwge/h+xE6fqJsket0Wjj3oZQt1AWn1tsFpuj1GhqWHBmAe092/OQx0Nyx/kbpeDfRhAEpoRNIflaMvsu7bv/E3q8Ah4tYc1MKC3QfUAt25C2gezr2UwJmyJ3lLvLPQtb3obggdDWgN+FKP5GEAQmh00m+VoyO7J2yB1H57ZlbiP7erZBju5BKfh3FOMfg6etJ7+c/uX+B6ttYNQ8KL8K654zqlU7M8lXOQAAFFBJREFUtZpafjj5Ay1cW9CzaU+549xZTSWsmArWjjD8a2XNvRGK9o+mqUNT5p2Yd/93zUZMFEV+OfULzZya0atpL7nj3JFS8O9AbaFmUqtJHLh8gLMFZ+//BO820OdNOLde6p1vJLZmbiWtKI2pbacazI0hf7PjA8g5KRV7B6PZUE1xC0uVJU+1eYrTBaeJvxQvdxydOZxzmFMFp3is1WMGu2mQUvDvYnSL0dhZ2jH/zPz7HwxSnx3/7rDhVShM0204LRBFkbkn5uLv5E9/v/5yx7mz9L2w7yvoOAVCYuROo2iAYUHD8LLz4vsT35vsKH/+6fm4WrsadB8qpeDfhZOVE6NajGJj2sa6bdmmsoAR34FgAaumQ22N7kM2wK6Lu7hw9QJT2041zNFIRRGsmgFuATBA6YRp7NQWap5o/QRHc4+SmJModxytSy1KZefFnYwPHY+tpa3cce5KKfj38EjLRwD47cxvdXuCiy8M/kzaLMWAe+2Iosi8E/PwcfAhJsBAR85xr0DxJRg5T2p/rDB6I4NH0simEfNOzJM7itb9evpXrC2sGR86Xu4o96QU/Hto4tCEgf4DWZ60nJKqkro9qe0YqdfOro8Ndh/c/Zf3cyL/BE+0fgK1Si13nL87tULaXaznP6GpEWzCoqgTG0sbJodNJuFyAifyTsgdR2tutlEYHjQcNxvDXjKsFPz7mBw2mdLqUlZcqMfGzIM/AwcvWDkVqgzvDsO5J+biaetpmBuUF2VLPYp8wqH7y3KnUWjZ2JCxOFs7m9Qof8m5JVRrqnm01aNyR7kvpeDfR6tGreji3YUFZxdQXVvHjZltXaX5/IJk2GxYO2QdyTlCYk4ij7d+HCsLK7nj/JVGA6ufhtpqGDkXLCzlTqTQMnu1PY+0fISdF3eaRFO1suoylpxfQm/f3vg7+8sd576Ugl8Hk8Mmk1uWy6rkVXV/UmBPaeVO4o/SFIWBmHtyLm42boxqYRg78PzFnv9C2i4Y+CE0MuC7fhUNMrHlRBzUDsw7afyj/KXnl1JUWWSwN1rdTin4dRDlE0UHzw58c+wbrlddr/sT+74tNVhbPQsuyz9neTr/NPuy9/Foq0cNbyXBuVhpzX3b8dIyTIXJcrJyYnzoeDanbya1KFXuOA+ssKKQuSfmSvXBq4PccepEKfh1IAgCr3R6hcKKwvqNSiytYNwCqffLkomyd9Wce2IujlaOjA8xsJUEuWdh5TRo0l7ZwcpMPNrqUawtrPnx5I9yR3lg3x77lvKacl4Jf0XuKHWmFPw6au3emqGBQ1lwZgEXSy7W/YkOnjDuNyjNg2WPSfPTMrhw9QLbs7bzSMtHcLAyoGWOZYWweAKo7WDcQmljGYXJc7NxY0zIGGJTY8kqyZI7Tr0lX03m9wu/M6bFGAJdAuWOU2dKwa+H5zo8h4VgwReH67nG3qcDDJsNGftg4+u6CXcf3/9/e3ceX/OV/3H89cmCJKggadCEsfya1L4OBoNWH120SrVjm9LRJp1aivZh0I52bPXzU8V0WmKZ6u9R1dKFdkpRRGmolIZYaonGTmKLSCS5yZk/vldpiHzvkvu9NznPxyMPue655/v2lXzyzfmee07yfIIDghkY40UbfhfYYMVf4PIJ44fiXXWsTqR50JDGQ/ATPxbuWWh1FIfNTJpJSEAIL7Z40eooDtEF3wERIRE82+