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@ricklupton
Created March 20, 2013 16:54
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Adding point mass to a string
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{
"metadata": {
"name": "Adding point mass to a string"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"%pylab inline\n",
"np.set_printoptions(linewidth=150, suppress=True)\n",
"import scipy.linalg"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.kernel.zmq.pylab.backend_inline].\n",
"For more information, type 'help(pylab)'.\n"
]
}
],
"prompt_number": 117
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Set up a discrete mass model of a string with lumped masses joined by springs, and define a function to calculate the mode shapes and modal frequencies of the system:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"N = 21 # number of masses\n",
"m = 1 # mass of each mass\n",
"k = 1 # stiffness\n",
"\n",
"def calc_eigen(i_extra, m_extra):\n",
" # mass & stiffness matrices\n",
" M = m * eye(N)\n",
" M[i_extra, i_extra] += m_extra\n",
" K = 2*k*eye(N, k=0) - k*eye(N, k=1) - k*eye(N, k=-1)\n",
" \n",
" # eigenvectors and values\n",
" w, v = scipy.linalg.eig(K, M)\n",
" \n",
" # normalise\n",
" scale = 1.0 / sqrt(diag( dot(v.T, dot(M, v)) ))\n",
" v *= scale[newaxis, :]\n",
" w = sqrt(w)\n",
" \n",
" return w,v"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 118
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Extra mass in the middle"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Calculate the mode shapes and frequencies with an extra lumped mass of 0, 5, 10, ..., 40 in the middle of the string, and see how this changes the frequencies and mode shapes."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"m_extra = arange(0, 40, 5)\n",
"\n",
"mm = [calc_eigen(N // 2, me) for me in m_extra]\n",
"freqs = array([w[:5].real for w,v in mm])\n",
"modes = array([v[:,:5] for w,v in mm])"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 119
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First let's see the modal frequencies: the even modes are unchanged, as expected, because the mass is being added at a node. Modes 1, 3, and 5 reduce in frequency, and modes 3 and 5 appear to be tending towards modes 2 and 4."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(m_extra, freqs); legend(range(1,6)); xlabel('Added mass in centre'); ylabel('Modal frequency');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
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Vn0jV1dUYMWKExW4dsxWrVMjIyEBSUhIMBgPmzJmD0NBQZGZmAgDmzp2LTz75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\nXgAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x829bc50>"
]
}
],
"prompt_number": 120
