{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Frequecy Response of a Mass-Spring-Damper System
to Harmonic Seismic (Position) Inputs

\n", "

MCHE 485: Mechanical Vibrations

\n", "

Dr. Joshua Vaughan
\n", "joshua.vaughan@louisiana.edu
\n", "http://www.ucs.louisiana.edu/~jev9637/

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "\t\"A
\n", " Figure 1: A Mass-Spring-Damper System \n", "

\n", "\n", "This notebook looks at the frequency response of a simple mass-spring-damper system like the one shown in Figure 1.\n", "\n", "The equation of motion for the system is:\n", "\n", "$ \\quad m \\ddot{x} + c \\dot{x} + kx = c \\dot{y} + ky $\n", "\n", "We could also write this equation in terms of the damping ratio, $\\zeta$, and natural frequency, $\\omega_n$.\n", "\n", "$ \\quad \\ddot{x} + 2\\zeta\\omega_n\\dot{x} + \\omega_n^2x = 2\\zeta\\omega_n \\dot{y} + \\omega_n^2 y$\n", "\n", "For information on how to obtain this equation, you can see the lectures at the [class website](http://www.ucs.louisiana.edu/~jev9637/MCHE485.html)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np # Grab all of the NumPy functions with nickname np" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# We want our plots to be displayed inline, not in a separate window\n", "%matplotlib inline\n", "\n", "# Import the plotting functions \n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Define the System Parameters\n", "m = 1.0 # kg\n", "k = (2.0 * np.pi)**2. # N/m (Selected to give an undamped natrual frequency of 1Hz)\n", "wn = np.sqrt(k / m) # Natural Frequency (rad/s)\n", "\n", "z = 0.25 # Define a desired damping ratio\n", "c = 2 * z * wn * m # calculate the damping coeff. to create it (N/(m/s))\n", "\n", "wd = wn*np.sqrt(1-z**2) # Damped natural frequency (rad/s)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can define the normalized transfer function as:\n", "\n", "$ \\quad G(\\Omega) = \\sqrt{\\frac{1 + (2\\zeta\\Omega)^2}{(1-\\Omega^2)^2 + (2\\zeta\\Omega)^2}} e^{i \\phi} $\n", "\n", "where\n", "\n", "$ \\quad \\phi = \\tan^{-1}\\left({2\\zeta\\Omega}\\right) - \\tan^{-1}\\left({\\frac{2\\zeta\\Omega}{1-\\Omega^2}}\\right)$\n", "\n", "Let's plot the magnitude and phase of this for a few different damping ratios" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Set up the normalized frequency range\n", "w = np.linspace(0,20,2000) # Normalize Freq, 0-20 with 2000 points in-between\n", "\n", "# Define the normalized transfer function for several different damping ratios\n", "z = 0.0;\n", "mag_normal_un = np.sqrt((1+(2*z*w)**2)/((1-w**2)**2+(2*z*w)**2))\n", "phase_un = (np.arctan2(2*z*w,1) - np.arctan2((2*z*w),(1-w**2)))*180/np.pi\n", "\n", "# Let's mask the discontinuity in the undamped phase response\n", "# Let's mask the discontinuity, so it isn't plotted\n", "pos = np.where(np.abs(1-w) <= 1e-2)\n", "phase_un[pos] = np.nan\n", "\n", "z = 0.1;\n", "mag_normal_0p1 = np.sqrt((1+(2*z*w)**2)/((1-w**2)**2+(2*z*w)**2))\n", "phase_0p1 = (np.arctan2(2*z*w,1) - np.arctan2((2*z*w),(1-w**2)))*180/np.pi\n", "\n", "z = 0.2;\n", "mag_normal_0p2 = np.sqrt((1+(2*z*w)**2)/((1-w**2)**2+(2*z*w)**2))\n", "phase_0p2 = (np.arctan2(2*z*w,1) - np.arctan2((2*z*w),(1-w**2)))*180/np.pi\n", "\n", "z = 0.4;\n", "mag_normal_0p4 = np.sqrt((1+(2*z*w)**2)/((1-w**2)**2+(2*z*w)**2))\n", "phase_0p4 = (np.arctan2(2*z*w,1) - np.arctan2((2*z*w),(1-w**2)))*180/np.pi\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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WQyxrpAGBvy2GU9rydSx7oh2CT0eVEikzUhMz0w8zMy5TP0nj4Es15K5Ygfwt\nW5C/pS7idePj4xmqiFKFmemHmemHmRmXMPNsuPr6etnV1ZXtMoiIiMg8ws+Qm8fU74a8Xm+2S6A4\njI6ORjxv5r9wqCpaZqQeZqYfZmZcpm7SOCZNL5HGXYy1PYKTtZvhPXo0gxVRNBwrox9mph9mZlym\nbtLiXa+E0kfGMD6wtrY27Dn3y13wO53w9L6ayrIoSZEyIzUxM/0wM+MydZPGiQNq8Bw4gBObajH+\n6H9GvM7tdoc9JwoLAZyfKUpqiJQZqYmZ6YeZGZepmzTuOKCGabsd8swZuLvtEa/r6+sLe66g4Tbk\nrluHvKs2p7o8SkKkzEhNzEw/zMy4TL0ER7wbnVJ6yInA06+cRZFXOq+pqQl7znb3u2G7+90prYuS\nFykzUhMz0w8zMy5TP0njtlBqyL+6Hrnr16Og4baI11mt1gxVRKnCzPTDzPTDzIzL1F3KxMREtksg\nAPlXXIGVzz+HgltuiXhdb29vhiqiVGFm+mFm+mFmxmXqJo17d+ol2v50XCdNPdxTUD/MTD/MzLhM\n3aRZLKYekqed8vLysOemX3sNJzZdgfGfPZbBiiiaSJmRmpiZfpiZcZm6SePsTnXEsk5af39/2HOe\n1/sgXWcwvXt3KsuiJEXKjNTEzPTDzIzL1E0aJw6o4ew/fhMnazfDd/xExOuKisLP/jy/Thobb5VE\nyozUxMz0w8yMy9RdCsekqcH9/PPwnz4N75EjEa+LNO4if8sWWKqqYL3lphRXR8ngWBn9MDP9MDPj\nMnWTxr071SDHA7Nsha0w4nWR9qezrFmNFc89g6IPfCCltVFyuKegfpiZfpiZcZl65Dy3hVJDwR23\nA7k5yNuwIeJ14+PjGaqIUoWZ6YeZ6YeZGZcw87IF9fX1squrK9tlEBERkXmIWC809etOr9eb7RIo\nDqOjoxHPxzJDlDIrWmakHmamH2ZmXIZp0oQQDwkhtgshGoUQjbHcwzFpeok07kJ6vRi6bRucn/5M\nBiuiaDhWRj/MTD/MzLgM8bpTCPE4gCYppSP4swRQKqV0RbqPrzvVIP1+QAgIEfkJsN/vD7tsis/p\nxMkrrkROaSlWvcYtUlQRKTNSEzPTDzPTjnledwohtgN4eaZBC6qK1qABnDigAjk9jaGbb4Vzx6ej\nXut2u8OeO79O2mTKaqPkRcqM1MTM9MPMjEv7Jg1AM4D2Cw/Ma9jC4o4D2ec7dQregQF4enqiXtvX\n1xf2nCjyeD0dAAAgAElEQVQoQME77kDBXXemsjxKUqTMSE3MTD/MzLi0XoJDCFECoCT4+0YALgB1\nANpieZJWUFCQ3gIpKjkxs0aaLeq1NTU1Yc8JIVD+ve+mrC5KjUiZkZqYmX6YmXHp/iStEoHGrERK\n2S6l7ATQBuDJcDcEJxd0CSG6Tp06NTvgcnBwcHb/s9HRUfT09MDv92NychLd3d2YnJyE3+9HT0/P\n7Eya/v5+3p/k/Sdzc5F31VWYvvWWqPfn5eUpVz/vj3y/3+/Xun4z3j8+Pq51/Wa8f3h4WOv6zXh/\nrLSeOCCEaADQgXmTBIQQ3QhMJOiMdH9NTY3kY2J99PT0YPPmzdkug+LAzPTDzPTDzLRjmokDDgAI\n8WrTicBrz4i4d6deYtmfjmulqYV7CuqHmemHmRmX1k1alAkCUcekWSxaD8kznfLy8ojnz+z6Ok5u\nroNvZCRDFVE00TIj9TAz/TAz49K6SQuyCyEq5x2rBBB1ATTO7lSDjHHnh5l3/uFM2/fBPzoKz/7I\n11HmRMuM1MPM9MPMjMsITVpT8BcAQAhRB8AhpbRHu5GL/2Xf1NNP48SGjZj8/e+jXltUVBTxfE5R\nYIaonOBmw6qIlhmph5nph5kZl/bv+6SUnUKIEiHEQ8FD5VLKbbHcyzFp2ed+aS/k1BQ8fftReMcd\nEa+NNu6i8J3vhPfoUeRtuiKVJVISOFZGP8xMP8zMuMI2aUKITwEoTvH3uaSUKV/MSkrZHv2qhbh3\nZ/bJsTEAQM6SJVGvHRwcjPgfI9t9jbDdF9O2rZQh0TIj9TAz/TAz44r0JM2Zhu87nYbPTBi3hcq+\ngptvhnvPHlhv2hr12vFxvsbUDTPTDzPTDzMzLq3XSUsWN1gnIiKiDDPNOmlJ8cY4q5DUEMtKzdLn\ny0AlFKt4V9em7GNm+mFmxmXqJo1j0vQyswVHONOvvooTNZsw/qMfZ6giiiZaZqQeZqYfZmZcpm7S\nbDFs6k3pJaWMeZ202traiOe9Bw5Cjo3BvWdPKkqjFIiWGamHmemHmRlXQktwCCE2A2gAUA6gBOc3\nOncCGEBgnbKfp6rIdOHEgewb/cAH4RsewvLODogo69a53W4UFhaGPS9m1kkLzhil7IuWGamHmemH\nmRlXzE/ShBC3CiEeE0IcBLATwFIEmrJOAC0A2gDYg8dvF0L8QQjxeyHEJ9NQd0pwx4HsklLCvXs3\nvG8cAGJ4mtbX1xfxfH59PSwbN6JgW0zL5FEGRMuM1MPM9MPMjCvq7E4hxHoAzQg8IXtMSrkv5g8X\nohjA/Qg8detIxxppyairq5N2e9SNCShN/JOTOHHJZUCBFWsGDkW9fnJykn9b1Awz0w8z0w8z007M\nszsjvu4UQtyGQIP1KSnlmXirCN7zCIBHhBC3CSF2SSl3xvs56cJtobJLFBSg4M53IHf16piut1qt\naa6IUo2Z6YeZ6YeZGVfYLiX4BA1Syp2JNGjzSSmflFLuVOn158TERLZLMDUhBMq/+whKHv5yTNf3\n9vamuSJKNWamH2amH2ZmXGGfpEkpDwM4nOovVOmVJ/fu1Ess255Inw/IyYEQMT9NpjTiVjX6YWb6\nYWbGpf0G68mwWEz9j6+d8vLyiOellBh5370AgGX//V+ZKImiiJYZqYeZ6YeZGVdcg7KEEEuEEPcI\nIT4vhHhfmGs+JYT4ZHCZDqVxdmf2Sbc75mv7+/ujXjP9yiuY7u6G5ELFSoglM1ILM9MPMzOueJbg\n+DwCG6Q/jsCSG08IIXxCiM9deJ2U8hEEluLoTmWh6cCJA9nl3rsXx6trMP6Tn8Z0fVFRUcTzQgiI\n4DWSGw4rIVpmpB5mph9mZlwxve8TQnwdwHYAX0CgAXMisIDtNQA+LYT4IoBPSil/EbxlAHFMMc0W\njknLrmn7PmB6Gp433ojp+ljGXdjua4T30CGIkpJky6MU4FgZ/TAz/TAz44r6KCk4y7MOwHop5TeC\nszT3SSmfkFI2SSkvAbANwB3BxWtvTXfRqcK9O7NrZmeAnCVLYro+lv3pSr78t1j6ox9y4oAiuKeg\nfpiZfpiZccXyvm87gPsiLcMhpbRLKR+UUt6BwBO0+xHYgUBp3BYqu6xbb0Re7RUouP32mK4f5ytM\n7TAz/TAz/TAz44plx4F7pZRPZKiejKqvr5ddXV3ZLoOIiIjMI+ZXPbE8SYvcxWnMG8N+kaSO0dHR\nmK6THk+aK6FYxZoZqYOZ6YeZGZeppzdyTJo+PF5/TOMuJtqfwPHqjXDv2ZOBqigajpXRDzPTDzMz\nrliatMpEPlgIEdto8Cyy2WzZLsHUpM8XdT2zkXNu/OkPutCw60k4PGVRP9Ozfz8w5cZ0tz1VZVIS\namtrs10CxYmZ6YeZGVcsTdoZIcQ90S4KLnT7l0KIXUKITyGwpprSOHEgu4bfew+Gtt2BcOMipZR4\n6Cf78LJjFG6vHy2/2o+n+05F/MyZmaL+s2dTXi/Fzx3HYsWkBmamH2ZmXFGbtODitF+cv2jtjOAO\nBH9AYPHabinlTgQWvFV+DQTuOJA90uuFx26Hd2AACNOkdR12ou/YGZQW5eMjN6wHAPz4xSMRP9d6\n223Iq6lBwdatqS6ZEtDX15ftEihOzEw/zMy4Yh2Tdj+AvwruMPBycD20g0IIH4BHADwupbxUSvlU\n8HoJDSYcFBQUZLsE0/KfPQcAEMXFEGF2fvjRC0cAAPdduxYP3FSJRVYLXh10oe9Y2NVgkL/pcizv\n+D2sb78+5TVT/GpqarJdAsWJmemHmRlXTE2alNKBwNi07wIoRWDxWoHADgSVwadtAAJLdgBoBvBk\nyqtNMW4LlT05pSUouOtOLPr4AyHPn5mYxt6BEeTmCNx7dQUK8y1451WrAQB/ePVEJkulJFit1myX\nQHFiZvphZsYV07ZQACCldAHYEcOlnbqsqzYxMZHtEkxLCIHyR8Kvd/zSwCj8EtiyrhTFtsD2Xast\ngadvLw9wurkuent7sXnz5myXQXFgZvphZsaV8kdJkXYmUA337lTXCweGAQDXX7ps9thNtetRkJeL\ngaExjJwLP1BWTk+HnYxAmcU9BfXDzPTDzIwrbJMmhFifjmU0VNrb02KJ+UEiZZDfL/HSoREAwNsv\nWzp7fOWKZahbVwoA2DswEvJe6fHg1NabMfrR0K9RKbPKy8uzXQLFiZnph5kZV9gmTUp5GMCOVDVV\nwSU6dgFwpOLzUoGzO7PLH2a/uTdHxuGa8GDZEisuXlo0e7y/vx9XVwb+Y7TvSOgVXuT4OHyDg5je\nuzf1BVPc+vv7s10CxYmZ6YeZGVfE151Sym8AqBJC/EwIkdAL72Bz9ikEZoHuklIeSeRz0oETB7Jn\nov0JnKiuwWRH54JzrxwNNGC1FaUQ4vxKLkVFRdhUUQIA6Dse+q26WLwYACDHxvjKUwFFRUXRLyKl\nMDP9MDPjivq+T0r5iBDiMQDNQogtALoAdCDwRMx1YdMVfD1ahsBM0EoElu4oRaA5e3/qy08Ox6Rl\nz7TdDvj98B09uuBc76ALAFAbbMhmVFRUYJnHh9wcgcNDY5ic9qIwf+6/wiI3F0Uf/hD8k1NzGjzK\nDo6V0Q8z0w8zM66YBmUFJwM8CABCiKsAvB/AFwGUCCEqcX5NNBcAJ4B9AF4GsCP42lRJ3Lsze/yu\nQCOWU75wq6dXZ5q0tXObtMHBQVRUVKBqxSIcOHEOb5w4h80Xly64v+Tru9JQMSViJjPSBzPTDzMz\nrrhHzksp9yHQhGmP20JlT+G73gXf8AisW2+ac/zMxDQGRydgzcvBpSsXzzk3HhzDVrO6GAdOnMPr\nb50J2aSROsbDjDskdTEz/TAz4zL1oCzuOJA9hXfdiWWP/wy5ZXObrAMnA2uhXbpiMSy5c//1rK6u\nBgBsXFMMAHjjhDarvZjWTGakD2amH2ZmXFGbtEQnDOjA6/VmuwSa5+BMkzbvKRoAjI6Ozjk3MDQW\n9nMkZ+4qYSYz0gcz0w8zM65YnqRtC+7Z+TshxCfnr52m0rpn8eKYNPUcCjZpl6xY2KQNDg4CANYF\nl+V4c2QcXt/CV9bjP/wRjm/YCDeX4ci6mcxIH8xMP8zMuKI2acFlOL4A4HYEZms2CyHWXXBJc1oq\nywCbzZbtEkzLf/YspM+34PjBU+GfpNXW1gIAbFYLVpcWwuuTGBxduLWX59AhwOsNzCClrJrJjPTB\nzPTDzIwrltedxQCuBlAqpbxdSvnpeWudlQoh9gohviaEuDUduxSkCycOZIdvaAgnr9qC05/9/Jzj\nHq8fh4fHIARQFeJJmtt9fiuoyuWLAACO4YWvPHNLA+Pc/C6OWcu2CzMjPTAz/TAz44rldefXAXwq\nyp6c9Qg8besAcFoIMRrcXUBp3HEgOzz9b0BOTcF3/Pic40dGxuD1SawptaHIunDicV9f3+zvK5cF\nm7RTC5u0gjtuR95VV6HglptTWzjF7cLMSA/MTD/MzLhiWYKjKkqDdlpKmSOEqAPQAGA7gK9LKb+b\nkgrTiLM7s8N/OrCjQO68NdIiTRoAgJqamtnfV64INGkDQ+cWXJdXXY3lv/rvlNRKybkwM9IDM9MP\nMzOuWJ6khd4kcd55KaVdStkipbwEwJakK8sAbguVHdZrrob1lpth++AH5xyP1qRZrdbZ31cFX3ce\nHub6QCq7MDPSAzPTDzMzrli6lJIo55tCHGsRQnw+xHGlTEwsHHRO6Ze7ahWW/vA/UbD1xjnHozVp\nvb29s79fW16E3ByBwdFxuD0LJyCQGi7MjPTAzPTDzIwrlibtzLzZnHMEdyCYf+wwgKrEy8oM7t2p\nDinl+ZmdISYNAHP3p7Pm5eKiMhv8MrAUx4LPc7shuQ5e1nGrGv0wM/0wM+OKpUlrhcbLbERiscS9\nKxalyfA5N85MeLC4wIIVxaHHCpaXl8/5eWaG5/xFbaWUGLrzLgzf+c70FEsxm58ZqY+Z6YeZGVcs\n66Q9CaBKCPG+OD+7MrGSMoezO7NDTk7ObrA+49AFrzqFECHv6+/vn/PzTJN2OMTOA97DR+Dp64Oc\nnExFyZSg+ZmR+piZfpiZccU6cn47gCdibdSCa6uF/pNWIZw4kB3D9zbi1Nab57yOPBBlPBoAFBUV\nzfm5KsyTNCEEckoCQyn9Z7hWWjbNz4zUx8z0w8yMK6YuRUppB/AgAo3ad2JYsPbrALqTLS7dOCYt\n86TXC8+rr8HvdAJSzh4/P2kg/L9a88ddrJ+d4bnwSdqiT34CBXe+AznLl6eibEoQx8roh5nph5kZ\nV8yPkqSUbQg0ag8isGDtd+bvMCCEWCeE+BmA+6WUO1Nfbmpx787M87tcgN+PnPJyiLy82eOHImwH\nNWP+/nQVZTbk5giccE1iat4Mz8V//BmUf/cRCD4tzSruKagfZqYfZmZccY2cl1K2CSG6ADyOQLO2\nA8D8MURnANyWqgLTidtCZV5OeTls/+eDyLtg8cXJaS+Ojo4jN0dgfXAngVDGx+fO4rTk5uCiMhve\nHBnH0ZFxXLZKmx3JTGN+ZqQ+ZqYfZmZccU9vDL76rBJCNCDQpK1HYC01B4CO4IbsWuCOA5knhEBp\ny9zJwgNDY5ASWLesCPmW8E++qqurFxxbt7QIb46M4wibNCWFyozUxsz0w8yMK+F3QVLKTinlfVLK\neinlJcHN17Vp0ADAy3W0lDAzs/OSCK86AWB0dHTBsXXLAgNm3wyx84D/zBnIC8a9UeaFyozUxsz0\nw8yMy9QDdjgmTQ0zkwYui9KkhRp3sS74evTIyNzJA+69e3FiUy3GWltTVCUlgmNl9MPM9MPMjMvU\nTZrNZst2CaYj3W54jx2bc+xAjE/SamtrFxxbtzTwJO3IvCdpvhMnAb8f090LNsSgDAqVGamNmemH\nmRlX2DFpQohPAShO8fe5pJTfTfFnziGEeFxKeV8s13LiQOa5dn4RE489juXPPoO8qkr4/RIDUbaD\nmuF2u1FYWDjn2MXBJu3o6Di8Pj8suYG/d+QuWwYA8J8+nep/BIpDqMxIbcxMP8zMuCI9SXMiMFMz\nlb/S+iemEKIOQGOs13PHgcyb7u0FpIScCDz5Ou6axMS0D0sXW1G2yBrx3r6+vgXHbNbANlIen8Rx\n1/ndBfLrrkLBtgbY7rs3tf8AFJdQmZHamJl+mJlxhX2SJqV8IpOFpEhZPBdzdmfm+YeGAQC5ay4C\ncH482iVRnqIBQM0Fy3ZcaN3SIpw6M4Ujw+NYWx54siYKClD+H99PRcmUhHCZkbqYmX6YmXEZZkya\nEKJRStkZzz3cFirzFn3m01j8+c8ht6wUAHDw5FkAkRexnWG1hn7SdvHsuLSFOw9QdoXLjNTFzPTD\nzIzLEF1K8DWnPd77JiYm0lANRbL4wR1Y8hd/PvvzwRj27JzR29sb8vj5GZ5c0FE14TIjdTEz/TAz\n4zJEkwagUkrpiOVCIcR2IUSXEKLL5XLNTl0eHBxEf38/gMCaMz09PfD7/ZicnER3dzcmJyfh9/vR\n09MzuyZNf38/70/y/v5jLgDAYjke9f41a9aE/P6ZtdL6B0fm3O/zejH+1jGl//mNfv/y5cu1rt+M\n9xcXF2tdvxnvLygo0Lp+M94fK6H7Yp/B15ztF/wspZQi0j0z6uvrZVdXV/qKo4jOTnpw+9efgtWS\ngye/eNvszMx4OcfcuOsbz6DIakHnzltntyk785WvYqy1Dcs7fo+8jRtTWToREVGiYupRAM2fpAkh\nKhHYjiohnN2ZWf7JSXj275/9eWZT9crli2Jq0Gb+pjJfaVE+lhTmYdztxcg59+xx39AQICU8r72e\nZOWUqHCZkbqYmX6YmXFp3aQBaADQIIR4aOYXAAR/vz3azZw4kFln/+5rGGq4He6ubgDxjUcDgKKi\nopDHhRCzrzwvHJeWu3QpAMDndCZcMyUnXGakLmamH2ZmXHFvsK4SKWXb/GNCiGYpZUss9+fn56e+\nKArL8+prgd94PQCAAydin9kJABUVFWHPrVtahN6jLhwZHsPVleUAANt998Ez4EDBLTcnXjQlJVJm\npCZmph9mZlymfpTEvTszyzcSGNife1FgjbQ3gk1a9erYNraItD/dxUuDMzwv2B4qr2Yjlj76H8i7\n7LKE6qXkcU9B/TAz/TAz49L6SdqFhBANAHYEf/84gNZo66ZxW6jMWvLnfwbfyZOwXHQR3B4fDg+P\nI0cAl6xYFNP94+Phl9hYH+J1J2VfpMxITcxMP8zMuAzTpAUbsrgWs+WOA5llu+/8jl0DQ2Pw+SXW\nLytCYX5s/xpWV1eHPTc7Jo0L2iolUmakJmamH2ZmXKZ+3en1erNdgmm9cTzwqnPDqiUx3xNpfZmV\nxYWw5uVgdGwa5yY9s8f94+Ozr1kp8+JdE4iyj5nph5kZl6mbNI5Jy56Z8WjxNGmRxl3k5AhcHNy3\n880LXnmOfujDOHXjTfDzdUBWcKyMfpiZfpiZcZm6SbPZbNkuwTR8Tifce/diZvHk2SZtdexNWm1t\nbcTzoZbh8J85A3n2LHxH3oy3ZEqBaJmRepiZfpiZcZm6SePEgcw588W/wsj77oW3bz+8Pv/sQraX\nxbj8BgC43e6I59cFZ3gevmBcWu7KlQAAH18HZEW0zEg9zEw/zMy4TN2kcceBzJmeWSMtz4LDw2Pw\n+CQuKrNhUUFezJ/R19cX8fzFs5MHzj9JW/TgDhTecw/yN18Zf9GUtGiZkXqYmX6YmXEZZnZnIji7\nM3P8o6OAxQJLRQXe6A/sABDPeDQAqKmpiXh+3dKZMWnnn6QVbN2Kgq1b46yWUiVaZqQeZqYfZmZc\npm7SuC1U5pR89SuAJReisBD9szM7Y3/VCQBWqzXi+YryIuQI4PjpSbg9PljzchOul1IjWmakHmam\nH2ZmXKbuUiYmJrJdgmnYGu+F7b3vBQD0HTsDIPadBmb09vZGPJ9vycGaMhv8Ejg6ytmcKoiWGamH\nmemHmRmXqZs07t2ZeW6PDwdOnoUQQM2a+F53xrI/XdXywOSBQ6fOv/L0nToF39BQfIVSSnBPQf0w\nM/0wM+MydZNmsZj6bW9WHDh5Dl6fxPpli+KaNAAA5eXlUa+5ZEXgFerM7FEpJYbuvAvDd71rdvkP\nypxYMiO1MDP9MDPjMnWTxtmdmTH96qtwP/8CAOC1QRcA4PKL4nvVCQD9/f1Rr7kkuKTHQPBJmhAC\n0u2G78QJ+LnzQMbFkhmphZnph5kZl6mbNE4cSD8pJUY//FGMfPgjkF4vXg+OR9t0UUncn1VUVBT1\nmpknaQPBJ2kAYKlYCwDwD7NJy7RYMiO1MDP9MDPjMvX7Po5JSz//iZPwDw8jp7QUyM3Fa28FnqRt\nSuBJWizjLlaXFKIwPxfD59xwjU+jpCgfSx76S0w98ywsl1TF/Z2UHI6V0Q8z0w8zMy5TP0ri3p3p\n5xsODNjPq70Co2PTOOmags2ai3XLFsX9WbHsT5eTI2YnDwwMBZ6mFdx6C0oe/lsINuUZxz0F9cPM\n9MPMjMvUTRq3hUq/vE2bUPIPf4/ir3wFrwefotWsKUZujoj7s8Zj3CR9dvLAybEoV1K6xZoZqYOZ\n6YeZGZepX3dyx4H0E7m5KHr/+wEAr3UcAABckcB4NACorq6O6bqqFTPLcJyLciWlW6yZkTqYmX6Y\nmXGZ+kma1+vNdgmmMjOzc1NFYk3aaIybpM9fhgMAvIcPw3vkSELfS4mLNTNSBzPTDzMzLlM3aRyT\nljluj292p4HL18Q/aQCIfdxFVbBJcwyNwecPrI02/N57MHz3eyF9voS+mxLDsTL6YWb6YWbGZeom\nzWazZbsEQ5NuN85969vwDDjQd+wM3F4/qlYsQklRYgP4a2trY7puSWEeVhQXwO3145gzuPVXbg78\no6PwnTiR0HdTYmLNjNTBzPTDzIzL1E0aJw6k18R//RJnW76B8e99D/YjTgBA3bqyhD/P7XbHfO3M\nK88DJwOvPC2VlQAA//Bwwt9P8YsnM1IDM9MPMzMuUzdp3HEgvTz79gEActdWwH7kNIDkmrS+vr6Y\nr92wKtCk9R8PvGIt3rkTi//iz5FXU5Pw91P84smM1MDM9MPMjIuzOylt/GfPBn6z5Rq8+rvAwNa6\ndaUJf15NHA1W9erAuLf+44Ea8rfUIX9LXcLfTYmJJzNSAzPTDzMzLlM/SeO2UOlV/NWvYOnjj+Hg\nsnWY9vpxyYpFKLYlvqCs1WqN+dqNq5cAAPpPnIXfz43VsyWezEgNzEw/zMy4TN2lTExMZLsEQ8st\nK4P1+rfBfjj58WgA0NvbG/O1y5YUYNliK8amvHjLyZyzJZ7MSA3MTD/MzLhM3aRx787MmJ00sD65\nJi3e/emqg0/T9gfHpXkdh+F+/oWkaqD4cE9B/TAz/TAz4zJ1k2axmHpIXkZMeXx47a1Ak3TVxYmP\nRwOA8vLyuK7fGByXtj84Lu30X3wWI3/0QXjfeiupOih28WZG2cfM9MPMjMvUTRpnd6bPuW//E85+\n81uwH3Fi2uvHhlVLkhqPBgD9/f1xXb9xTXBcWrBJE4uKAL8fntdfT6oOil28mVH2MTP9MDPjMnWT\nxokD6eEbHsbZ5haMf/d7ePHACADg+kuXJv25RUVFcV0/M8PzjRNn4fNL5G3cCADwj3ALlUyJNzPK\nPmamH2ZmXKZ+38cxaekx3dUFAMjduBG7DwYWj73+smVJf2684y5Ki/KxsqQAJ11TeHNkHBfv2I6c\npUtR+K53Jl0LxYZjZfTDzPTDzIzL1I+SuHdnmljyAADO29+FY6cnsaQwDzUJ7td5oUT2pzs/Lu0M\ncpctw+IHdyCnOPlaKDbcU1A/zEw/zMy4TN2kcVuo9Cjc1oCV+7qx7/IbAQDXXbIUuTki6c8dHx+P\n+56Z5vC1wTNJfz/FL5HMKLuYmX6YmXGZuknjjgPpk7t8OXYfCo5Huyz58WgAUF1dHfc9tWtLAAC9\nR0+npAaKTyKZUXYxM/0wM+MydZPm9XqzXYJhTbi92HfECSGA66pS06SNjsY/4H/j6mLkW3IwMDSG\ns5Me+JxOnGttg/8Mn6xlQiKZUXYxM/0wM+MydZPGMWnps+fQCDw+icvXFKOkKPEJGh6/B6enAovh\nJjLuIt+SM7tFVO/R05h4vB1nH/4Kxv79+wnXRLHjWBn9MDP9MDPjMnWTZrPZsl2CoUgpMfrAxzHc\neD+efP0UAOCWmhVJfea37d/ER3/3YXzpxb9G6fqShD5jc3AR3VeOupC7YjkAwPPaa0nVRbGpra3N\ndgkUJ2amH2ZmXKZu0jhxILV8h49g6g8dGD84gBcOBJbeuKVmZVKfecXSWuTnWrFvyI6vvfTVhD7j\nyrUzTdpp5NdeCQgB/2mOUcsEt9ud7RIoTsxMP8zMuEzdpHHHgdRy794NAOi95b2Y8vhQs6YYq0sL\nk/rM29fdge/f8QPcf9n7cWX+VQl9xhUVJRAC2H/sDHwVa1H+4x+h9P/9fVJ1UWz6+vqyXQLFiZnp\nh5kZl6kXs+XsztTKq66G5dJLsbv67cAJD267PPKrzmnfNOynulG77ErY8sK/el6cvxgfqvkIJtdP\nJlTX4sI8VC1fhEOnxrD/+Fls3npjQp9D8aupqcl2CRQnZqYfZmZcpn6Sxm2hUit/Sx2K/9CB3SOB\n18iRXnVO+6bx1T0P42t7v4qON38f0+dbrdaEa5t95fkmX3NmUjKZUXYwM/0wM+MydZcyMTGR7RIM\n54WDw8FXnUvCvuqUUuJfev4JPcP7UGwtwbWrrovps3t7exOu68rg5IF9bzoT/gyKXzKZUXYwM/0w\nM+My9etO7t2Zer/edwwAsG3TqrDXPHW0E08PPoX8XCsevv4rWFkU/toLJbM/3Zb1ZQCAfW+ehtvj\ng/cnP4acnsaiT34i4c+k6LinoH6YmX6YmXGZ+kmaxWLqHjWl3Lt349TxEew5NAJLrsA7rlwd8rqj\nZ4/i33r/FQDwYO2nsb64MubvKC8vT7i+8kVWXLZyMdweP1456sLZb30LZ770t/CdOJHwZ1J0yWRG\n2Xec0UkAACAASURBVMHM9MPMjMvUTRpnd6bG5B86MNJ4P37xr0/AL4EbNyxHaYgFbH3Sh290fR1u\nnxs3X3QLblvbENf39Pf3Lzj25tkj+PLuL+HA6Tei3n9NVeA/ZC8NjCBv40YAgHvv3rhqoPiEyozU\nxsz0w8yMy9RNGicOpMbkEz+HBPCHvDUAgHfXrQl53fj0GI6dO4aLFl2ET2/+YwgR36brRUVFC445\nzjjQfaoL33i5GW5f5LWCrr0ksD3V3oFRFDQEG0QPtwZLp1CZkdqYmX6YmXGZukvhmLTUcL+8F/tX\nXYbjvjwsW2LFtWH26lxiLca/NPwb/v6mf0ShJf7100KNu7hxzVasW7IepyZOof3AYxHvr60ogTUv\nBwdPnsPUPfdj+TNPofDee+Kug2LHsTL6YWb6YWbGZeomjXt3pkbpN/8Rzz7wBQDAXVeuRm5O+Cdk\nq4pWRVwTLZJQ+9NZcix48MrPAACeONiO42PHw95vzcvFVcFZni8fPo28Sy+N+2kexYd7CuqHmemH\nmRmXqZs0bguVGmc3X4OnRyRycwTeV5++v9GNj4+HPF5TXoPb1jbA6/eirfffIKUM+xnXVJ1/5Unp\nFy4zUhcz0w8zMy5TN2nccSA1nth7FD6/xM0bl2NlSXLbQEVSXV0d9txHL38ARXlFsA9146WTe8Je\nd21w8sCeQyPw+cM3c5QakTIjNTEz/TAz4zJ1k+b1ctB4sqamffhF11sAgA+8bV1av2t0NPzTrxJr\nCT5a8wAA4NDpQ2Gvq1y+CKtLC3F6fBq9R09j5EMfxpmv7Up5rRQQKTNSEzPTDzMzLlM3aRyTljj/\nxARGPvIx/OKbP8LZSQ8uv6gYV1SUpPU7o427eMf6O/GPN38b9112X9hrhBC4qXo5AODZ147D/exz\nGGt7BP7JxPYFpcg4VkY/zEw/zMy4TN2k2WyJDWAnYOInP8XEU0/jMVfg/8MPXHfx7DmP34MfvP59\nvHDs+ZR+Z21tbdRrqkqqYLVEfo19c01g4/dnDzphufxywOPB9Msvp6RGmiuWzEgtzEw/zMy4TN2k\nceJA4sZ/+CM8e8nbcCJvMSrKbbgl2PgAwKOv/wBPHGzHbw//JqXf6XZHXgctVldcVIKyRfk44ZrE\nyQ88gJzSUuSWh142hJKTqswoc5iZfpiZcZm6SeOOA4kTm65A+9sDrxU/flMVLLmBf5UOnzmMXw78\nArkiFx+q+UhKv7Ovry8ln5OTI7B1Q+CV5961V2HVa73Iu7wmJZ9Nc6UqM8ocZqYfZmZcpm7SOLsz\ncXs+9nmcsizC2nIbtm1aOXt8Ud4iVBVX4dNX/jGqy1I746imJnWN1Mwrz2f6T6XsM2mhVGZGmcHM\n9MPMjMsQO4wLIbYHf7sl+L9NUkpXtPu4LVRi3B4f/v25AQDAx28+/xQNAJbZluEfb/l2Wr7XarWm\n7LO2rCvDogILBk6N4fDQGNYvX5Syz6bzUpkZZQYz0w8zMy7tuxQhxHYpZVvw1w4A3cFfUU1MTKS3\nOIP66e43cdI1harli7Bt06qMfW9vb29C94Va3DbPkoPbLg88AfztK8fhP3cOPufppOqjhRLNjLKH\nmemHmRmX1k2aEGLBmg9SyjYAZUKIhmj3c+/O+Ey/9joG/urL+EHwKdqfvaM64hZQqZbI/nQnx0/g\nA7++D4/2/WDBuTuvXA0A+F3vCQx98EMYuvkW+M+dS7pOOo97CuqHmemHmRmX1k0agEoArSGaNUfw\nXEQWiyHe9maE9Hpx+o//BN8b8GDC48eNG5bhmuDq/ZlSXh7/9+WIXLh9bvz8QDsOn3HMOVdbUYLV\npYUYOjuF14or4B8dxdTTz6SoWgISy4yyi5nph5kZl9ZNmpTSDmBLiPFnlQg0ahFxdmfsJp54Aq+d\nlXj6shtgyRH40zs2ZLyG/v7+uO9ZbluOd65/N/zw4zeHfz3nXE6OwJ21gadpz11xKwDA/fwLyRdK\nsxLJjLKLmemHmRmX1k0aMNuozRJCNAJwSCk7Q10vhNguhOgSQnSNjo7OrtQ8ODg4+y/66Ogoenp6\n4Pf7MTk5ie7ubkxOTsLv96Onp2d2C47+/n7T3D8+OY3v3PQApBC4p24FKsps2P3qizh69GjG6rfZ\nbAndf7l7E9697j249aLbFtx/5fLA69pnpxfh7Pvuhe2+e5X8/1/X+/Pz87Wu34z3A9C6fjPe7/F4\ntK7fjPfHSoQaVK2r4GvPJwHcFsvszvr6etnV1ZX+wgyg9cmD+P5zDly8tAiPPvg2PLr/e/gfxy/x\n2S2fx80Vt2S7vKRs/95L6D3qws67L8d7tlyU7XKIiMjYYh7Mrf2TtHmaAdwXS4MGcO/OWPUfP4tH\nnz8MANh59+V46q3f438cv4Qlx4KLl1wc5e7USdf+dPdcHRh02773aMiZoJQ47imoH2amH2ZmXIZp\n0oQQDwFollJGHYs2g9tCRTfh9uKv21+Bzy9x37VrMZXfj9befwUA/Mnm/4v1xVHnZ6TM+Ph4Wj73\n1pqVKC3Kx8GT5/DK0Zj6e4pRujKj9GFm+mFmxmWIJi24mG37hQ1aLEtwcMeByM7+/f/D3+1sw+Do\nBKpWLMItddP4xsvN8Es/3r/hA7h17W0Zrae6OrU7GMzIt+TgvcHXnO27D+PM330N0932KHdRLNKV\nGaUPM9MPMzMu7Zu0YDPWNdOgCSFKYmnQAMDr9aa1Np1N/vo3+OWv9uLJxVWwWnLwf9+5HC1dX4XH\n78E71t2FD1Z/KOM1xTvgMh7vq69Abo7A0/3DOPofP8bpP/8LvvpMgXRmRunBzPTDzIxL6yZNCFEJ\noANAtxBCCiEkgNPBY1FnBHBMWngv/cMjaL3hwwCAz961EVM5xzDhncANa27EjisfhBCZW8R2RjrH\nXSwvLsBN1cvhk8BvrnkPvA4Hpl94MW3fZxYcK6MfZqYfZmZcWq/mGnx6lnC3YLPZUliNcQydnULL\n1k/C67fgnqsr8J4tF8EvV2N98XpctLgCOSI7vX1tbW3KPktKidbef0VRXhE+tPEjEELgg29fh6f6\nTuF3l96A9+x+AmXcNixpqcyMMoOZ6YeZGZfWT9KSxYkDC41NefC5H9nh9FtQt64Un70zMNYhR+Rg\n7ZKLs9agAYDb7U7ZZ0lIPPfWs3j8wGN4ZvBpAMCmi0pwTVU5JmUO/vdbP0Xh7dtS9n1mlcrMKDOY\nmX6YmXGZuknjjgNzuT0+/OWP9+HgyXNYW27D1+7fDEuuOv+K9PX1peyzckQOHtj0CQBAa++/4tT4\nKQDAx7YGZqs+/vooxt0cs5isVGZGmcHM9MPMjMtQi9nGq66uTtrtnMUHAK6f/xe+1OfDS55FWLbY\nirZPXotVJYUp+3wpJU68PoSx4XF4Jj3wTHnhnfbBkpeL3PxcWKy5KCqzYfGKRVi0vAh51oVv4icn\nJ1FYmNqadu39O+w5sRs15Zfj727YhRzk4MF/34tXjrrwmYZL8ZEbM7fEiBGlOjNKP2amH2amnZiH\naWk9Ji1ZOTnqPCXKJmfrI/jrPafRvfZKLC6w4Jsf3pLSBg0A+n53EM//296Yr1+0vAirN63A2z6+\nBQWLrQAAq9Wa0pqEEPiTzX+KN5z96Bt9Hf918Oe497L78PGbq/Bnj3bj0ecP467SaZSULoFlzeqU\nfrdZpDozSj9mph9mZlym7lImODAcZ98YwBdfOovutZtQtvoFbLr2d1hVlpvy71l1+XKsu64Cl2xd\nh413XIra925E3f1X4Mp7anD5OzfgslsrsebKlViychFyLDkYGxrHgaccGD50fmp5b29vyutaYi3G\n/637cwDAj/b/ECfGT+DaqqW4pqocY1NetD78fQzffTf8k5Mp/24zSEdmlF7MTD/MzLhM/SQtPz8/\n2yVk1dDZKXyu8wQOrq3G0kt/gZyi43hzzIJJ7wRseeFnvkop4XzThUH7caypXYlll5RH/a6ytSW4\nY+dNMdXl9/nheussps5OYdWmFbPHKyoqYro/XltW1OOeS+/Ffx/6JSY8gcb9j7ddhpcdu/HbDTfh\nHb1/wOIf/wSLPvHxtHy/kaUrM0ofZqYfZmZcph6TZuYN1g+ePIfP/ciOobNTWLPKCc/KH6KsoBxf\nuGYnqss2hrzn7KkxHHhqAAPPvwnXW2cBAGu3rMadf3NrJktPG4/Pg7zcvNmfv/zzV/HbV47jbY4u\n/H+5h1D+H9/PYnVERGQQHJMWCzPO7vSfO4fOvQ58/aVhTLh9uHJtCZo/cDOOTV6Bi5dcjEX5i+dc\n75ny4vCLR/HGkwM4/tqp2eMFi61Yf30Frnzf5Rmrvb+/P+T2J+6xafz2K0/Dujgfl9+1ARVXrUpo\nsd0LGzQA2HHrJXi67xR2V9Zjf8N7cEPClZtXuMxIXcxMP8zMuEzdpJlt4sDZl7rwD9/5DX637loA\nwO1XrMRfvWcTrHm5KCnaNHudlBKn+ofxRucABl44Cs+kBwCQm5+LyuvX4tKb12NN7UrkZHh5jqKi\nopDH/V4/XG+dgXtsGkdfPoaydSXYfM/lqLrh4qRqXFlSiE/cXIV/6TiAf+h2ov46HwryUj9ez8jC\nZUbqYmb6YWbGxdedJnndebB7P/7m+y/gcHkFLH4f/uyujWi8bt2cJ05+nx+9v9yP/o5DOHP83Ozx\n5RuWYsNtVai64WJYi9Qcxzd5Zgr9HYfw2q/ewMTpwCD/xcuLUPveGmxoqAq5pEcsvD4/Ptq6GwOn\nxvDRGyvx6YZLU1k2ERGZT8yvekzdpNXW1kqjz4rx+vx49PnD+P4zA/D4JVZhCrs+cSOq15YtuPbA\nUw48/a3AfpW20gJcekslNtxahdKK4kyXHdLg4GDUAbI+jw8HnnbglV/0zTaaBcVWXPHujbj8rssS\najJfHXThU999Cbk5At/ZWoZNV1bh/2/vzMPkqM57/Z6q3nv2Xbs0kkBIMsuIzRgQBoGXGF18LezE\nN3FCHCSb2PGSGGKTOHEch8i+BO9BEHAS42tAIraxwTZiszFgBCO0o22E9mX2rWd6rXP/6OqZnp7u\nmR5ppOma+d7nOU93VZ069VV91V2/Ost3zIry0zqHqUY+PhMKC/GZ8xCfOQ7pk5YPk31aqJ1HO/na\nUy/R6nmW0sVHuci9mi++9/0U+dxZ88+5fAYNH15KzXlVzGqYfs6bM0cjFAqNmsd0m1xw00LOv2E+\nB187ypYndtCyv53XH9nC1p/sZOkfnM/SmxfhL/Hlfdy5tSYfuXI2j/3+MF/56U6++dUvMevpJ1G+\n/MuYquTjM6GwEJ85D/HZ5GVK16RN1ubOQ8+8yHde2M6WeSfwV21HGRYu5eHe6+5lXunUiqCvtebY\n1pNsXr+dEzuaAXD5XKz4wtXMuXTmqPsf7z3OHc+tYUnlOziw9Ubebo7y3l3P8/krayn568+fbfMF\nQRCEyUfeNWmFVVVyjonHJ9fcjJ29YdbefR+3Nz3D7kufI1CzFQVcV72CB2560PECra2tbfRMGSil\nmHnxNFZ+7SZW3nMTsxqmEw/H6Tjcldf+JZ4SyrxlbG/dyuwlz+NS8KvF1/P8zpNjtmUqcjo+EyYW\n8ZnzEJ9NXqZ0c2c0Gp1oE8aFzlCU//fKQTZsOoxn0Vv4io5R0l7Ohccuo+bANGI9ccxvusHhXRaO\nHDlCZeXogXNzMW1xDdP+4XoivRE8efZNK/IU8dV3fY0v/e6LHOx9iztu+lO+/esmvlV/Ixe19DKv\nuui07ZkKnKnPhHOP+Mx5iM8mL9Lc6dDmTq01bzedYMPuTp7ecpxwNE5ZOMEy1zGmnXDhbh8UIeWz\nSvnAV1cQKHf2BLyWZU1Y2JTeaC/98X6q/FX8/YZtPLvjJHOqgjx8+5UEfVP6XWdEJtJnwukhPnMe\n4jPHIQMH8sGJAweisQQv/NeT/HR7M2+WzqGqL86SrgiL+hJ4eqNAcjonX4mX+VfPYcHyedSeX3Va\nwV0LjUgkgt8/MUKzyFNEkSdZa/allUs40NzLgeZe7l6/hf/70QZcBTbIolCYSJ8Jp4f4zHmIzyYv\nU7ombfHixXrXrl0TbcaoaK3ZevQUj275LVve0pgtQRa2h5nTGSEQH/Sfr9jLnCtmUv/O2cy4eBqm\na3IJh8bGRpYtW3bOjtdzqpcdT+1hzhUzmb6kdsi2o+193P4fr9ERinJTxx7uvu0avJdccs5scwrn\n2mfCmSM+cx7iM8chcdLyoaGhQW/evHmizchKIhZj2/Ob+F2Xi+cjvyAe3IIyLKI901j5xHWYttuC\nlQHmXTmLee+cRd3imoILmzGe9Pf3n9O3xW0/e4tXH24EoG5xDQ23LmVm2pRTO450csdDvyeqFbfu\neZ7P/ttnMadPO2f2OYFz7TPhzBGfOQ/xmeMQkZYPhdYnrbs/RuPb7bz89Mu80hyn3Z8MIlu55AcY\n7h7KjHn80aI/Zs7bFfS19TPn8hlUL6icFE2Z+XCu+13Eowne3LCDHb/YQzSUHGRSvaCChg+/gzmX\nzUQZihe2H+fu9VuxlMFtsSbW/Msd58w+JyB9ZZyH+Mx5iM8ch4i0fJjo5s4jB5rYsuc4R4552X+8\nm1cTcXSa76rCXVxT6+bqmy9j8cwiyv1lE2ZrIbBlyxYuvvjic37caF+UnU/vZduTbxHuigBQPruU\npR9YxMLl83j41V/yZMsP6Wtu4M8v+jB/co2zQ52MJxPlM+H0EZ85D/GZ4xCRlg8XX3yx3rJlyzk5\n1qmuLl7ZvoN9u9+m8+BJ3J2a0o5igr2DIRyeWlTOjEXVXDq9iCuqTBZfslDejtJoa2ub0GHmsUic\n3c/sZ+tPdhFq6wPAE3RTemWQx8t+SF9JL+GO83jf9D/lszddNGVqOEdion0mjB3xmfMQnzkOEWn5\nMN7NnQlL09wd5tjJTvY8/gqtx3rpC5sYVoKiPgtXfPh0TAkzAZVBpl80gxW3NVAU9I6bPcLZIRFL\ncOCVw+x4ag/Ne1qTKxU0zzrOm1e/QgQ/F3o/xldvfo+M+hQEQRAyEZGWD0uXLtU7duwYMY9lWYRC\nUXr6YkQMRUcoyqnWdl7b/jitsVb60HiMG2kNFXGyK0w8oTm/tZ+rjvYOKyvsixCuiOOu8TJrRgVX\nLl/GjAXTJnVn//Fk9+7dLFq0aKLNGELLvjZ2PL2HppcOkohZ7Fm5g/2V29HaoOLgBXznD79AybTq\niTZzwihEnwkjIz5zHuIzxyEiLR9mVM/Sd3zwb1DKRFkKpcGwDMxIMUYYTAvcVnLuLA38dnYxByp8\neMt3Uzr3mYFyeo5eS39Lsj9AZZGHOQbM23mMYi9Uzypl/vILWbiklmCZTMh9Jhw5coRZswpz2oT+\n7jBdx3uoWFDKvb//d15tTd4frs3v4//+yS3ULxx9ntDJSCH7TMiO+Mx5iM8ch4i0fJhTVq+/tPyf\nRs0XVxD1mOxeXIWeVUKpJ0yo71cEFFR7q7iy4UPMrqtiWpkfn9s8B5YLhc4zm5/h/t/+huOd7yJg\nmPzjhy/h2kU1E22WIAiCMPGISMuH2TNm6y/f9RU8dbW4PW5Ml4nf42da6QxK3AmKg27KZ1TiK5L4\nM4WA094WQ90hvvroG7x4LAzAqstn86kbz8NjKva/dJDyGaVULaiY1AMMnOYzQXzmRMRnjkOmhcqH\nkvIS/uKvbptoM4Q8CYVCE23CmAiWBLnn9mt55OWD3P/cPjZsOszrB9r49IIadt6/CYCSuiLmXzOX\n+qtmUzmvfNIJNqf5TBCfORHx2eRlStekFVowW2Hysvt4F//wxHYOtYbwxOP8UTiGrzlCtDs2kKeo\nKsCcy2cy94pZTFtSgylN54IgCJMRae7Mh3MZJ004c5weCygcTXDv3Q/w80A9qDg1S9dR1VzFpa3v\nJNhURrgzMpDXE3Azq2E6cy6bycxLpuEvdeagE6f7bCoiPnMe4jPHkbdIm9KxH6LR6ESbIIyBI0eO\nTLQJZ4TPY/Klr32c+wIHmNV2glDbRbRMa+ZXF/6Utjta+OA33sslq5ZSMaeMaF+Mpt8d4vn7Xua/\nP7aBjWt/O9HmnxZO99lURHzmPMRnk5cpXZMmzZ3OYjLNTxftDbF+yykeerURVbSLWNf5/MGSC/mL\n6+ZTWeyl60QPh14/yuE3jnFyVzPBygB/eP//clyftcnks6mC+Mx5iM8chzR35kNDQ4PevHnzRJsh\n5El/fz9+/+QaadvaE+E/XtjPk5uPYmnwkmDl0hr+5Kal1NhNnIlYAmUoRwY9now+m+yIz5yH+Mxx\nSHNnPoTD4Yk2QRgDu3btmmgTxp2qYi9/u3IJj6y+gsuP7SCCyfodbfzv+17knid3crS9D9NtsqX1\nTRpPvUHcio9YXqitjyc+9xRP3v0Mr/3Xm7z96uGBeUYngsnos8mO+Mx5iM8mL1KTJjVpjmGyvy3G\n9u1j630P8uPuYl6ZfxkahaHgyvOC7A/cA0CJp4SrZ1zD8pnXsajigmHNn13Hu9nwuaeJh4eKuWBl\ngOqFldSeV0X1wkqqF1TiCQyfS3a8mew+m4yIz5yH+MxxSHNnPkifNGcxVfpdWN3dHA4rfvjyQX69\n/QTxhIW/ajvFtdvA0z6QryZQy7Uzl3PreR/G7xr8gw73RDj5VgvNe1tp2ddG875WoqHYsOOU1BVR\nOa+C2vOrWPL+83B5xz9s4lTx2WRCfOY8xGeOQ0RaPixevFhLNbFz2LJlCxdffPFEm3FOaeuN8GTj\nUZ741RZaPUFc/hb8FXsort5PXPUAsPrCT/CB+ptzlqEtTefxblr2tnFqbyvNe1tpP9SJFbcG8qz4\nwjXMv3rOuNs/FX3mdMRnzkN85jhEpOWDxElzFlM5FlDPEz/huQc38KvpDWybuRhLgbvoOMWl7byr\n7npWLJnDsrkVuPIcXJCIW3Qe7aLt7Q7C3REueO9C3HnUpPW0hDi29STFNUHKZ5fiL/WNOOJ0KvvM\nqYjPnIf4zHGISMsHae4UnISOxYi89Dvaiyt5IVrM01uO09TcO7C9yAVXX1DH8sV1XLmgEr8nKbqe\nO/wsW5u3sLhyCVdMu4JyX8Vp2/Dcv/2O/b85OLDsLfJQOq2YkmnFlNQVUzKtKLlcV4y/bGQBJwiC\nMEURkZYPS5cu1Tt27JhoM4Q82b17N4sWLZpoMwoGrTX7TvbwzC9e5cXtxzhaPmNgm9dlcMncCq6Y\nX8mm8Pdo6k4265d6y/jv9z5y2uKp7WAH23++m44jXXQe7cra1y2Fy+fCW+5m/uVzufK2BhFsDkF+\nZ85DfOY4RKTlw4UXXqi3bds20WYIeXLkyBFmzZo10WYUHDoWo+d732f/0y/yillF4/Uf4q3ewf8A\nZfZTWfM2lbWnmFs2g9UXfZzp5f6coilmxUCD2xx59KfWmv7OMF0neug+2UP3iR66T/YOLEd6kjN6\nuDwmH/vhrbh9ozen9neH6T7RS1FVgEC5H2WIsDvXyO/MeYjPHIeItHyQ5k5hMqG1Rvf1YQSDtPVE\n2HSgjdf2t/L7rYfoVJ4heWtKfFw0u4yLZpdz0Zxy6muKMA1FX6yP2zd+nP5YH7NL5jC/bD7zS+cz\nt7Se2cWzKPIU521PpDdC14kefMVeSury22/9X/2C9kOdABgug0CZj0BFgECFn0C5n2CFf2A5aK/z\nlXillk4QBCchIi0fpCbNWcjb4ukR+vlTbL33+7zpm8auaeezd+El9EQSQ/IEXYpFM0o5b0YRu/VD\nHA/vRTP8v+HPlvw5/3vhh/I+9lh9tu3Jt9j34tv0toYId0VG3wGYtWw67//y9XkfQxgZ+Z05D/GZ\n48hbpI1/YCQHYVnW6JmEgiEUCk20CY4kePMf8M4PvJ/Lmg6AlcBcsJCDrSG2Hupgy+EO3ty0m2Zf\nKY2HOmk81Am8B2W8m5KyDupquvEXtRIzmwkl2ognRn6pi1txfnPkBVymm5lFs4j2Rsdk64UrL+DC\nlRcky4rE6esM09feR197P6H2fvra++nr6CfU3kdfR3I5n2ZUSIYieforz9N6oB1fiQ9/mRd/iQ9f\nqQ9/qRd/qQ9vsRdfsRdvsQdfUfLTE/CMXvgkQn5nzkN8NnmZ0jVp0twpCBD64SMc/vH/sKczxsEL\nLuXwuz/AW8e76QgNF1iGghkVAepriphfU0R9TTFzqgLMrAjg97h4/eQmvvr7rwzkv/0da7h5/spz\neTo50Zbmic8/TdvbHWPa77zr63n3Z67KK2+kN0J/ZxhP0IMn4Mb0mNIUKwhCJtLcmQ8SJ81ZSCyg\ns4vV34/yeFCmidaalu4Iuw618uaX13K4uJYj5TM4XlaHpbLHYqsKmMyo9uGqbES7m8Hs56balbxv\nyTV43WbWfXa3v8W/Nd6L1/RQ7a+myk7V/mpmFs9kQdnCcRU52tL0d4cJd0Xo7wrT3xkm3B1Ofu8K\nE+mJEu6NEumJJFNvlIXXzeOaT14xatmxcJxHbnuCaN/giFfDZeAJuJPJFm6egAdPcHBd/VWzqZxb\nPm7neKbI78x5iM8ch4i0fJAZB5yFRNWeGOIHDxJ56XfE9u3DuO46Ti2+lAPNPRxo7mX/oRYObtvH\nqeJq4mbuZscKn8m08gB1FUHqynxMK/MzrcxPh7Wbh/Z8g4ROZN3vzsv+lqtnXJOz3JgVY2/7Hrwu\nLzWBWko8JWd6uqeN1prn73uZln1tREMxIqHokFkdcjH9HbXc/M83jprPSlg8+42X6DnVi8vnxuN3\n4fK5cftduP1u3D5XMvkH13n8bmovqM4rUHEK+Z05D/GZ4xCRlg/S3OksZH66wkPH4/R857v0b3qd\nEy09dHzoo7Q2vJMjbX0cae/j8IkOTnZHSBi5RYIyIxQHeigvDRMsieD29qJc3Zgui/dM/ygLKmdR\nVeylIugZNqPCT/Y9wQ92PgyAS7n456v/hcWVS3IeKxIPs7NtJx7TS4mnhBJvCcXuYkwje03fmRKP\nJoj2RYmGYmmfg99j/TFmXzqD6gWj14JEQlF+9Of/QywcH5MNc6+YyXu+dN2o+ayExe/WbaKnQXsK\nWAAAHyVJREFUOYTb58LldeHymrg8Llzpy2mfbq+LuiU1YxKBwvgj/42OQwYO5IMMHHAWkUgEv98/\nekbhnKFcLko+91lKgNos20PNzfT941c4tfcQpyLQ84cfo2PpMk52hTnZ2c+Jkx2c7FJ0J6ro7hm+\nfyPHgGPJYwEVRR4qi71UFnkpD3hw+SuZ5llKVHdiGIpTHYoyo4+ygAd/lv5gT+x7gkf3/L9hxwm4\nAtQG67j7ir+nJlCT83zjVpwDXU24DQ9V/iqKRwlJ4vKYuDx+AmVnft96gx7+z0MfpPtkL7FwnFh/\njFh/nFg483NwWzwSZ8G18/IqP9wTYffGJrQ1thf3+qtmc+Nd146aLxFL8Mza39LbEsLlNjE9yeTy\nmJipZXfaOvuz/qrZeYdwScQSJGIJTLeJ4TKmTH9A+W+cvExpkRYOhyfaBGEM7Nq1i2XLlk20GcIY\n2H3kCMu+/z2qgaVZtifa2+m8++9oPXiMlphB9LbVdJ+/lJaeCK09EU41HeHU/sN0BMro8hfT1hul\nrTcKpCu6wfAbX/z9EeAIkJx1oSzoodzvoizopTToQXnrmOa6iJjqIa5DRHSIcCJEX7yPw92HaA11\nUO2vzvlw//HuH7F+7+MAuAwX9y7/JvNKc4ugIz2HeebgM7gMF36Xn4DLj9/lx+8KUBeso75s/piu\np7fIS/UC75j2yZdAmZ+PfH8ljb/ZzNzZ84hH4nZKEI/EiaV9T61PxBIsuHZuXuVHQzGObT1JIpq9\naTsXzXtbuelvl4+ar78rzON/+XPCPYOhWwyXgekyMNwGpsu0P40BEefymly48gLmvXP2qOVrrTnw\n8mFCbX3JcnOUOfhp4PKYlM4oOetiUf4bJy9TurmzoaFBb968eaLNEPKkv79f3hYdxpn6zOrpoff7\n/05sfxOxcITEpz9L5/S5dISidISitLyxjZO/fJZuXzFd/mJC9efTHSihoy9KJJZvTbmFMqOgFdry\n4jYVxX43xT43JX43xT4XxX43Qa+LiHmItxO/Ik4fbsPDLTM/TU2wiqDXlUye5KffY2IYige23c8v\nDvw855H/7bpvsqBsYc7tm068xqN7foypTOqCdXzyor8k4A7kzN8X62Nb61ZMZeIzfXhdXnymD4/p\nodRbht81ui/O5u8s3B2htzWUrPGKJojHLBLRBIlonHjUGlifiCWIRxNYcYsF18ylct7oAyti/TGe\n/NIzdB7vwYpbefUHBFh43Tyu/9y7Rs3XfbKHH6/5WV5lprP4vQvzGngS7Yvy1Jefo9cWgYZpJ5ey\nP420T5UUhh6TJe87j/IFpaP6TGvNwdeODojMkco2XAaGkRSflfXlGGZ+Tana0mitUYaaMrWYp4n0\nScsH6ZPmLKTfhfM42z7TWhPdtInE4SPoSAT/ypsxSpKDB/qjcZo3beHgP/wzXaEoPf4SrI/9GeG5\nC+jpj9ETjtOx/yCdTYfo9Qbo9QYJBUuJ6fF5uAQ8JkF/FHfJHtzuKC5PHNMVR5kxMKJ4DB/v8K2i\nyBvE7zbxe0y89qffnfz+wsnHeeHEkwNl3nvtt1lYkbv27d+3fo9fvv101m1e08u3r/8e04LTcu7/\n+slNbNj7OIYyqQ3U8omL7sDn8uXM3xFu5/WTr2MqA7fpwWN4cBkuXIaLmkAN04tm5Nz3bKMtjZWw\nhV/cwopZJOLJZcv+1Jamqr4CM8fo4yHlac3Op/fSdaJnYP+hn5Z9nMTAcbSlueiDizn/+tFrTPs6\n+nnsjieHjA7OhwXL5/Luz1416u+s63g3j37yyRHzZGPRjQtY/qkrR83X3xVmw2eeoq+jHwDDVCjT\nwDDsT1Ml1xnGwDbTZXDJrUtZuHz0JnkrYbHpkS1JkZlR7kD5hoGyj5MSnfXvmkNJbVFe59rS1Eao\nNVm+MtRgMlXyeEbquMn1pssYU01pSm+pMSjYKS3SZHSns5ARTM6jUHym43GIxVAZtQ1WVxehR35E\n4sQJsCyKP/0pYlU1AyKu9fevc+Le79CLi36PD/VHf0x09lxCkQR9kThde5vo3v82/W4/fR4fkapa\n+g03fWNs0hvBckxfG8qMoeNeEpEKTEPhs8Wcz23gQeMxwOt1Q7CZHu+rYERAxdEqhiaKpeJ4jSDX\nltxBsacEj8vE6zbwuAy8LtP+NPj18Ud4pfnXA0f/2pXfYl7ZHFymgds0MDPmUv3Om99i46Fnclr/\n/RvuZ2Zx7kj4P93/E/5r5w9QSlEbqOVfr/kGpd7SnPm3tmzlF01PopTCbbgHBKHLcFEbqON/zb9l\nxEEgXZEuNjc3AlAbqOWCisUjPmC11pwInQDAVCYuw8Q0XJjKxO/y4xphQMzpEI/EifQmRwVbiWRt\nYGLgux5Yl/rUGqYvreGt/W+N+jvTlmbbz96i+1TvkDKGlR23sCyNTlho4KJbFlN/1ejNweHuCD/5\nwi/pPtVLlslKcrL4fedxzScuHzXf6YrMBdfO5Ya/vnr08k/08Ognxl5TuuT953H1mtHt7+8Ms+Fz\nT9HX3s+an/2xiLR8kDhpzkJiATmPyeAznUigQyHQGqN0qICwurvp2/AEVksLGAbBj38cs6Icy9L0\nRxN0vPEmJ+/5OqG+KP2+IO5P/RXxWbPpjyYIxxJ0b9pM5/MvEnF5iLi86KuuJlZTN7A9dKKZvrYO\nIi5vMo/XTyL/lpLTwMLlb0GZMay4n0R4qO9MpXC5FG5btLn9LajiLRhmDGVaGKYFKoFSFi6KmB67\nBa/pw2UmBaHbVAOCz20aHI6/yM7wzwCNRwX5YO3fUeqtxGUqXEZSFCa/K0zD4OljD7O5/cWc1v/T\n5fcxp3Rucj8jeSzTUAPi8lub7+O5w88O5P/eDf/OrOLcAuTBbQ/w8wPZH9zF7mK+ff33qPTnvr9f\nOPw8j+99FICaQC13XfbFEZurt7Zs5akDP0drjWmYGMrAUAamMqn21/BHiz6aVYSmfmcnQid4+dhL\naKDGX8O1M5ePKEJDsRDbW7eBZsjxDGVS7a9metH0nPtCUsS29rdgaU2Jt2SgOV1bekDoWQmNtpKf\nVsIiHo8nB6ckABSl04pRRn739ImdzfQ09w4pM3UMK2EN1J4m12s0moXL51Exu2zUshOxBK8+3EhP\nSyi5b+ocrGS5OpFaHkwAF39oSV41gf3dYf7n87+ktyU09USaUmo10G4v1mutv57PftLcKQjCRKK1\nJrZzF1Z7O8rjxnPZZShz8CGcOHmS3v94CKurC+XzUfzZz2CVltMfs0Ve41ba7vsWkb4wcX8A7+c+\nT2L6TCLxBNG4Rc+rm+j6yZNETTcxlxtz5S0kZswkGreIxi16d++lb+9+YqabqOnGmr+QeFExkbhF\nJJ4g0tNHLBIlbriIudxn6yqASoA2gFGaxlUMT/ExlIqDslBGwhaFCax4gEjnArJ191FoXIbCXdSM\nr3I7yrBQiSBG+3JcCY2pNC63C7fXYwtDA5ehCHt30u19Ea3ioDQoC00CsHBRzCL9CXxGEYahMJSy\nBSED3/fFnuTt2Iu2DQbvLft7il3VGLZwNJUa/G4oftP2n+zpfSXn6X/yvH+lxj9jIL85cFwwDYMf\n7fsur7e8NJD/ny7/JjOKZg3YZyjsT4VScP/2b/Pi0edyHu/+FQ+OKNQe2v4gP2v6KZBsTv/+Deuo\nDlTnzP/4nsf40Vs/HJgXWKEwVHIUbo2/hq8vv3fEWIfPH36O9Xsfw9Kaan81X7ri70YUvW+cfJ2f\nNf0ES+s0AWqgUNQEavj4O27HbeS+r/d37uPZQxuxtKYmUM0HF34IU+WuqT3We4yXjv4WjbbPTaGU\ngYGiKlDNtTOSA2CmVHOnLdDQWj9gLzcAa7TWa0bbd+nSpXrHjh1n2UJhvNi9ezeLFi2aaDOEMSA+\nm3gSJ09idXejfD5cs4fWGll9fYR/9Wus7m6MYBD/zR9gz8GDAz6LHz1K7wMPYnV1o4IBAp//PFZJ\nKbGEJpaw6Nu6nbb7vkUs1E8iEMR/513oumnEEhaxhEXo1U10PPyfxDXEPT68q1fDzNmD2xvfpPe3\nvyNumMQNF+YNK9C1dcQti3hCE9nfRHh/E3HDxFImatEidFk58YRF3NLEWlqJtnUktxsGVnkFCbeH\nhKWJJzTxWJz4Wa15HA2N4elBqThW3I9OjDIgw4jhKTqaFKDKIilgLZTSJGJBYj2zGKnPuentwFe+\nB1QCKx6kv+WiEfO7g8fwV29NHktZoDRKWSh0cv9jN2IkFAagDIXhcg0RfKpkF0b5y8l940W4Wz6C\niQ+VJghVLIrSGtPtIlzaSF/RC0BimFmGFWBm31/iVSWo1L4KjEQCQ2sMl8lxz69oMV4GQGFyMV/A\np8rsvHa/sZRtKHbHH+N4YlPO83930d2UuGpQSqEYPGaqjNd6/puD4cH9V1Z/mTL3tGQ+GGKnUooX\nWh9iX+i1nMf7s7lfo8o3nWsX1UwpkdaotV6Wsa5Jaz1qT80LL7xQb9u27ewZJ4wrR44cYdas3P1b\nhMJDfOY8xttnOhZDRyIo0xzWJ1BrTbypCd3biyoqwr1gwdDt4TDhF19E94ZQRUF8N9yAcg/WfCRa\nW+l79DGs3l6MoiKCf/anGEWDncRj+5vo/e53ifX2ootKCHzhC+iKSuIJi4Sl6d+2g87vfpd4f5RE\nUTHBv/lrdHUNcUuTsDR9b26h66H/JBGJooMBAn/5KdS06Vg6ub2/8U16fvwolmVheX34b/tz1IwZ\nA9vDb24h9MxGEiopIn23fBCmT8eyNAmtCW/fQbjxTSzDIKEM3FdfjaqtJWEfP7r/AJGmJixlkDBM\nzMWLoaycuKWxtCZ24iSxUy0kDANLKdS0GeiAn4RFsoyeHhKhEFoZaBS6qAjtdmNpjWWBFYthJRJY\nykArhc4x5dvZQQ8mpfOrSR0QvRZW3IdO5B7UAoCK4w6cGhSgWLY4tLBiRcT7c8dEBDBcITylb6OU\nRSJaRLR7HiOKZE8n3vK9tuhNPz+wYoOi+fdfec/UEGlKqTKgQ+uhw7GUUo3AXVrrZ7PvmUSaOwVB\nEIQzQScSEI+DYQwRkCkSp06h+/pQRUWY1UObArVlEdu2DR3qQ5UU4166dEgfMh0OE/7Nb9D9/RjF\nJXiXX4tyDQ5WsLq76X/qaXt7Mf6VN6O8g3H0Eq2t9D32OLq/H1VcTPBP/hgjMNg8GD92jNDDPxjY\nXnTHJ1HFJUkRpyG6v4nudQ9ghcPo4hKCn/kMqqwMS2u0hvBbu+m5/wGsSARdVETR5z6HqqqyRaAm\nsmMn3eseIBGJQmp7TQ2WTgr08Nbt9Dz8A6xoFB0MEvz0X2HU1WJpsLQmsnU7PY88ghWLowNBgmtW\nY9TVJbdbmsj27fQ+vgErHgefn8Btt2FMq0On7N++g9CTP0dbFng8+D/6UVRdHaTK37GT/o0bkwLW\n5cJ/yy2oujq0TsqryM6dhF9+JbldGXjf9x6M2rTyd+8msvlNWwSD59prUTU1yf21Jrp/P9Fdbw0I\nYPely1CVVXzjow1TRqQ1AM9prcsz1m8ENo7WN01q0pyF1Mo4D/GZ8xCfOQ/xWW50NAqJBLhcWUW0\n1d2NjkZRPt+QWtgUiZMnkyI2m8hO1QSHwxglJcO6EwyI8HAYo6QU1wWLUiJ8ykwLVcHggIF0OoGs\nQ27sPmyr7cWIUko6pTmHKqB1oo0QxoT4zHmIz5yH+MxZ7NBaZ5uEZRhOF2ljxh5gkBpk8IbW+tIJ\nNknIE/GX8xCfOQ/xmfMQnzkLpVTe/awmQ/j2iizryoC2c22IIAiCIAjCeOF0kfYGSUGWSQUgk3IK\ngiAIguBYHC3StNadwAF7lGc6ZaON7LR54CyYJZw9xF/OQ3zmPMRnzkN85izy9pejR3fCwECA+Vrr\nu+zlvIPZCoIgCIIgFCqOF2kwINQOkGz6zHtaKEEQBEEQhEJlUog0QRAEQRCEQkUpVU+yEimfrlgD\nTLkQHKc7GbswcdhN2F/UWt860bYI+ZGaUxdITdl2l92HVChQbJ+l+vfOB9ZqrQ9MoElCniil1sv/\nY8HTADxo96HvJDnw8S6t9YiDHKeUSEubjH2DvdyglFon/dcKE1ucfcRerJ9IW4T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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's