RZ1qatZde5XY69uNnT0HEk7FgAP75fKvmKk3gqkbVpa3mm8TNetd0a61+H1I3QcxZE/d7qNJqHhQeH0y+6H58f+pzk9GSr45i25eQWtp7aSlzzOEIrhVodxyG64DtoSOMhhAeFM+OHGY6v7/3AG9DgfvjPK3BsW2nEu0VuQS5Ttk0hqkoUzzV9ziPHNCV5GSS+A22fh1betQ2c5jnDWgwjLDiMSYmTyC+0ZrjTEbZCGzN3zCSqShQDogdYHcdhuuA7KDgwmJdav0TK+RTHd/Hx84e+i4wlGD7+s/Emo1K2YPcCjl05xmvtX6Oiv5fsAXtyJ6waCXU7wUNvWp1Gs1BIYAgT2k3g4MWDfLjP+1eaXXFwBUcuH2FMmzEE+nvhu9RLoAu+E3rW78l9Ne5jzs455NhyHHtxUCj0+wjyc4yZO7kml2xwQurlVBalLOLR+o/SoXaHUjuOQy6fgGUDjXciP70EfPCbRnOv7lHd6RrZlXeT3+VU1imr4xQrMy+Tf/30L9rc3Ybukd2tjuMUXfCd4Cd+jG07lrPZZ81tklJUeDQ8uRDO7IEPnzL2xXUzpRSTEycTHBDsPdPGMk/B+z0hLwv6L4WQmlYn0ryAiDCh3QQApm6f6rXLJ8cnx3M59zJj24713v0jSqALvpNa392aHnV78O+Uf3Mu+5zjHdz7kDG8c/wHWPq029fcWXlkJUlnkxjdejQ1gmq4tW+nXDljFPurGTDoM2PTGE2zq1W5FsNaDGPzic2sP+Z9+0MfzzzOhwc+pFfDXsTUiLE6jtN0wXfB6NajsRXamLtzrnMdNO5trBlzLBGW/gnyst2S6+K1i7yV9BYtw1vSp1Eft/TpkitnjWKfdRYGfQqRba1OpHmhgTEDia4ezfTt0x17R7sHzPpxFoF+gYxsOdLqKC7RBd8FkVUiGRQziFVHVrHjzA7nOmnaF3rPN3Z3WtbfGNt30VtJb5GVl8XE9hPxE4v/i7PSYcljxnDOwOV6+qVWrAC/ACa2n0h6Tjr/3PVPq+P8KuF4AuuPrWdok6GEBYdZHccluuC7KK55HPXuqscrCa+Y2xnrdpo9bayumZpg3MjNv+Z0nh1ndrDyyEqGNBlCw9CGTvfjFlcz4IPH4dIxGPgJ1O1obR7N6zUNa0q/6H58dOAjUjJSrI5DWmYa478bT0z1GJ9ZIO1OdMF3UUhgCLO7zSa3IJdRG0eRW5DrXEct+hsbdR/ZAB8PApvj/eQV5DEpcRJ1KtchtlmsczncJfsCfNALLqTCgI+hXidr82g+Y0TLEdQMqsmkxEnYCq3bKvRq/lVe2vAS/n7+vN3tbSoFVLIsi7vogu8G9e+qz7RO09h7fi9Ttk1xfpZBy0Hw2Fw4vM6Yungt06GXz0uexy+Zv/Ba+9esXQ0z85RxZZ9xCPp/ZCwVrWkmValQhXHtxrH/wn7nZsG5gVKKv2/9O0czjzKjywzqVC4by37ogu8m3aO6E9csji8Of8EnP3/ifEetB8Njc4wr/QXdjJUkTVh+cDkL9izgiYZP0KmOhVfTRzfDvM5wPtWYetnAN+cra9bqUbcHPer2YO7OuY6/wdENFqcsZl3aOka3Gu0972FxA13w3ejFFi/SuU5npv8wnZ1nXdjPtvUQGLzKuMJf0B32rLhj8zVH1zA5cTJd7unCxA4TnT+uK5SCLbONYZzg6hC7ERo+YE0WzeeJCG92fpM2EW14dcurJBxP8Nixt57cypydc3io3kNlYtz+Zrrgu5Gf+DG9y3RqV67NmE1jOHv1rPOd1esEcZshohl8OhRW/w1sebc023JyC+O3jKdleEtm/nGmNZuSX7ts3HdY/zrEPA7Pb4Cwez2fQytTKvpXZG63uURXj+blhJednwnngONXjjN281gahjbkHx3/4bNvsCqOLvhuVrVCVWZ3m022LZsxCWPIK7i1SJvvrBYM+Qp+/1fYPg+W9ITM078+vfPsTkZvHE2jao145/53rBm3P7sP4rvBz6vhwanw1PtQsYrnc2hlUuUKlXnvgfeoXbk2IzaMYN/5faV2rOz8bEZtHIVCMafrHIIDg0vtWFZxqeCLSHURWScih+x/3rJWqIhEishGEdkvIntF5CVXjukLGoU2YsofprA7fTfTtk9z7a3i/oHw8HR4chGcSYH5nSF1EwcuHGD4t8OJCIngvQfeo0oFDxdZpSD5Y1h4v7FUwuAvoeNwvVuV5nahlUKJ7xHPXRXu4oV1L5TKtoiFqpA3Et/g0MVDzOgyg8iqkW4/hjdw9Qp/HPCtUqoR8K39cVE24GWlVAzQHhgmIve5eFyv92C9BxnaZCifHvqU4RuGk5Hj4vaGTfvC899CpWr8svRJ4r7sR4h/BeJ7xHt+6YSj38GiB+HzWKjV3Bh6qvcHz2bQypWIkAjiH4xHRIhbF8fprNMlv8ikM1fPELs2ltVHVzOi5QhrJz2UMlcLfi9gif3zJcATRRsopU4rpXbaP78C7AfKxhynEoxsNZJx7cax/fR2eq/szfo0F9cICY/h1KBlxNZrBAX5xB9OodY3E4257p5wahf8f29jaOnyCWM20eCvoEqEZ46vlWt1q9Ylvkc8V/OuErsulvTsdJf6U0rx5ZEv6bOyD7szdvN6h9e9a8+IUiCuDDeIyCWlVLWbHl9UShW7BYyI1AM2A02UUredZC4isUAsQFRUVOu0tDSn83mL1EupjN8ynn3n9/F4g8cZ126cw0MwGTkZLE5ZzPKflxPgF8CiP77NfftWw/b5UJhvbCLSZawx7u9u6Qdh4xTYtxKCqkPnMdD2Ob3/rGaJXed2Ebs2Fj/xo390fwY3HuzwzlOXrl1i8rbJrE1bS4uwFkzrNK3MDOOIyI9KqTa3fa6kgi8i64HbXcK9CiwxW/BFpDKQAExVSn1mJnibNm1UUlKSmaZeL78wn/nJ81mwZwF3B9/N1E5TaRtR8iJi6dnpRqE/uBxboY1H6z9KXLM4oqpGGQ2unIGEGbBzCfgFQvN+xnTIep0gqNqdO7+TK2fhaAIc/Ab2fmZsMt5hGHQYDpWqOt+vprlB6qVU5iXPY80va6gUUOnXwl+9UvUSX7vl5BYmbp3IxdyLDGsxjGcbP4u/n78HUnuGSwW/hI5/BroqpU6LSC1gk1Lqlvl4IhIIfAV8o5SaZbb/slTwr0tOT2bCdxM4fuU4fRr1IaZ6DGHBYYQFhREWHEaNoBoE+gVyLvsci1MWs+LgCmyFNnrW70lss9gbhb6oC0ch4X9h3yrIvwriB7VbQf2uxkdkOwi4w45XuVmQ9j2kbjL2mT1nnw0RFArN+0Pnl/X69ZrXOXLpCPN3z2fNUaPw97u3H4MbD6ZGUA3yC/LJyMkgPSed9Ox00nPS2ZOxh1VHVtGwWkPe7Pwm0dWjrf4nuF1pFvz/A84rpaaLyDigulJqbJE2gjG+f0EpNcqR/stiwQdj+tesH2ex4uAKClTBb54ThNBKoWTlZVGgCniswWPENo01/+umLQ9OJtkL9yY4kQSqAAKCoFrU7WfRqELjPkChDQIqQVSHGz8oIpqBn569q3m31EupRuH/ZQ0V/CoQFBDExdyLt7QL8AtgQPQARrYa6T1bfrpZaRb8GsAnQBRwDHhKKXVBRGoDC5VSj4hIJ+A7YA9wfdfvCUqpr0vqv6wW/OtshTYuXrvIuZxzv16BXP+zon9FBsYMJLKKi+OK1zIhbatR/K/cYWZD6O+gQTeIbA+Bvr9IlFY+Hb18lKX7l1KgCn79zTk8OJyaQTUJDw4ntGJomRq+uZ1SK/ilrawXfE3TNHe7U8HXv6trmqaVE7rga5qmlRO64GuappUTuuBrmqaVE7rga5qmlRO64GuappUTuuBrmqaVE7rga5qmlRNe/cYrEUkHnF0usybg4iL0lvHl7ODb+X05O+j8VvKW7HWVUmG3e8KrC74rRCSpuHebeTtfzg6+nd+Xs4PObyVfyK6HdDRN08oJXfA1TdPKibJc8OOtDuACX84Ovp3fl7ODzm8lr89eZsfwNU3TtN8qy1f4mqZp2k10wdc0TSsnfLrgi8hDIvKziBy2b7FY9HkRkbn253eLSCsrchbHRP5oEUkUkVwRecWKjHdiIv9A+3nfLSLfi0hzK3Lejonsvey5fxKRJPvObV6jpPw3tWsrIgUi0teT+e7ExLnvKiKX7ef+JxGZaEXO4pg59/Z/w08isldEEjydsVhKKZ/8APyBI0B9oAKQDNxXpM0jwGpAgPbAdqtzO5g/HGgLTAVesTqzE/k7AqH2zx/2lvNvMntlbtzjagYcsDq3I/lvarcB+Broa3VuB859V+Arq7O6kL8asA+Isj8Otzr39Q9fvsJvBxxWSqUqpfKAZUCvIm16AR8owzagmojU8nTQYpSYXyl1Tim1A8i3ImAJzOT/Xil1fSfpbcA9Hs5YHDPZs5T9uxUIAbxpdoOZr32AEcCnwDlPhiuB2ezeykz+AcBnSqljYHwfezhjsXy54NcBjt/0+IT97xxtYxVvzmaGo/mHYvy25Q1MZReR3iJyAPgP8BcPZTOjxPwiUgfoDczzYC4zzH7ddBCRZBFZLSKNPRPNFDP5/wcIFZFNIvKjiDzjsXQlCLA6gAvkNn9X9CrMTBureHM2M0znF5FuGAXfW8bBTWVXSn0OfC4iXYDJwAOlHcwkM/lnA39TShWI3K65Zcxk34mxHkyWiDwCfAE0KvVk5pjJHwC0Bu4HgoBEEdmmlDpY2uFK4ssF/wQQedPje4BTTrSxijdnM8NUfhFpBiwEHlZKnfdQtpI4dO6VUptFpIGI1FRKecPiWGbytwGW2Yt9TeAREbEppb7wTMRilZhdKZV50+dfi8i7PnbuTwAZSqmrwFUR2Qw0Bywv+JbfRHDh5kkAkAr8jhs3TxoXafMov71p+4PVuR3Jf1PbN/C+m7Zmzn8UcBjoaHVeJ7I35MZN21bAyeuPrf5w5GvH3v59vOemrZlzH3HTuW8HHPOlcw/EAN/a2wYDKUATq7MrpXz3Cl8pZROR4cA3GHfOFyul9orIC/bn52HMTngEo+hkA89albcoM/lFJAJIAqoChSIyCmNGQGaxHXuIyfM/EagBvGu/0rQpL1hN0GT2J4FnRCQfyAH+pOzfzVYzmd8rmczeF/iriNgwzn0/Xzr3Sqn9IrIG2A0UAguVUinWpb5BL62gaZpWTvjyLB1N0zTNAbrga5qmlRO64GuappUTuuBrmqaVE7rga5qmlRO64GuappUTuuBrmqaVE/8FK0rDyyqhOgkAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"find_nat_freq(45)"
]
},
{
"cell_type": "code",
"execution_count": 329,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 60-element G string (Hz)\n",
"1st natural frequency = 196.0568723200582 \n",
"2nd natural frequency = 391.9837461956978 \n",
"3rd natural frequency = 587.6507093798888 \n",
"\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"find_nat_freq(60)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"60 nodes are needed to converge."