plot the magnitude of the frequency response\n", "\n", "# Make the figure pretty, then plot the results\n", "# \"pretty\" parameters selected based on pdf output, not screen output\n", "# Many of these setting could also be made default by the .matplotlibrc file\n", "fig = plt.figure(figsize=(6,4))\n", "ax = plt.gca()\n", "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n", "plt.setp(ax.get_ymajorticklabels(),family='Serif',fontsize=18)\n", "plt.setp(ax.get_xmajorticklabels(),family='Serif',fontsize=18)\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "ax.grid(True,linestyle=':',color='0.75')\n", "ax.set_axisbelow(True)\n", "\n", "plt.xlabel(r'Normalized Frequency ($\\Omega$)',family='Serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel(r'$|G(\\Omega)|$',family='Serif',fontsize=22,weight='bold',labelpad=10)\n", "\n", "plt.plot(w,mag_normal_un, linewidth=2, linestyle = ':', label=r'$\\zeta = 0.0$')\n", "plt.plot(w,mag_normal_0p1, linewidth=2, linestyle = '-', label=r'$\\zeta = 0.1$')\n", "plt.plot(w,mag_normal_0p2, linewidth=2, linestyle = '-.', label=r'$\\zeta = 0.2$')\n", "plt.plot(w,mag_normal_0p4, linewidth=2, linestyle = '--', label=r'$\\zeta = 0.4$')\n", "\n", "plt.xlim(0,5)\n", "plt.ylim(0,10)\n", "\n", "leg = plt.legend(loc='upper right', fancybox=True)\n", "ltext = leg.get_texts() \n", "plt.setp(ltext,family='Serif',fontsize=16)\n", "\n", "# Adjust the page layout filling the page using the new tight_layout command\n", "plt.tight_layout(pad=0.5)\n", "\n", "# If you want to save the figure, uncomment the commands below. \n", "# The figure will be saved in the same directory as your IPython notebook.\n", "# Save the figure as a high-res pdf in the current folder\n", "# savefig('Seismic_Freq_Resp_mag.pdf',dpi=600)\n", "\n", "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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P4zLrSMDbkDSPRWyUj7goGyInvV6PxsZGNDQ0yPo5lZWVyM/Px86dO7F79260\nt7ejrq4u6HMbGxtlq40aMAkkJCQoXcKi8dl1n8O9a+/F1k9uAgBs7B6CqdP/lkTFxcWRKo2EgfIR\nF2VD5GI0GpGfn4/y8nKUl5fL+lm1tbXT9p7csWMHampq5jzPZDLJWRYAasAkQZPwIyc3MQ+fWPsp\nFF61CvFLkqEbc2Hw3Q6/xzud/ueHEeVRPuKibIgcGhoakJ+fH5HPMhqNs14zGAxBjbo1NDRgx44d\ncpQ1ifbQkQCthB95jDGUfrwYbzx8CBnvW+EcGoU2YfZ6bK2trSgrK1OgQhIMykdclI3yXvjBQZxr\n6gzpnGVlubjlO9uFuP5MNpsNJpNJ9lEvL6vVCoPBMO01vV4/WYv39zM1NDTg7rvvlvX2I0ANmCTo\nKUhlFF2xDE8lxSB9YAzv1B3HNZ8pnX1MUZEClZFgUT7iomyI1Pbt24eqqqqgjw92AnxVVZXPZspm\ns8FqtU57zduQWa1Wvw1YoOZMStSASYC2IlKGSqWCdUMm0t/sQMd7vT6P0Wq1Ea6KhILyERdlo7xw\nR5pEuf5Moc6rCmauViC+mihvQzZzZMyrrq5u2pwxOVHnIIGhoSGlS1i0Utdk4NnL9IjZ4XtOQUtL\nS4QrIqGgfMRF2RApmUwmv02PXAwGw6ylLrzf+2rOTCZTREa+vGgETAK0F6RylhgS8KwuBhcmfD8I\nQfvZiY3yERdlQ6Rks9lCnlM131uQpaWls163Wq1+56AZjUaYTKbJyfuHDx+GzWZDdXU1du7cKfnD\nA9SASUCjoX+MSllicC8BYrb6HoVMS0uLZDkkRJSPuCgbIqXS0lIYjUZUV1djz549QZ0z31uQALB7\n9+5ptxXr6+unNXbehmvnzp2zbj3W1tbCZDIFXW+o6BakBOgpyMjjnOPPrY+hhzcBAM77acDa2toi\nWRYJEeUjLsqGSK2+vh41NTVITU1FZWVlRFbCr6qqgslkQl1dHaqrq1FQUDCt0WpoaPDZ6NXW1mL/\n/v0wmUyorq6WpVbGOZf8ootNcXExp/kSkeUcH8GuZ++CVh0Hc+P90Gpi8PK3y6FSsWnHmc1mupUi\nMMpHXJRNZDQ1NS265T7q6upQU1MDk8mE9vZ2pcuRxJQc2VzHetEImARoDljkaTVxyEtcAufECAxp\nfXCOu3BxYPbCkfQDRGyUj7goGyKXnTt3or6+PqIT3kVEDZgEaC9IZWxId2+Vok/rAuB7HhjtZyc2\nykdclA3hQHP3AAAgAElEQVSRi3dj7L179ypdiqJo9rgEaCsiZWxI34AXzz4PVYIZwHqctw6hbOX0\nx5wdDocyxZGgUD7iomyIXCK1zpboaARMArQSvjLWp68HADjYBwCb8DkRv7CwMNJlkRBQPuKibAiR\nFzVgEhgfH1e6hEUpNc6ApUlLMYFRaOJ7YLZc+hv7+wdN+MuXnoLp6FnlCiRzslgsSpdA/KBsCJEX\nNWASoDlgyrlmyXXQsBhwV+y0EbCB3kHYOwfw7mPNClZH5kLzjMRF2RAiL2rAJJCQkKB0CYvWPWvu\nRe0N/42JkTSctw7Du6xK0S2rERMfA/upQXSd6FG4SuJPcXGx0iUQPyibyKHloBa2cPOjBkwCNAlf\nWemJOqQkxGBkbAKWQfdoZHxyHDZ8xD2H5d0/N9N/4ATldM5eOoSIgbKJDI1GQ3dRFrixsTHExMSE\nfB41YBKglfCVt9S7JdGUeWDFH10LdZwKF473oONol1KlkQBaW1uVLoH4QdlERkpKCqxWq9JlkHmw\n2Wxh3QmjBkwC9BSk8nJT4wEAF2zDk69pdbEovqMIAHCYRsGEVFRUpHQJxA/KJjKys7PR09ODCxcu\nwOl00n+nFhDOOQYGBnDhwgXk5uaGfD6tAyYBlYr6WKVlp7gbsC7b9NHIjR8pQtsLp9FzyoIP3j2P\nFZfT6t4i0Wq1SpdA/KBsIiMuLg5r1qxBV1cX2tra6Kn6BSYuLg5Lly4NawSMGjAJDA353giaRE62\n3jMCZh+e9vqJ91uxaed6vPn7Rhz+n6NYvmUJmCrorbqIzFpaWlBSUqJ0GcQHyiZy4uLisGLFiqCP\nb25upmyiQFgNGGOsBEC+5wsATABMnPNF+cw/7QWpvBy9+zbw1FuQgHs/u5QiPY7+rRXWsza0HzqL\nVdesVKJE4gPtNyguykZclE10CPreGWOshDH2W8bYBIAmAPsBVHm+9gNoYoxNMMZ+wxhbIUexotJo\naCBRadn6eDCVc1YDlpaWBk2sGmX3bgAAvPtYM8ZHJ5QokfiQlpamdAnED8pGXJRNdAiqAWOM/Rbu\npqsCAANgB3AGwBHP1xnPawzAFwG0M8Z+I0fBIqKnIJVnd51BenEt7LFvwOW6NIm1ra0NALDmhgIY\nlusx0OPAsadPKFUmmcGbDxEPZSMuyiY6BGzAGGPJjLHTcDdeDwPYASCVc27gnK/inG/2fK3inBsA\npHqO+SmALzLG3meMJcn9h1AaTcJXHmdjYIwjJvkUrI5La+rodDoAgEqtwrbPlwEATrx0SpEayWze\nfIh4KBtxUTbRYa57Z0YADQAqOef2uS7mOeYAgAOMsYcAVHuucdl8CxUZzQFT3prUQoAzaOJ70dnn\nQHqS+wmuqXMllpTk4OovbUVsQugL5hF50FwWcVE24qJsooPfoRvG2LcAVHHOvxhM8zUT59zOOa8A\nUM0Y+8J8ihQdrWKsvISYBGSM34DhixvQ3X9pBe+Z+9kV3byaJuELhPYbFBdlIy7KJjr4HQHjnD8s\nxQdwzh+R4joio62IxLAh6Ra8d/wDXOi7NBHf4XAEOIMojfIRF2UjLsomOtDkJQnQSvhiyPGsBdZl\nv/RQRGFhoVLlkCBQPuKibMRF2UQHWRowzzphiwatXCyGyQZsylIUFotFqXJIECgfcVE24qJsooPk\nDRhj7Am41wR7V+pri4rmgIkhO8U9Ejl1BIzmSoiN8hEXZSMuyiY6yDECxqZ8LQrh7AFFpJc9ZQTM\nu6FtcXGxkiWROVA+4qJsxEXZRAfJGzDO+S641wIrl/raoqJJ+GJIitMgQavG0OgE+ofHAABOp3OO\ns4iSKB9xUTbiomyiQ8gNGGPsC4yxlwJtN8Q5PxDO0hULFa2ELwbGGHJSpk/Eb21tDfp876gZiZxQ\n8iGRRdmIi7KJDuGMgFXDPbqVH+ggz96R32SM7WOMXR9WdQsEPQUpjmx9PFQaB14+9zI45ygqKgrq\nvH/85DXUfe05OB00ny+Sgs2HRB5lIy7KJjqE04CZ4L7FmM8Ye9zzdf/UAzyLuDbBvVF3JYAGxthf\n5l2toGgrInFkp8RBl/M2nr9Qi3e63oZWqw3qvLHhMVg/sOHwfx+VuUIyVbD5kMijbMRF2USHcDqH\nSgD1AGoA7PJ81Xr2fUz2HFPh+fVhzrkKwBYANzLG7phvwSIaGhpSugTikZUSh4mxRADAsd5jaGlp\nCeq8D322FEzF8N7zJ9F1okfOEskUweZDIo+yERdlEx3CacB2ALDDvTm3twH7PYBVAB70HGPw/PoQ\nAHDOjQB2A/jifIoVFe0FKY7MlDiMOXIAACesrUHvmZa2MhUld60DOPDKr97CuJPWdosE2tNOXJSN\nuCib6BBOA/YAgO2c8wc55096vioA3Ah3MwYAegDgnPdPOa8ec8wbW6g0mrn2NCeRkpUch3FHNsAZ\nTPZ26FJ0QZ9bds8GpC5Ngb1zAIf/h25FRkJaWprSJRA/KBtxUTbRIZwGLJVz3jzzRc55Q6CTPE9F\nGgIds1DRU5DiyEqJA3fFAqOZcHEXGo4G/L/lNOoYNa776jYwFcOxp9vQffKijJUSAGhra1O6BOIH\nZSMuyiY6hDUJ39dTjYyxGzD3CJc+jM8THk3CF0dGUhwYA4b7swEAnRMdIZ2fuTodxR9dC+7ieOVX\nb2KMbkXKSqcLfoSSRBZlIy7KJjqE0zk8CfdTjQ8xxu70fO2D+xbjNFMbNU+DZgq/VHHRHDBxxGhU\nMOhi4ex3z5FwaUNfJHfzx4uhX5IC2/l+vP1fRqlLJFPQXBZxUTbiomyiQ8gNGOe8EkAz3BPu93u+\nKgEYATzIGHsJAAdwBkCdp1H7AoAnAAR/P2gBob0gxZKVEofR/pX4TMG3sD3lhpDP12g1uOFfroRK\no0LrC+/jg8PnZaiSALSnncgoG3FRNtEhrHtnnPMyuJ9ofMTztYtzvplz/jCAdLibrwq41wF7EEAt\ngFTP91GHtiISS2ZyHACGFLYGrpHwsknPN2Drp0oAAK/8x1sYsg1LWCHxcjgcSpdA/KBsxEXZRIew\nH9/jnNf6eb1syrcHGGNNcM8Na+Ccnw3380RGK+GLJduzHVGPfQQ7riwM+zrFH12Lc8ZOdLZ04fCf\nj+LaL39IqhKJR2Fh+PkQeVE24qJsooMks8enLMA6i2dfyEc452ek+CwRjY/TRG2RZKa4G+Iu+wgs\nFkvY12Eqhuu/tg1ZhRlIXer3/+JkHuaTD5EXZSMuyiY6hN2AMca2M8YOM8YmAFg9r21ijJ1ijG2U\nrMIFgOaAiSXL04D12EfmPVciMV2Hj1XdhOKP0t5rcqC5LOKibMRF2USHsBowxtjjcD/1WAaAeb7A\nOT8C4EsADjLGlktVpOgSEhKULoFMkZXsbsC6+0dQXFyscDUkEMpHXJSNuCib6BByA+bZaHsX3FsR\n7QBw99T3PQuy/h5AtRQFLgQ0CV8s3luQ3fYROJ1OhashgVA+4qJsxEXZRIdwRsDuBrDDsxXRAc55\nnY9j/gGgfH6lLRy0Er5Y0hK1UKsY+hyjOHrsPaXLIQG0trYqXQLxg7IRF2UTHcJpwMo45wfmOCYf\nUbrqvS/0FKRY1CqGjCQtACAtbyUePlyFP7c+pnBVxJeiIppbJyrKRlyUTXQIpwFrYIzdP8cxu+Be\nmHVRoK2IxOO9DWkdHsMbHYdQd+oJjIzTSKVotFqt0iUQPygbcVE20SGczqEOwCOMsRcZY3cwxjYB\nAGMsyfNk5EsAbgDwuJSFimxoaEjpEsgM3on4R1rPYEXKSri4C6f63le4KjJTS0uL0iUQPygbcVE2\n0SHkhVg557WMsTIAD8A9Cd/L5vmVATByzn8qQX0LAu0FKR7vUhSu2CRcu+Q6dAyeR2JskuSf09HS\nhRMvncLln9mEpKxEya8f7WhPO3FRNuKibKJDuFsRVcA9Gf8sLi1D4f2q5pxvlqrAhUCjCXtDASIT\nbwM2MMZwx2V34i+37cfKlJWSf475SCfaD32A5753AMN2usUZqrS0NKVLIH5QNuKibKJD2JOXOOd1\nnPMCzrkKQAGAVM65inP+oHTlLQz0FKR4sjzbEbV3uleMVqvUsnxO6a71SFuZCnvnAF74wUGMDo3J\n8jnRqq2tTekSiB+Ujbgom+ggyexxzvkZzrl96muBtieKNjQJXzyZnjlgtmF512iLTYjFrd/djuTs\nRPSetlITFiKdTqd0CcQPykZclE10kKVzYIylAOiT49oiojlg4vHeguwbnpD9sxJS43HbD8qRmKFD\n14levPBDasKCRXNZxEXZiIuyiQ5+Jy8xxu4M85oGTJ+cH/VoL0jx6BNioNWoMDAyjiHnOBK08s7T\nS85KxO0/KsfT/1qPrlZ3E3bLv21HbEKMrJ+70JnNZvphIijKRlyUTXQI9FOpDgAP87psHucuOLQV\nkXgYY8hIjsN56xC6+0ewMkP+JxSTs5Nw+4934Jlvu5uw577TgJu/cz3ik2mhXn8cDofSJRA/KBtx\nUTbRYa5bkHYAB3x8ncGlpx7tAI7MeK3dc9yiQCvhi8l7G7Ingk8npuS4m7CkrET0nLLg6b3/wGAv\n/cfSn8LCQqVLIH5QNuKibKJDoAaMAyjlnN849QtABdy3Gfd4nno0cM43c85XeZ6IvBtAGoA98pcv\nhvHxcaVLID54F2PtntKA9Y30Ydwlb14pOUn46E9uhGG5Hrbz/XjqwZfQd84294mLkMViUboE4gdl\nIy7KJjoEasDsAKw+Xv8dgBp/C616NufeDaBq/uUtDDQHTEzeETBvA3Z+wIzPv3QfHjlWI/tn6wwJ\n+MhDO5BVmIHBi0M4VHtY9s9ciMxms9IlED8oG3FRNtHBbwPmGdnq9/HWFgBz/TRpArBoFmNNSEhQ\nugTiw2QD1n9pBGyCT+DNzjfBufxTFLWJWtz2gxtQevcGbLidbhn4UlxcrHQJxA/KRlyUTXQIZxkK\nE4C5FlutgO/Rs6hEk/DFlDljBCwvcQlStamwO20wD0Tmb5AxWg22fHIjVlxOTyz54nQ6lS6B+EHZ\niIuyiQ7hNGBPANjMGHufMfZNxtidnk24tzPGvsAYOwzgW3A/Rbko0Er4YvLOAevxjIAxxrAhw/03\nx2MXaTNbEbS2tipdAvGDshEXZRMdwtmMu5oxtgXAXfA9z4sBaOCc751vcQsFPQUppqlzwDjnYIxh\nffoGvHb+VRy72ILb8j+scIWkqKhI6RKIH5SNuCib6BDuZty7ANwI4CDck/WnLkexy/O05KJBWxGJ\nKTEuBgmxaoyMTaB/2L0yfXG6ewTs+MVjcHG6daw0rVardAnED8pGXJRNdJjPZtwNnPMdnsn6U5ej\neFLKAheCoaEhpUsgfqR4/jvlvQ2Zo8tFenw6+kf7YXOKtTTExJj82yaJpqWFbgWLirIRF2UTHfw2\nYFJuph3tG3PTXpDiykl1b1rrnYjPGMPXSr+Bz677PPRavZKlTXPyYDsevfsveO03b2NkYPFMsKXt\nVMRF2YiLsokOgUbA7mGMPT7fD/Bc4+75XkdkGo28+wyS8C1JTwIwfTHWjRkluPOyu6Bi4tw6TtDH\ngzHgxEun8fg/PY2TB9rBXdG/m1daWprSJRA/KBtxUTbRIdA6YI8AUDHGDjPGrg/1wp6nIk8BsHLO\nfz+fIkVHT0GKSz02CGB6AyaipaW5uOsXtyFnXSZG+p145Vdv4el//QcsZ/qULk1WbW1tSpdA/KBs\nxEXZRIeAQwCeyfZGAAcYY+8yxvZ5lp1YMfW2ImMs2fPanZ5jTgGoB3CAc/4lef8IyqNJ+OKavAXZ\nL3YDBgCGZXrc/uMduP4bVyA+JQ5dJ3pR943n8PIv3sRAz6DS5clCp9MpXQLxg7IRF2UTHVgwK4Iz\nxnYCqAWgh3uPyICHA7ABeGCxTMjfvHkzb2xsVLoM4sNhkwVf+WMjNi1PxW8/v1XpcoLmHBxF419a\n0PrC+3CNu6DSqLDultXYdPd6xCfTsieEECIoFuyBQQ3dcM7rOOcGuOdyHfR8wMwvO4ADcC9DYVgs\nzRdAe0GKzDXkvoW3EEbAptImxuLKL2zGPf95O1ZdswKucReOPdOG/33g73jrv5owbFtYfx5/aE87\ncVE24qJsokNIs8c9G23XAQBjLAWAwfOWlXNul7i2BYO2IhJXHNzNcU//CFwuDpUq6L+cCCE5Owk3\n/MtV2HhHEd79czPMTZ1o+fsJXDxtxe0/3qF0efPmcDiULoH4QdmIi7KJDkHdgiSB0S1Isd1UdRD2\noTE8983rkJa0sBcw7D1tQeuLp5CxyoCim1crXQ4hhJDppL0FSQIbHx9XugTih8VimdwTcuZtyDHX\nGGpbfoc3Og4pUVpYMlal4dovfyhqmi+LxaJ0CcQPykZclE10WFQNGGNsN2Nsj/dXP+/v9HzNet8f\nmgMmLrPZjMwpe0JOZRux4VnTM/hdy29pWyKF0FwWcVE24qJsosOiacAYY1WAezNxznktAJP3Nc/7\nuz3v13nmujUwxmqCuXZCQoIcJRMJFBcXXxoBsw9Pey89Ph2Z8ZmwO214v+99JcqTXfNf38Prv3sX\nZmOnkFsdFRcXK10C8YOyERdlEx0WxRLujDE9gD2c88l7s5zzOsbYIwAqPS9VcM7LprxvZIyVB3N9\nmoQvLqfTiSw/I2CMMWxfVo7HT/4v5l5dZWF67/n3MdjrQOsL7yNWF4NlZXlY+aGlWFqai5j4GKXL\ng9PpRHx8vNJlEB8oG3FRNtFhUTRgAPLhXptsJqunyWoEUOrjfRtjrJxz3hDo4rQSvrhaW1uRlZID\n4NKG3FPdU3gvbs2/Tah9IaX0kR/vQFtDO86+Y4b1AxtOv3YWp187C3WMCjnrspC3MRtLN+XCsFwP\npsAToq2trSgrK5v7QBJxlI24KJvoIMktyAW82bYN7sVl/TZo8N2YeeeLNTLGGm022+Q9ebPZPLlN\nhMViQXNzM1wuF4aHh9HU1ITh4WG4XC40NzdPTqRsa2uj82U6HwAyPE8+mjots85XMzW6znQJW/98\nz2+/cBplH9+AD1fdgPVfLkDZJzcgqzAdE+MunG++gHf+eAR1X38O/+8zT+DAvx/CW/sP48R7JyJW\nf1FRkdD//Bbz+bm5uQu6/mg+3/v+Qq0/ms8PRdjLUDDGtgOogrtB4ZxzDWNsE4AnAOzknB8N68Iy\nYYz1AVjJObfNeG0f3Nst1XDOC2acsx+AiXNeiQBoGQpxuVwudNmduPMXryEjWYtn/uU6pUsSwrBt\nBB0tF3C+uQvnmy/AYRmafO+qL27Fulsi85Sly+WirbwERdmIi7IRWtC3EsK6BckYexzAzpkfxDk/\nwhj7EoCDjLFSzvkH4VxfJg8A2AvPnK8ptx7nbWhoaO6DiCJaWlqwfkMxGAMsA06MT7igUdN/uOL1\ncVh1zUqsumYlOOewdfSjo/kC7F2DWLF1ScTqaGlpQUlJScQ+jwSPshEXZRMdQm7AGGPfArALQDXc\nG26nAnjc+z7nvIEx9nvP+/dIVOfUz9/t+fxg7PKOeHkm3ZumTKxvhPvWo9HzvcHH+XoAcy64Ehsb\nG2Q5JNKWLl0KjVqFtEQtLg44cXHAiWw9TV6dijGG1CUpSF2SEtJ5rS+8j2PPnkRSlg6pS1KgX5IM\nvec6ccnBLXi7dOnScEomEUDZiIuyiQ7hjIDdDWAH5/yA9wXGZo24/QPuW5GS8ywhURvmucap3zPG\nDABMcM/18jUL24BLDZpfGs1ieZZh4UlLSwMAZCbH4eKAE939I9SASaS/exC283bYztthbuqc9l5c\nihb6vBQkZyciKVOHpKxEJGUlIm1FKrS6S39h8eZDxEPZiIuyiQ7hdA5lU5svP/Lhu6FRDGNsJ4AG\n74iYZySsgXNu8nxvYozpp84RA6Cf6wlIgJ6CFFlbWxsKCwuRlRKH1g47euyUlVQuv28TCssL0He+\nH7bzdvSZ7Z6GrB8jdie67D3oau2Zdk5cshaf+sOdUMeoAVzKh4iHshEXZRMdwmnAGhhj93POHw1w\nzC4EMXIUYXvhrsnbYFXg0hpggPuBgqlzxEoBzNl8AaDJkALT6XQAMLkYa1eABmzCNYEP+s8iX1/g\n9xhyCWMM+iUp0C9JAXDplgjnHA7LEGwd/RjoHsRAtwMDPYPo7x5EclbitOUuvPn48s6fjuBcYwfi\nkrSIS576FTf9+0QtYnUxiImPgYrm90kmUDZEWdGUDXdxuFwc3MWhjlH5uqPm09jwGOwXBsAnLp3v\n/nLN+J5PfkZGgQFJmYlBXb/zWBe6TvROq2/yWhOuWdfmLo4lJTlYdfWKoP/s4TRgdQAeYYztAlAD\n4CwAMMaSAGyBu4G5AdObGxFUAij3LMqaBqDSO/oFuG9tepaWKIdnaQrOeUUwF6Y5YOLyzpXwtx3R\nVH89/SQea/0jvrW5ElcvuSYi9UUjxhgS03VITJ/7h0SguSwX3uuB9QNfq8P4t2xLHm75v9cHdaz9\nwgAsZ/qg0aqh0WoQo9VM/l4z5fdKrI8mAppnFBjnHBNjrskf+tyFKT+QXT4bgOSsxMnR37kM9Azi\nYrvVZwPAXRytradmvOZCVmEmstakB3X9U6+eQWdLl99mxddry8pysfFjRUFd/+VfvonzRy74uKYL\nrolL151qyaYc3Pa9G+a8NuccdV9/Dv1dg0HV4pWcnYiP13wsqOvXV72OkQFnSNfvPNYtbwPmaVTK\n4H6qcMeUt7z/pWQAjJzzn4Z6bTkFcyvRM78sZLQXpLjMZjOWLl2KbE8D5msxVq/kWPdydgfONVAD\nFiHefHy5/UflsHX0Y6Tf6fkawUi/E8NTfj/S74RzwInR4TGMDo1hbHgMnPOg/hb9zLfrpy2/4Y9K\no4Jao4IqRoUVly/FdV/ZFtSf7f1XTLhwvAdMxcBUDCrPr0zNZr+mYlCp3YvjZq/NCOr61nM29J6+\n9IwQ8z6UPvWPzqa/l7k6DSm5wS3b2PpuG1T9MQAu/aDkLg5w9w8ozgF4fuXu/0H22kxkrg6uAThn\n7MSF97rdm1BwzG5aONyNjWeEAxzIK8nG6uvyg7p+419apjQArinX5J4GwDX5vfdr+ZY8XP2ly+e8\nNuccz/7fBnQe7w6qFi/DCj12/fLDQV3/73texFBfaFMmEjN0+OTv7wjq+m8+2ogRe2gNhuOiI6gG\njHOOi+1WDPUNz3ksgMl/B7SJwQ1mMMawfOsSdB7rnjx35r9Ps19TYdnm3KCvf93XtqG77eLkv7OB\nr+3+yl6bGdT1vcKaPc45r2CM1cN9227ljLerOecPhnPdhYq2IhKXw+EAENwI2Lacbfjd0d+gufcI\n+kb6kBqXGpEaFzNvPr6oY9RIWxF8BtzFAebzoSCfyu7dALOxE+POCYyNjGPcOY5x54Tn10vfu8Zd\ncI27gBGg75w9uFo4x9v/ZcSwLbQfoLq0BHzqD3cGdf1n/60h5OsnZurwyUeC+wH99i+bMTY4Htr1\n0xPwyUeDq//lX7wRcgPQ+V53UA0Y5xwn609j8GJoSwRdbLcGfawmXjN5y2yysfb+nvn+ob10U/AN\nQMld69F5rMvHD30V+gfs0KemzmoElpTkBH392753A3pPW3w0FCq/TUZafnD/PjLGcOfPbsWIfWR2\n/WrVrGuH44r7N4d1XrCWb1mC5VvkXZIn7IVYp12EsZUArJzz4P7rFGVoIVbx9faP4PZ/fxWpuli8\nsMf/Laofvf0DvNv1Du5f/wV8dNXcP6hIdPPO95gYc2FifAJxidqgf2BYzvah++TFWbeJpt5+uTQa\n4/7K2ZCFZaXB/ZA+eaAdncfcIzC+/js++dqUt5ZsysGa7cHNcTx5oB2dx7vdDa23sfX86v1nwFSe\nsTXPr3kbs4P+odXR0oXutl6AMTCGWT/0wTw/oKeMGGatTvfMOZzbSL8Ttg77pev4GcGY+n6CIZ7m\nEZL5CrqjlKQBm7wYYys452clu+ACUVJSwpubm5Uug/hgsViQlpaGCRfHNT+sx4SL49X/Ww6tn3kY\nb3a8gZ8cfggrU/Lxy+v/I8LVLj7efIh4KBtxUTZCC7oBC7nVZ4ztm/L1Tc9rDzDGJgC0M8YmGGO/\nCfW6CxnNAROXd28utYohw7M4aKB5YFuyt0IXo8MZuwln7GciUuNiFureaSRyKBtxUTbRIZyx1gK4\nnyjcBcDkuf1Y43nvQbifhNzKGHtImhLFl5CQoHQJxI/i4uLJ33uXogjUgMWoY7B9qfspnAuDnX6P\nI9KYmg8RC2UjLsomOoQzCf8w3AuU3ghMbk0EADbO+cOe1+4G8BKAf5WkSsHRJHxxOZ1OxMe7V77P\nSpl7LTAA+My6z2Jz9lZszNgoe32L3dR8iFgoG3FRNtEhnBGw3Z4vrx1wT/OcXMLBs75WcM8KRwFa\nCV9cra2tk7/PTJ77SUgA0Kq12JS5CSpGk3HlNjUfIhbKRlyUTXQI5ydM/oyJ9t7Nreu9LzDGNgE4\nMo+6FpS4uDilSyB+FBVdWrMmO8X9N8YuW3Br0xD5Tc2HiIWyERdlEx3CacDOMMY2AgBj7C7vi5zz\ng1OO+QmA382ztgWDtiISl1arnfz9kjT3XL3z1tDWBiLymZoPEQtlIy7KJjqE0zk8COAgY+y3AB7x\nvFYNAIyx7Yyxw3CPih2WpkTxDQ3RD3RRtbS0TP5+icHbgNEImCim5kPEQtmIi7KJDuFsRVTHGLMB\n2An3ZtX1nPNHGGM3ANjvOcwO4CDcey5GPdoLUlxTt7nJTomDWsXQ0z+CkdEJxMUGtycbkQ/tNygu\nykZclE10CHcroga4m6+prx0AYJCiqIVGownrHyOJgKmLFWrUKuSlxuOcZQgdfUMoyEpSsDICgBaT\nFBhlIy7KJjrIMnmJMfYFxtjcG4JFCXoKUlxtbW3TvvfehjSHMA+sb8SKpu5Gn9u9kPmZmQ8RB2Uj\nLsomOsg1e3wVgL0yXVs4NAlfXDqdbtr3S70T8S3BN2B/av0jvv/Wd/FG5yFJayOz8yHioGzERdlE\nh4uxdmUAACAASURBVLA6B88I10uMsVOMMcuMrwkA38IiWgeM5oCJa+ZciXBGwFanrgEA/PVUHY2C\nSYzmsoiLshEXZRMdwtkL8i64F13dAfe2RKkzvrwbUe72eYEoRHtBimvmnmlL09x/cwxlKYrty26A\nXquHyW7CqIuylhLtaScuykZclE10CGf2+F4ARrj3g7R6vm8H8ATck/ArAXDO+ZNSFSk62opIXA6H\nY9r3kyNgIdyC1Kq1+MnVD6N/tB9aNa2/I6WZ+RBxUDbiomyiQzgNWD6A7ZzzZgBgjD0OoJxz7l35\n/gBjrJExdj/n/FGpChUZrYQvrsLCwmnfh7sURW5iLnKRK0eJi9rMfIg4KBtxUTbRIZw5YCne5svD\niEvbEXnVArg77KoWmPHxcaVLIH5YLJZp32vUKuSmurck6uijBXSVNjMfIg7KRlyUTXQIdyui5d5v\nOOdnAKR5tyfyaAeweb7FLRQ0B0xcvuZKLA1jIj6RB81lERdlIy7KJjqEcwvySQANntXwOed8K9wr\n4B9kjH0B7lXwaySsUXgJCQlKl0D8KC4unvXa5JZEIcwDI/LwlQ8RA2UjLsomOoQzAvaQ57wyAGWM\nsWS4J96nAqgDUA9gJWaslB/NaBK+uJxO56zXvGuB0QiY8nzlQ8RA2YiLsokOITdgnHM7gFIAuwBs\n5pz3c85tcN9yPAv3MhQHsIiWoaCV8MXV2to667Xl6YkAgDO9g5Euh8zgKx8iBspGXJRNdAh3L0g7\n3Lcip75mhHtdsEWHnoIUV1FR0azXCjLdDZipZxCcczDGZh0zF845fnP011AzNSqKvxTWNYjvfIgY\nKBtxUTbRQbY9dBhjp+S6tmhoKyJxabWz1+0yJMYiJSEGgyPj6O0PbyifMYam7kY8f+Y5HDi3aO62\nS85XPkQMlI24KJvoMK/OgTG2gjFW4uPrLiyirYiGhmgukahaWlpmvcYYQ75nFKy9ZyDsa3+m6LMA\ngEePPwLLMD0WHg5f+RAxUDbiomyiQ1i3IBljv8UimuM1F9oLUlz+9kwryEzEkbN9MPU4sO2yjLCu\nfe2S6/Dq+VfQ1N2IXxh/hu9f8UOoGI2GhoL2tBMXZSMuykY5Q2ND6B+1wzE2hKExBxxjDjjGHVBB\nhStyr4BWE/yUpJAbMMbYTwBUeL61wb0d0UwGACmhXnuh0mjC6mNJBKSlpfl8PT8zCQBgmscIGGMM\nX930NXz14JdxtLcZT53+G+647K6wr7cY+cuHKI+yERdlI40JPoHmniOTdzCuyrsaCTH+l5U63PUu\nHnrnR5jgEz7fH+fj2LH8xqA/P5zOYSeAPkzffmgWxtiiWZuBnoIUV1tbm89tO/KnTMSfj9Q4A75a\n+nX88O3v47HWP+HynG3ITaQti4LlLx+iPMpGXJSNm4u7cLS3Gb1Dve6RqDEHHGODcIw5wMFxb+En\nkJeY5/f8V82v4BfGn01+P+4aw635H/Z7vC4mEWnx6QDnSIjRISEmATqN+1dDXBq2Zl8eUv3h7gW5\nJ1Dz5VEZxrUXJJqELy6dTufz9ckGrHcQLheHShX+U4xbsrfirst24Zn2pzAyPhz2dRYjf/kQ5VE2\n4orWbIbGhvB0+1PoGerGBJ/AztW7sDRpmd/j3+x8A9WHf+L3/TWpawI2YMUZG1G+bAc4AENcKq7I\nuypgfUVpRfj9jX+Y888RrHAasAMIbrmJRbMaPs0BE5e/uRLJ8THISNait9+JTtvw5Or44bpv3Wfx\nybWfgkZFt6NDQXNZxEXZiEvUbMZcY3jV/Aq6HF0YHBvAwOgABscGMTg6iHHXGD63/n6UZG7ye35z\n7xH8T9ufJ79flrw8YAO2Lm0dblx+Eya4C4kxOuhidNDFJEIXo0NqXCqKMzb6PRcA0uPT8dXSr4f+\nB5VIOD8tdgNoYow9wTl/OcBxZwAsihvVtBekuMxmc8CJ+L39Tph6BufdgAGg5isMgfIhyqJsxBWp\nbIbGhvCXk/+DC4MXMOoaxT1r7kVR2jq/x7f0HsWvjvzC7/vnB88HbMA2Z23BVzd9HS7uQmpcKjZl\nlgasLzXOgC9v+urcfxBB+f2J4dnX0Z9auPeD3A+gEe7J+FMVANDPv7yFgbYiEpfD4fD7Xn5mEt4+\nbUF79wCuKcyMYFXEK1A+RFmUjbiCzWaCT+DNjjdwfvA8Bkb70T/aj4HRAfQ77RiZcOJTaz+NKwPc\ndjPZ2/H303+b/H516uqADdj6tPX4TNF9GHeNIzE2CYkxiUjy/KrXpiJLlxWw3lh1LMqX7wjqzxYN\nAv2VvRYAD/A+g3s7ol2SVrQA0Ur44go0UfXSWmC0JZFSaCKxuCgb8Uy4JvDCmedwbsSM5xqfwS0r\nbw3YELXbTuPhxiq/73cMdgT8vKK0dfjOh76HUdco9Fo91hgC/39Cq4nDztV3B/5DkElz3TM5A8AU\nxnULAKwI47wFaXx8XOkSiB8Wi8XvI9uXZbuXomjr7I9kSWSKQPkQZVE28ugY7MBZ+xnYR+3od9ph\nd9rRP9oPx5gDt668DVtz/D9JZx4wo/bYpenVserYgA1YfkoBPlN0H0bGnUiKTUKyNhnJsclIik1C\nSqx+zhEpFVNhc/aW0P+QJChzNWDlnPOz4Vx4MS1DQXPAxGU2m/3+ECnITIRWo8J56xDsQ6NISZDn\nYYrjF4+h29GF65fdQAu1zhAoH6IsyiY45wfO44zdhMGxQZRkbkKOLsfvsReHL+KfGirA/dxc0mv1\nARuw5cnL8Y2yf8H7Z97HuoJ1KMvaHLA2jUpDI1ICC9SA1cH3IqvBWjS3JhMS5j+Bm8ijuLjY73sa\ntQqrc5JxzGxDW2c/Ll+VLksNfzj+e5y2nYaxx4ivlX4DsWp6atYrUD5EWYspGxd3YXB0AH3OPvSN\n9MHutGNgbADF6RuxLNn/U3h2px1fPvAluOAeb9ictQXf2fY9v8frtXrsWH4j+kf7kaJNQUpsCpI9\nv6ZoU7AubX3AOhljuH7pdlybdx0tfxQF/DZgnPNpbTNjLNnzelD3azjnT86vtIWDJuGLy+l0Ij4+\n3u/76/JScMxsw3sddtkasPvWfQ4PvfMjvN7xGpYnr8Dda+6R5XMWornyIcpZDNlM8Al8541vo9XS\n6nN18w3pxfjxVfv8np8Um4Rb82+DdcSK5NgUlC8vD/h5GpVGkqf2FkM2i8Gcz83P3PeRMQYANZzz\nf5KxrgWFVsIXV2trK8rKyvy+vzYv2X1ch122GjZmlOAnV1fjiZOPozhj8YwqBGOufIhyFmo2vzv6\nGxh7jLA7bbgi9yp8LcA6T+OucXQ5ujDBJ6CL0cEQZ4Beq4dem4qk2GRct/T6gJ+lYirsLv6i1H+E\nOS3UbMh0ARswxthhAKVwP/E4VQVjrJxzvlq2yhYQegpSXEVFRYHfz3NvWdraYQfn3PsXDMmtTMlH\n5da9slx7IZsrH6IcpbLpHerBe5b30DfSB5vnlmCf0/37koxS3L/B/wpJE64JvNFxCPZR91+oxl1j\nAT9Lq9aidsejmOATC2pqAP17Ex0CrQP2AABvi92AS09D5gMoB1DAGHuIc/6v8pYoProXLy6tVhvw\n/SWGBCTHa2AdHEW3fQTZehrWj6S58iHKkSob5/gI2u0m2Eb6kJeUh+XJKwIev+e1b8IyYvFdkzpw\nTWqVGr8tr4XN2YfUOAMSNHPPz1Wr1FBDPedxIvn/7d17dBxXnSfw75Va3ZJab9lxYlsYy3kYxzhG\ndl6QQCBKOANMgEUmwCww58zEHmZh98xw1ia7M3v2MZyMMmd39nBmYe3AhJxlMiT2Lo/ZhVlsluGZ\nQCThKI6jQGQnkZ2X1ZIsqdXqVqvv/lG3pFKpqvqh6q7bpe/nnD5Sd1VX/7p/3V2/rnvrXn5uwsHr\nCNgBGJNu75dSnrcuEEK0wZiS6BCAdV+Azc3NBR0CuRgeHsbevXtdlwshsGtLK558IYGzr1xmAVZh\n+fJDwXHLTTaXxeX0FCbTk+io70RHfYfndu7/2RfwwtRvAQDN0RZ843ce9TzS/JFr+vDcxHNoi7Wj\no74dbfXtaI+1o72+HVub8o/+3hRtQlO0Ke961Yyfm3DwKsD2A/hDe/EFAFLKKXWE7KmyRVZFOBek\nvgqZruMtm1UBduEy3rPrygpEtZqUEt9/8XuI18Vx25bbUSuq6xd5qTjVjb7M3Pzkwo9x8qUfLDUH\nTmeWz8OKR+L4H+971HMarhuvvAk1ogbtsXbs27Q/bzP/B3bcgw/suMefJxFS/NyEg1cB1gZgyG2h\nlHJIGFoKPTMyrCIRzgGoq0LGMdq11egH9uyF8nXEz2d2YRZHn/4KJCRO/OZxfGLnP8fNV90S+nHD\nOM5U5T2XOIsfvnwKU+lJdDZswKE9n3F8n5m5+d75/4OziWeXbhcQaI21oj3Wjj0b9+adA/XjOz+B\nj+/8hL9PYp3j5yYc8lUOhYwD1gFgRQEmhGgFMCGlXBc/43kWpL5GRkbyTqmyp6sNQgBnLkxhfmER\n9XWVf9s2R5vxr288gofPfA0vTb+EB371RWxp2oIPXv1hvLvrPXn7vlSrQvJDq03MT2ByfmKpg/rk\n/CQm5yfQGmvFvdd93PMo09+PPIrTl34NwBgW4VO7fh/xuviq9czcHLnxfrw4fR6t0Va017ejJdqK\n2pp18dWuLX5uwiFfAeY1F6SXDqw+czK02AlfX/H46h2LXWtjFNdc2YzfvDqDZ8amcGN3ML8ub9ty\nO26+8hb83xe/j2+/8C1cnL2IL5/+Gzz+/GP4r+/+ElqiLYHEVU6F5Gc9kFJidmEWtaIWjXXeHccf\nefZh/M/fnnBd3rvtbmxocB/T7o9u+GM8Mz6M1mgrutt2OBZfwHJu2uuN/lekD35uwiFfAfaQEGIA\nwJTHOn1CCPvyu1F68VZ12AdMX4X2ldi/vRO/eXUGA+cSgRVgAFBXW4cP7LgHv7P9/fj5Kz/Dt1/4\nFqbTxhAZYRT2viyFDG3yjy9+H18dPoZMLoNITQRfvvO/40qP6Wza6zuwoWEDmuuaV3RQb4u1Y0fb\n1Z7FFwBsbtqMzU2b88Ye9txUM+YmHPIVYAfgPaWQBOA+1fo6wbkg9TU2NlbQl9X+7R149BcvYuD8\nWmbf8k9tTS3eufVdeOfWdwUdSlkVmh+dTcxP4ORLP0AilcCUGq9qat44SzBaE8Vfveu/eBY8M5kZ\nLOQW0BhpxLaWN6OpzvsMvnt2fBD37Pig309jlTDkJqyYm3DIV4CtpRkxnD/ZHXAqIn0lk8mC1rth\nWztqawSeu3gZs/MLaKqvK3Nk/pnNzOA/PvnvERF1eOvGPXjf9vejNdYadFgFKTQ/lTS3MIefXfwp\nxlOXIEQNPnT1h9EQcR+e5DsvfAvfeuF/OS6L1zXlPaP1wLUfxT+7+iPa9avSMTdkYG7CIV8B1iel\ndP5m8SCE6APwWGkhVR+OhK+vQjuqxmMR7FLzQp5+aRK3XXdFmSPzT3oxg7HpMSSzSZxJPIPJ+Qn8\n8d7PBh1WQcrVkTiRSmBifgLTmcuYTk8bfzPTEBD40NUfRlO02fW+3x39Dh4d+cbS9R2tO3DTVTe7\nrv+B7t9FU7QZjZFGNY1N21LTYEOkoaDZFXQrvoDy5YbWjrkJh3wF2KkStzuIddQJP5vNBh0CuUgk\nEgWfsr1/eweeGZvCwPmJqirAOhs68dDdX8Mz48/g/OVzuH3rOz3Xfy35Gr76zFFEaurQWb8BGxo6\n0dHQidZoKzobOtHV/KYKRV5YfrK5LAZfH8DE/AQEBN7VdYfnEakfX/gn/OeBv3Jd/ubW7bhty+2u\ny+/ougPJhSTqIzFsjm9BzybvOfc2Nl6BA9d+1HOdalTMZ4cqi7kJB68C7FCp43tJKc8LIQ6VGFPV\nYR8wfY2NjRVegHV34OGfnMNTo87ToOisKdqMWze/Hbdufnvedc9dHsWvXvuV6/I/2fd5vLvrPa7L\nX0++jkdHvoHMYgaNdY342HWfwMbGja7rv5Z8FY88+3XMLsxiMbeIrMwim8sivZhGZj6DI+/4Aq5u\nu8b1/idf+gG+8vR/W7oeqYmgd9tdrutvbNiINzVvQ6QmgpZoC1piLWiNtqI52oJNjZtw81W3uN4X\nAK6MX+U53+B6UcxnhyqLuQkH1wJMSvnQWja81vtXk8bG/PONUTD27NlT+Lpd7YjHIhh9YxYXJuaw\ntSOceX375nfgr+/4El6ZvYjx1DgS8+MYT41jJjMDKSXenGeuvqcvncaPxv7f0vXr2nfi7je/13X9\nM+Nn8PNXfua4TEDg0twlzwJs36b9uHvbeyGEQGd9J27JU0Dt6rwef3Pnlz3XofyK+exQZTE34SDC\nenp7JfX09MihIddJAyhAqVQKDQ2Fz+/47048jR888xo+d/e1+L13bC9jZNVrUS5i+NIwZjMzqI/U\nY+8Vb0NdjftJC4tyESOJ54xhFkQEtTURRGpqEauNIZqL4qq2/EMiUOUV+9mhymFutFZw9yuOIOoD\njoSvr7Nnzxa1/rvesgkA8E/PvVGOcEKhVtTibVe8DbdvfSduvPImz+LLXP/6Dbvxtit68NaNe7Cr\ncxeubb8O21rejFdGX61Q1FSsYj87VDnMTTiwAPMBz4LU165du4pa/9arNyAaqcGZC1NIzKTLFBWZ\nis0PVQ5zoy/mJhxYgPmAUxHpKxYrbg7FxlgEN+3ohJTAT0Z4FKzcis0PVQ5zoy/mJhxYOfhgbm4u\n6BDIxfDwcNH3uWOpGfJ1v8Mhm1LyQ5XB3OiLuQkHFmA+4FyQ+ipluo7brt2I2hqBgfMTGGczZFlx\nOhV9MTf6Ym7CgQWYDyKRfOPZUlBKGSunLR7FbddtxGJO4nunL5YhKjJxLCN9MTf6Ym7CgQWYD3gW\npL5GRkZKut89PVsBAP/71xfBoVrKp9T8UPkxN/pibsKBBZgP2AlfX/F4vKT73byjExuaY3g5MYen\nX57yOSoylZofKj/mRl/MjT7mFxbxymQKz16Yws+eL+7ELbad+YB9wPRVal+JSG0N3r93Mx756Xn8\nw9AF7N3W7nNkBLAvi86YG30xN+UjpcTsfBYTyQwmkxlMzKYxMav+Txr/G8uM/+cyiyvu/+R/cJ8V\nxI4FmA84F6S+xsbGSv6y+sDbtuCRn57HqWdfw+fuvg5tcRbafltLfqi8mBt9MTfFWcxJTM2ZBZVR\nSE2qQmpiNq2Kq4wqtNJYWCy820ldrUB7PIb2eBTtRe4jWID5IJfLBR0CuUgmkyXft6szjluv2YAn\nfjuO4796Gfe9+2ofIyNgbfmh8mJu9MXcAJlsbukolP1o1URyZZF1eS6DXBFdeRujtehoiqI9HkNH\nPIqOpig6VJHV0RRFR5P6Px5FU30EQhQ8+9AKnAvSB/v375cDAwNBh0Fl8OsXJ/CZh59CS0MdvvOn\n70RDlL9ZiIjKIbuYw2Qyg8SsUUyNz6SRmE0vXU9YjlbNzmeL2nZrYx061FGqjqbYyv+b1P+q4KqP\n1q7laRRcjXFv4oNstrg3AlVOIpFY0ynbe7e1Y/fWVpy5cBnfHbyIe2/d5mN0tNb8UPkwN/qqptxI\nKTEzn0ViNq2KqAwSqrCamM1gfHb5/6m5DAo9JlRbIyxFlPsRqo6mGNoa6xCp1e9kORZgPmAfMH2N\njY2t6YtKCIFP3rYdR755Go8+8SI+fGMXohH9PsjVaq35ofJhbvSlQ27SC4uYSGaWC6mlokoVWZbC\nKpMtrJuOEEBHUxSdTTF0qkLK/L+zOWYcoWoyCqvm+jrU1JTW9KcLNkH6gE2Q+srlcmseJiSXk/jk\nV36B0Tdm8bm7r8XvvWO7T9GRH/mh8mBu9FWu3ORUZ3Vrk59ZTC03CRrLZopoAmyM1apCShVT5v/N\nMUvBpe+RqiKxCbKS2AlfX+l0Gg0NDWvaRk2NwGfvvhZ/8o0hPPyTc3j/3i08I9InfuSHyoO50Vex\nucnlJCbnjKa/8Zk0Ls2kkTD/zqYxPjOPSzPG0arFAnur19YI25Gq5UKqozmKDeb/TVH2nXXBV8UH\nHAlfX2fPnsW+ffvWvJ1br9mIm3d04pejCXztx6P4/Pve4kN05Fd+yH/Mjb7M3JSjsGppqFsqpszC\nakNzbGVzYFMMLQ3V3wQYNDZB+qCnp0cODQ0FHQY5SKVSvv2Kf+H1GXzqK7+AEAIPH7wF117V4st2\n1zM/80P+Ym6Ck6+weuNyCgk1blWhhVVrYx02NMWwodlo+tvYbP2/fqm4itWt6QxAYhNkZbGfhL5i\nsZhv27p6UzM+ctObcPyXL+Mvvn0Gf3vwljD0VwiUn/khfzE3/ivHESsWVtWLBZgP5ubmgg6BXAwP\nD2Pv3r2+be8zd16Dn//mEn7z2gwe+ek5/MEdHJx1LfzOD/mHuSnO/MIiLk3P443pNC7NzOPSdBpv\nTM+vuK3YpsCVxZTRBLihJYapV1/GLT1vZWFV5ViA+YBzQerL7+k6GmMR/NsPXo9/8fUB/O2Pz+Hm\nHRuwu6vN18dYTzidir6YG4OUEtOpBVyaMQuq5cLKett0aqGg7XkVVoUesUpsqkNnO5uHqx37gPmA\nw1CsP3/9/efw2JMvY2NLDI8cuhUdTWyuIao22cUcJpKZpSLKOFq1srC6NDOP9EL+M91rawQ2qiLq\nipZ6bGyJLf01bjMKLR6xCj32AaskngWpr5GREezcudP37X72ruvw3CvTGH55Cn92/Gl86VP72R+s\nBOXKD61dtefG3iT4xuXVhVViJl3QHIGN0VpsbKlfVVBZb2tvjFbsrMBqzw0ZWID5gJ3w9RWPx8uy\n3bpIDb544Ab8/tEnMPTiJL74nWfx5x/azdOyi1Su/NDa6Zobs0nQXlit7H81j+lUYQOFtsejnoXV\nFc31iNfrtavUNTdUHDZB+oBNkOvXsxem8NlHBpDKLOJjt27Dv3rvdRCCRRhRKbKLOUzMZvCGSyd2\ns5kwXcDUNpFagY3N7oXVxuZ6bGyOoY5Ti5G/2ARZSZwLUl9jY2Nl7Ux8/dY2/OXH9uLzfzeEbz7x\nEgSAf8kirGDlzg+Vzu/czGcWVxVWK5oEp+eRmC2wSTBWaxRSlsJqY3MMV7Qu39ZWwSbBSuPnJhxY\ngPmAUxHpK5lMlv0xbt6xAf+p7wb8+Ymn8fdPvITZ+SyO/O4u9gkrQCXyQ6UpNDduTYLWwurSTOFN\ngh1NUc/CamNLPeKx9b3r4ucmHNgE6QM2QRIAPPHbS/jCY6eRXsjhxu5O/MWBPWht5BAlVL2sTYIr\nh2BY7mt1aTpddJPgFWZh1VKvmgWNwmpDE5sEqeoVfNiVBZgP9u7dK0+fPh10GOQgkUigs7OzYo83\n/PIkjnzzNCaTGWxub8AXD9yAt2xprdjjV5tK54eWLTcJqj5Wtk7sr0+lMDm3UFCTYDwWcSysrLeF\nuUmw0vi50Rr7gFUS+4Dpa2xsrKJfVHve1I6vH7oFR755GiOvTOMPv/pL/MEdO/Cp27azSdJBpfOz\nHqxoEpy2HLmaKb5JUAijSdCrsGKTYOXxcxMOPALmAzZB6iuXywUyTEh6YRFfOfVbfPPJlwAAO65o\nwp++byf2beeXplVQ+alWC9kcxmfTK45amUMwmH/HZwprEqyrFUt9rJbODlzqb2WMxn5FSwObBDXE\nz43W2ARZST09PXJoaCjoMMhBKpVCQ0NwU3b8ajSB/n94FhcnUwCAO6/fhD+68xp0dXIcHyD4/OhC\nSomZ+ezKgsrs1G4ZgmEyWdjR9ngssnLYhWbLqOzqtrbGOs+zdZkbfTE3WmMBVkm7du2SZ8+eDToM\ncjA4OIh9+/YFGkN6YRGP/uJFPPLT85hfWESNAHp3X4lP396NHZuaA40taDrkp9yyizkkZtMOzYDL\nHdrHZ9KYX1jMu60aATV/4OrxrcwjWRubY2j0oUlwPeSmWjE3WmMBVkk8AqYvnX4pvn45ha/+aBTf\ne/oVLKqezTft6MQH923FO6+7Yl029eiUn2JlF3OYTGaQmDUKqPGZtPo/g/GZ5SNZE8kMCvmaNae7\nsRZSy/MJGtc7mmKorVBH9mrOTdgxN1pjAVZJ7AOmLx37Srw2lcLf/eJFfHfwwlJfnbbGOvTuvgrv\n3rUJe7e1V2wnGzQd87OQzS0XVepvQv1v/TuZzBR0hqAQQGdTzFZYWUZj13S6Gx1zQwbmRmsswCqJ\nTZD6On36NPbu3Rt0GI6mUwv4x6dfwXeGLmD09dml29vjUdx69Qbs6+7A/u0d2NQa3l+6lcpPdjGH\ny3MLmEhmMJE0iqfJ2QwmkplVxdXluYWCt9sej2JDcwydTTHL3yg6m42iamOLcVs1ngGr82dnvWNu\ntMYCrJI4Dpi+qmG8HCklnn91Gj989nX86OzruDAxt2L51o5G3PCmNuzc3IKdm1tx9aYmNET1OlpS\nqlLzI6VEMp3F1NyCUUwlM5iYTWNi6f8MJlWhNZHMYDq1UFAzIADU1gh0xI0iyiysNjTHsKEphk7L\n/x1N0aosrApVDZ+d9Yq50RoLsEpiEyT5RUqJc2/M4qlzCQycn8CvX5xEMr1yvKYaAXR1xrG1oxFd\nnY3Lf9sb0dkcQ31dbUDRF28xJzGXziKZzmI6tYDp1AIupxZweU79P5dZdZt5WSyk/U8RAmhrjKI9\nHkVH3PhrXqxFVqcaMHS9NAETke9YgFXS7t275ZkzZ4IOgxyMjIxg586dQYdRsuxiDs+/Oo2zFy9j\n5JVpPP/qNM5fSnoWH031EUuTWBRN9XWIxyJoikUQr4+gqT6CeCyCaKQGdbU1iNQI429tDepqBSK1\nNRAAclJCypV/c9IoErM5ifTCIjLZHNLZHNLZRaQXcsZ1dfv8wiKSqrgyLsvX59JZzKazSGXyn/nn\npjFai5bGOnTEjaNR1uKqoym2oshiUVW8av/shBlzozWOhF9J7Aypr3i8usfbitTW4Pqtbbh+a9vS\nbfMLixhLzGFsIokLiTmMTczhQmIOr06lMD6bxux8FrPzWbw0rv+EvQJAYyyCxlgtWhrq0NpQggi6\nPwAAFqVJREFUZ/xtjC5db21cfVtLQ926PGu0kqr9sxNmzE048AiYD9gESbowp6Exz+CbmM0gOW8c\nbZqdX0AybRRnyXQWmcUcFhclFhZzWFiUyOZyyKrrgNHUKYRAjRAQAiv+1tYIxCI1iNXVIhqpQSxS\nq64b/0fV//FYZPlSH1l5PRZBQ10t5wckojDhEbBK4lyQ+hobG0NXV1fQYVSMEAKtjVG0NkarYpDX\n9ZafasLc6Iu5CQcew/dBLpd/3jUKRjKpfzPcesb86Iu50RdzEw5sgvQBmyCJiIgIRTRB8giYD7LZ\nbP6VKBCJRCLoEMgD86Mv5kZfzE04sADzAfuA6WtsbCzoEMgD86Mv5kZfzE04sAnSB2yC1BfnTNMb\n86Mv5kZfzI3W2ARZSeyEr690Oh10COSB+dEXc6Mv5iYcWID5YH5+PugQyAUnSdcb86Mv5kZfzE04\nsAnSBz09PXJoaCjoMMhBKpVCQ0ND0GGQC+ZHX8yNvpgbrbEJspLYFq+vWCwWdAjkgfnRF3OjL+Ym\nHFg5+GBubi7oEMjF8PBw0CGQB+ZHX8yNvpibcGAB5oNoNBp0COSC03XojfnRF3OjL+YmHFiA+SAS\n4ZSauurs7Aw6BPLA/OiLudEXcxMOLMB8wLMg9TUyMhJ0COSB+dEXc6Mv5iYcWID5gJ3w9RWPx4MO\ngTwwP/pibvTF3IQDh6HwAUfCJyIiInAYisriXJD64pxpemN+9MXc6Iu5CQcWYD7gVET6SiaTQYdA\nHpgffTE3+mJuwoFNkD5gEyQRERGBTZCVlc1mgw6BXCQSiaBDIA/Mj76YG30xN+HAAswH7AOmL/aV\n0Bvzoy/mRl/MTTiwCdIHbILUVy6X4zAhGmN+9MXc6Iu50RqbICuJnfD1lU6ngw6BPDA/+mJu9MXc\nhAMLMB9wJHx9nT17NugQyAPzoy/mRl/MTTiwCdIHPT09cmhoKOgwyEEqlUJDQ0PQYZAL5kdfzI2+\nmButsQmyktgWr69YLBZ0COSB+dEXc6Mv5iYcWDn4YG5uLugQyMXw8HDQIZAH5kdfzI2+mJtwYAHm\ng2g0GnQI5KKrqyvoEMgD86Mv5kZfzE04sADzQSQSCToEctHZ2Rl0COSB+dEXc6Mv5iYcWID5gGdB\n6mtkZCToEMgD86Mv5kZfzE04sADzATvh6ysejwcdAnlgfvTF3OiLuQk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Now, let's plot the Phase Frequency Response\n", "\n", "# Make the figure pretty, then plot the results\n", "# \"pretty\" parameters selected based on pdf output, not screen output\n", "# Many of these setting could also be made default by the .matplotlibrc file\n", "fig = plt.figure(figsize=(6,4))\n", "ax = plt.gca()\n", "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n", "plt.setp(ax.get_ymajorticklabels(),family='Serif',fontsize=18)\n", "plt.setp(ax.get_xmajorticklabels(),family='Serif',fontsize=18)\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "ax.grid(True,linestyle=':',color='0.75')\n", "ax.set_axisbelow(True)\n", "\n", "plt.xlabel(r'Normalized Frequency ($\\Omega$)',family='Serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel(r'Phase (deg.)',family='Serif',fontsize=22,weight='bold',labelpad=8)\n", "\n", "plt.plot(w,phase_un, linewidth=2, linestyle = ':', label=r'$\\zeta = 0.0$')\n", "plt.plot(w,phase_0p1, linewidth=2, linestyle = '-', label=r'$\\zeta = 0.1$')\n", "plt.plot(w,phase_0p2, linewidth=2, linestyle = '-.', label=r'$\\zeta = 0.2$')\n", "plt.plot(w,phase_0p4, linewidth=2, linestyle = '--', label=r'$\\zeta = 0.4$')\n", "\n", "plt.xlim(0,5)\n", "plt.ylim(-190,10)\n", "plt.yticks([-180,-90,0])\n", "\n", "leg = plt.legend(loc='upper right', fancybox=True)\n", "ltext = leg.get_texts() \n", "plt.setp(ltext,family='Serif',fontsize=16)\n", "\n", "# Adjust the page layout filling the page using the new tight_layout command\n", "plt.tight_layout(pad=0.5)\n", "\n", "# If you want to save the figure, uncomment the commands below. \n", "# The figure will be saved in the same directory as your IPython notebook.\n", "# Save the figure as a high-res pdf in the current folder\n", "# plt.savefig('Seismic_Freq_Resp_Phase.pdf',dpi=600)\n", "\n", "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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GxYsXGR8fJ51OW35OjXkEAgG2bt1acguYDmB1wMmTJ9m7d69p5SUyCdydfwei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\nz/krxOjoaPaFFEAXT4BcVUUXV108AXJVEVk8qQvSAXTrgiQIgiAIIi0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the Phase Frequency Response over a larger range of frequencies\n", "\n", "# Make the figure pretty, then plot the results\n", "# \"pretty\" parameters selected based on pdf output, not screen output\n", "# Many of these setting could also be made default by the .matplotlibrc file\n", "fig = plt.figure(figsize=(6,4))\n", "ax = plt.gca()\n", "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n", "plt.setp(ax.get_ymajorticklabels(),family='Serif',fontsize=18)\n", "plt.setp(ax.get_xmajorticklabels(),family='Serif',fontsize=18)\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "ax.grid(True,linestyle=':',color='0.75')\n", "ax.set_axisbelow(True)\n", "\n", "plt.xlabel(r'Normalized Frequency ($\\Omega$)',family='Serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel(r'Phase (deg.)',family='Serif',fontsize=22,weight='bold',labelpad=8)\n", "\n", "plt.plot(w,phase_un, linewidth=2, linestyle = ':', label=r'$\\zeta = 0.0$')\n", "plt.plot(w,phase_0p1, linewidth=2, linestyle = '-', label=r'$\\zeta = 0.1$')\n", "plt.plot(w,phase_0p2, linewidth=2, linestyle = '-.', label=r'$\\zeta = 0.2$')\n", "plt.plot(w,phase_0p4, linewidth=2, linestyle = '--', label=r'$\\zeta = 0.4$')\n", "\n", "plt.ylim(-190,10)\n", "plt.yticks([-180,-90,0])\n", "\n", "leg = plt.legend(loc='upper right', fancybox=True)\n", "ltext = leg.get_texts() \n", "plt.setp(ltext,family='Serif',fontsize=16)\n", "\n", "# Adjust the page layout filling the page using the new tight_layout command\n", "plt.tight_layout(pad=0.5)\n", "\n", "# If you want to save the figure, uncomment the commands below. \n", "# The figure will be saved in the same directory as your IPython notebook.\n", "# Save the figure as a high-res pdf in the current folder\n", "# plt.savefig('Seismic_Freq_Resp_Phase_Extended.pdf',dpi=600)\n", "\n", "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Licenses\n", "Code is licensed under a 3-clause BSD style license. See the licenses/LICENSE.md file.\n", "\n", "Other content is provided under a [Creative Commons Attribution-NonCommercial 4.0 International License](http://creativecommons.org/licenses/by-nc/4.0/), CC-BY-NC 4.0." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# This cell will just improve the styling of the notebook\n", "from IPython.core.display import HTML\n", "import urllib.request\n", "response = urllib.request.urlopen(\"https://cl.ly/1B1y452Z1d35\")\n", "HTML(response.read().decode(\"utf-8\"))" ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.6.2" } }, "nbformat": 4, "nbformat_minor": 1 }