]
},
{
"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": 330,
"metadata": {},
"outputs": [],
"source": [
"def find_nat_freq2(N, mu, T, L = 0.64):\n",
" #modified version of the above find_nat_freq function to remove the graphs and allow the text to display strings besides g\n",
" x = np.linspace(0,L,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[isort]\n",
" v = v[:,isort]\n",
" freq = e.real**0.5/2/np.pi\n",
" print('1st natural frequency =',freq[0],'\\n2nd natural frequency =',freq[1],'\\n3rd natural frequency =',freq[2],'\\n')"
]
},
{
"cell_type": "code",
"execution_count": 331,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 60-element high E string (Hz)\n",
"1st natural frequency = 329.6628732000454 \n",
"2nd natural frequency = 659.1071584965982 \n",
"3rd natural frequency = 988.114412923931 \n",
"\n",
"Natural frequencies of 60-element B string (Hz)\n",
"1st natural frequency = 247.0748304582595 \n",
"2nd natural frequency = 493.98583425108916 \n",
"3rd natural frequency = 740.5692933408752 \n",
"\n",
"Natural frequencies of 60-element G string (Hz)\n",
"1st natural frequency = 196.05578023030412 \n",
"2nd natural frequency = 391.98156274026314 \n",
"3rd natural frequency = 587.6474360065606 \n",
"\n",
"Natural frequencies of 60-element D string (Hz)\n",
"1st natural frequency = 146.89843350538408 \n",
"2nd natural frequency = 293.69946380512823 \n",
"3rd natural frequency = 440.30575227830343 \n",
"\n",
"Natural frequencies of 60-element A string (Hz)\n",
"1st natural frequency = 110.01731758315894 \n",
"2nd natural frequency = 219.96168653677302 \n",
"3rd natural frequency = 329.7602066010026 \n",
"\n",
"Natural frequencies of 60-element E string (Hz)\n",
"1st natural frequency = 82.44585723617439 \n",
"2nd natural frequency = 164.8370475123807 \n",
"3rd natural frequency = 247.11894011639782 \n",
"\n"
]
}
],
"source": [
"print('Natural frequencies of 60-element high E string (Hz)')\n",
"find_nat_freq2(60, mu = de, T = Te)\n",
"print('Natural frequencies of 60-element B string (Hz)')\n",
"find_nat_freq2(60, mu = db, T = Tb)\n",
"print('Natural frequencies of 60-element G string (Hz)')\n",
"find_nat_freq2(60, mu = dg, T = Tg)\n",
"print('Natural frequencies of 60-element D string (Hz)')\n",
"find_nat_freq2(60, mu = dd, T = Td)\n",
"print('Natural frequencies of 60-element A string (Hz)')\n",
"find_nat_freq2(60, mu = da, T = Ta)\n",
"print('Natural frequencies of 60-element E string (Hz)')\n",
"find_nat_freq2(60, mu = de2, T = Te2)"
]
},
{
"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": 332,
"metadata": {},
"outputs": [],
"source": [
"def find_nat_freq3(N, mu, T, L = 0.64):\n",
" #another find_nat_freq function modified to return to frequencies instead of print them\n",
" x = np.linspace(0,L,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[isort]\n",
" v = v[:,isort]\n",
" freq = e.real**0.5/2/np.pi\n",
" return freq[0],freq[1],freq[2]"
]
},
{
"cell_type": "code",
"execution_count": 333,
"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": 333,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#create our audio signal\n",
"signal = np.zeros(18)\n",
"signal[0],signal[1],signal[2] = find_nat_freq3(60, mu = de, T = Te)\n",
"signal[3],signal[4],signal[5] = find_nat_freq3(60, mu = db, T = Tb)\n",
"signal[6],signal[7],signal[8] = find_nat_freq3(60, mu = dg, T = Tg)\n",
"signal[9],signal[10],signal[11] = find_nat_freq3(60, mu = dd, T = Td)\n",
"signal[12],signal[13],signal[14] = find_nat_freq3(60, mu = da, T = Ta)\n",
"signal[15],signal[16],signal[17] = find_nat_freq3(60, mu = de2, T = Te2)\n",
"\n",
"#set up audio data\n",
"r = 20000\n",
"t = np.arange(0,2,1/r)\n",
"sinewave = 0\n",
"for i in range(0,18):\n",
" sinewave += np.sin(signal[i]*2*np.pi*t)\n",
"\n",
"#play audio\n",
"Audio(data = sinewave,rate = r)"
]
},
{
"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
}