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The first mode becomes triangular as the concentrated mass becomes more important:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(modes[:,:,0].T); grid(); title('Mode 1');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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Q3BCj9KPNWP7nPywUc/NmVp2CIzJGuOlojYm7N3tycgBHR+DwYe3ON1ZS1d9p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\nScEAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x853c8d0>"
]
}
],
"prompt_number": 121
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The second mode is unchanged by adding mass in the middle:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(modes[:,:,1].T); grid(); title('Mode 2');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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QdwdU6r3B7Rw/1lGIAqKZPiEyZt6sBrjzwBOrFoaxjkJIOWr6CoZmpvySpJ5+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\n",
"text": [
"<matplotlib.figure.Figure at 0x8525250>"
]
}
],
"prompt_number": 122
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The third mode is becoming more and more like the second mode (above), give or take a reflection of the right hand side."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(modes[:,:,2].T); grid(); title('Mode 3');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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4OBiGQcDiAHiN9kJw0EY8edILOjqdYGISUysPa33hc1P6Tk6AkpIUWlrTsXv3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"text": [
"<matplotlib.figure.Figure at 0x8047310>"
]
}
],
"prompt_number": 123
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Extra mass somewhere else"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mm = [calc_eigen(5, me) for me in m_extra]\n",
"freqs2 = array([w[:5].real for w,v in mm])\n",
"modes2 = array([v[:,:5] for w,v in mm])"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 124
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(m_extra, freqs2); legend(range(1,6)); xlabel('Added mass in centre'); ylabel('Modal frequency');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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8uqK4uBj19fVYtGgRAgICnC6wPyRJQsYbGdin24dZE2ZhccxiLI5djISxCXwv\nAxFRD1waCAO9Mc1VOn5Us6EZxZXF2FWxCwWnCtBmbMOimEVYHLOYew9ERN24NBCio6MtM6yqqkJ4\neDgA8yWokyZNcnhjmqvY+1FCCFTUVqCgogAFpwqwT7cPMyfMNO89xCzGjHEzuPdAREOaWw4Z3Xff\nfVi2bBmWLFkCACgoKMD27dvx0ksv9b9SZwrsw4/q2HsoOFWAgooCtBhbLHsPCy5fwL0HIhpy3BII\n06dPx1dffeVwnLv050dV1FSYw+FUAT6r+gzJ45OxOGYxlsQu4d4DEQ0JbgmEhQsXYu7cubjzzjsh\nhMCWLVuwd+9efPTRRwMqts8FDvBO5WZDMz6t/NQSEM2GZiyKWYRFkxdhweQFGBk00oXVEhH5BrcE\nQk1NDTZu3IiSkhIA5kdWbNiwweMnlV2lp72HxbGLkTgukXsPRDQouPWy04aGBgDAsGHDnK9sANz5\nLKMWQ0vnuYdTBWjSN3Wee+DeAxH5MbcEwrFjx3DXXXehpqYGABAREYHNmzdj+vTp/a/UmQI9+HC7\nU7WnLFcufVb1GRLHJ1quXEoan8S9ByLyG24JhDlz5uDPf/4z5s+fD8B8c9rvf/97fP755/2v1JkC\nvfS00xZDCz4986nlyqUGfYPVlUvhweEer4mIqK/cEgiJiYk4cuSIw3Hu4iuPv/6u9jvLoaWSMyWY\nMW6G5col7j0Qka9xSyDcfPPNmDVrFlauXAkhBN566y0cPHgQ27dvH1CxfS7QRwKhqxZDC/ae2WsJ\niPq2esuVSwsnL+TeAxF5nVsCoba2Fhs2bMC+ffsAmN9bkJOTY7lz2d18MRC662nvYXGs+dyDQnL4\nlHEiIpdy+8PtvMEfAqGrVmOr1X0Pda11SBiXgKgRUYgcHomoEVGW/sgRkQhRh3i7ZCIahFwaCDfe\neGOPM5QkCTt37uxflU7yt0DorvJSJb658A109TpU1VWhqq7K0q+r02FY4DCboLD0j4jEhLAJUCqU\n3v4ZRORnXBoIERER0Gq1WLFiBWbPng0AlplLkoR58+YNsNw+FujngdAbkzDhfNN5u2HRERg1LTWY\nEDbBEhBRI6IQNbxL/4gojAgcwZPaRGTFpYFgNBrxr3/9C/n5+Th27BiWLl2KFStWYNq0aS4pts8F\nDuJA6Is2YxuqG6qhq7MfGlV1VRAQ9vcw2vu1w7UIVAV6+6cQkQe57RxCW1sb8vPz8dvf/hY5OTlY\nt25dv4tJ8PfnAAAVVklEQVR01lAPhL6oa62z3bvo0v9jw48YFTyq10NTY0PH8uQ30SDi8kBobW3F\nhx9+iK1bt6KyshKZmZlYtWoVNBrNgIvtc4EMhAGTTTLONZ2zOhRVVd+lv64K9W310A7XWh2Kihwe\nicjhkQgPDseIwBEYHjgcwwOHIzQglOFB5ONcGggrV67E8ePHsWTJEtxxxx1ISEhwSZHOYiB4Rouh\nBT/U/2B74rteh0utl1DfVm/pmg3NCAsIw/DA4VZB0bXrcXxQ5/iwgDAGC5GbuDQQFAoFQkNDe1xQ\nfX298xX2AwPB98gmGQ36BquQ6NrVtdahXt/LtPb+JkMTQtWhNkHR53BpHx8WEMYrsYi64X0I5FdM\nwoRGfaNNUNiESFvv0xr1jQhRh9gNkGGBwxCsCkaQKshhF6gMdNgmQBnAK7rILzAQaEgyCROa9E12\nQ6ShrQGtxtbOTm61HnayM8gGBKocB0ePndJOEPUyv0BlINRKNdQKtc0n94qoNz4XCIWFhVi/fj1k\nWUZ2djYeeughq+lvvfUWnnzySQghMGzYMLzwwguYMWOGdYEMBPIhJmFCm7Gt/6HiZCC1GdtgMBlg\nkA1Wn3pZDwkS1Eo1ApQBdgPDZZ/t/f1djlKhhEqhglJSWvWrFCq7w0pJCYWk4J7YAPlUIMiyjLi4\nOBQVFUGj0SA1NRX5+fmIj4+3tPniiy8wdepUjBgxAoWFhcjJycH+/futC2QgENkQQkAWsk1QuPyz\nPXwGMh9ZyJBNMowmo02/0WS0GTaajADQa2g4GzCO5tNbW4WkgFLR/il1++w+3oeGxw8b7/S2U+WO\n/1gBoKysDDExMYiOjgYAZGVlYceOHVaBMGfOHEv/7Nmz8cMPP7irHKJBRZIkqCQVVAoVghHs7XJc\nziRMkE1yj6HhTMA427ZrMHXUYRImyML8aTAZ0CbabMb70rBskvu13t0WCNXV1YiMjLQMa7ValJaW\n9tj+lVdewZIlS+xOy8nJsfSnp6cjPT3dVWUSkQ9SSAoolAqoofZ2KX6juLgYxcXFluGN2Oj0PNwW\nCM4c/9uzZw9effVVyyO2u+saCEREZKv7P5Y3bvShQNBoNNDpdJZhnU4HrVZr0+7o0aO47777UFhY\n6LF3LBARkS233SaakpKCiooKVFZWQq/XY9u2bcjMzLRqU1VVhVtuuQVvvvkmYmJi3FUKERH1gdv2\nEFQqFXJzc5GRkQFZlrF69WrEx8cjLy8PALBmzRr86U9/wsWLF7F27VoAgFqtRllZmbtKIiKiXvDG\nNCKiQag/204+WYyIiAAwEIiIqB0DgYiIADAQiIioHQOBiIgAMBCIiKgdA4GIiAAwEIiIqB0DgYiI\nADAQiIioHQOBiIgAMBCIiKidXwTC6dOAXu/tKoiIBje/eNrppEkCZ88CY8YAkyaZu6iozv6O4eHD\nvV0tEZFv6M/TTv0iEIQQMBqBs2eBM2esu6qqzv6AANuQ6Do8dizgxJs9iYj81qAOBEeEAGpqrAOi\ne2A0NgKRkT2HhlYLqPlObyIaBIZ0IPRFU5M5IHoKjbNnzXsRXQOje2iEhbmkFCIit2IgDJDRCFRX\n2+5ZdB0ODrY9FNU1NCIieFiKiLyPgeBmQgAXLtgPjI5xzc3mcOgaGhoNMGECMHGi+XP0aEDhF9d3\nEZG/YiD4gMbGzrDo+KyuNh+O6ujq64Fx4zoDoqPrPjx2LKBUevsXEZE/YiD4ibY24KefOgPixx/t\n91+8aL7U1l5YdB0eN44nw4nIGgNhkDEYgHPnrPcu7IXH+fPAqFG9721MnAiMHw8EBnr7VxGRJzAQ\nhihZNodC17CwFx7nzgHDhjne45gwAQgJ8favIqKB8LlAKCwsxPr16yHLMrKzs/HQQw9ZTf/6669x\n7733ory8HI8//jgefPBB2wIZCC5jMpnv1egeFvaGg4I6w2HMGHM3enRn1314xAheXUXkS3wqEGRZ\nRlxcHIqKiqDRaJCamor8/HzEx8db2pw/fx5nzpzB+++/j/DwcAaCjxDCfP6iIxwuXDAHSU2NdX/X\ncS0t5sNWXUPCXnB0HR41ClCpvP1riQan/mw73fa/Y1lZGWJiYhAdHQ0AyMrKwo4dO6wCISIiAhER\nEfjwww/dVQb1gySZN9ajRgHTpvXtO3o9UFtrPzjOnwdOnrQNkosXzTf6Odr76D4uONi9v59oqHJb\nIFRXVyMyMtIyrNVqUVpa2q955eTkWPrT09ORnp4+wOrI1QICzCetx4/v+3dMJuDSJdu9jY7+I0fs\n75UoFI5Do/vhrBEjeCUWDW7FxcUoLi4e0DzcFgiSCw8odw0EGjwUis49kdjYvn1HCPMjSOwdtqqp\nAb77Digr6xxXWwvU1Zm7gABzMAwf3hkSzg4HB/NcCfmm7v9Y3rhxo9PzcFsgaDQa6HQ6y7BOp4NW\nq3XX4miIkCTzYaawMPNd4H0lhPku8vr6zoCoq7MdrqrqfbrRaB0Q/QmXYcN4wyH5JrcFQkpKCioq\nKlBZWYmJEydi27ZtyM/Pt9uWJ43J3SQJCA01dxMm9H8+er3jUKmpMb/UqafpTU3mOhwFSEd/aGhn\nCHbvDw1luJDruPWy04KCAstlp6tXr8YjjzyCvLw8AMCaNWvw008/ITU1FfX19VAoFBg2bBhOnDiB\nsC6PFOVVRjTYmExAQ0PPgdF1uL7eHCCNjeauo7/rZ2Bgz4HR0zhH0xk0/s+nLjt1FQYCUc+EMF/y\n21Ng9NTvaHpzs/mcS38DpeseTHCw+UbHrp8MG/djIBCRS3QNmv4EStfPlhZzwLS0dParVLYhYS84\n+jqut2lD9eoyBgIR+TwhzOdiuoeEvU9XjAMGFj5BQebDckFBtp298R3jvP2IewYCEVE3BkP/w6e1\n1bpra7Md19N4tbrv4eFM0PR1fFAQA4GIyOuEMAdRX8Ojr+OcaavXMxCIiAj923byRY5ERASAgUBE\nRO0YCEREBICBQERE7RgIREQEgIFARETtGAhERASAgUBERO0YCEREBICBQERE7RgIREQEgIFARETt\nGAhERASAgUBERO0YCEREBICBQERE7RgIREQEgIHgdsXFxd4uYUD8uX5/rh1g/d7m7/X3h1sDobCw\nEFOmTEFsbCw2bdpkt82vfvUrxMbGIjExEeXl5e4sxyv8/T8qf67fn2sHWL+3+Xv9/eG2QJBlGevW\nrUNhYSFOnDiB/Px8nDx50qrNrl27cOrUKVRUVOCll17C2rVr3VUOERE54LZAKCsrQ0xMDKKjo6FW\nq5GVlYUdO3ZYtdm5cyfuvvtuAMDs2bNx6dIlnDt3zl0lERFRb4SbvPPOOyI7O9sy/MYbb4h169ZZ\ntbnhhhvEvn37LMPXXXedOHDggFUbAOzYsWPHrh+ds1RwE0mS+tTOvM3v+XvdpxMRkXu47ZCRRqOB\nTqezDOt0Omi12l7b/PDDD9BoNO4qiYiIeuG2QEhJSUFFRQUqKyuh1+uxbds2ZGZmWrXJzMzE66+/\nDgDYv38/Ro4ciXHjxrmrJCIi6oXbDhmpVCrk5uYiIyMDsixj9erViI+PR15eHgBgzZo1WLJkCXbt\n2oWYmBiEhobitddec1c5RETkiNNnHTyooKBAxMXFiZiYGPHEE094uxynTZo0SSQkJIikpCSRmprq\n7XIcuvfee8XYsWPF9OnTLeNqamrE9ddfL2JjY8WCBQvExYsXvVhh7+zVv2HDBqHRaERSUpJISkoS\nBQUFXqywZ1VVVSI9PV1MnTpVTJs2TTz77LNCCP9Z/z3V7y/rv6WlRaSlpYnExEQRHx8vHn74YSGE\n/6z/nup3dv37bCAYjUYxefJk8f333wu9Xi8SExPFiRMnvF2WU6Kjo0VNTY23y+izvXv3ikOHDllt\nUH/3u9+JTZs2CSGEeOKJJ8RDDz3krfIcsld/Tk6OePrpp71YVd+cPXtWlJeXCyGEaGhoEFdccYU4\nceKE36z/nur3l/UvhBBNTU1CCCEMBoOYPXu2KCkp8Zv1L4T9+p1d/z776Iq+3MfgD4QfXSV1zTXX\nIDw83Gpc13tF7r77brz//vveKK1P7NUP+MffYPz48UhKSgIAhIWFIT4+HtXV1X6z/nuqH/CP9Q8A\nISEhAAC9Xg9ZlhEeHu436x+wXz/g3Pr32UCorq5GZGSkZVir1Vr+A/MXkiTh+uuvR0pKCl5++WVv\nl9Mv586ds5zoHzdunF/eOPj8888jMTERq1evxqVLl7xdjkOVlZUoLy/H7Nmz/XL9d9R/5ZVXAvCf\n9W8ymZCUlIRx48Zh/vz5mDZtml+tf3v1A86tf58NhL7ex+DL9u3bh/LychQUFOBvf/sbSkpKvF3S\ngEiS5Hd/l7Vr1+L777/H4cOHMWHCBDz44IPeLqlXjY2NWL58OZ599lkMGzbMapo/rP/Gxkbceuut\nePbZZxEWFuZX61+hUODw4cP44YcfsHfvXuzZs8dquq+v/+71FxcXO73+fTYQ+nIfg6+bMGECACAi\nIgLLli1DWVmZlyty3rhx4/DTTz8BAM6ePYuxY8d6uSLnjB071vI/cnZ2tk//DQwGA5YvX46VK1fi\n5ptvBuBf67+j/jvvvNNSvz+t/w4jRozA0qVLcfDgQb9a/x066j9w4IDT699nA6Ev9zH4submZjQ0\nNAAAmpqa8PHHHyMhIcHLVTkvMzMTmzdvBgBs3rzZ8j+6vzh79qylf/v27T77NxBCYPXq1Zg6dSrW\nr19vGe8v67+n+v1l/V+4cMFyOKWlpQX/+te/kJyc7Dfrv6f6O8IM6OP6d/25btfZtWuXuOKKK8Tk\nyZPFn//8Z2+X45TTp0+LxMREkZiYKKZNm+YX9WdlZYkJEyYItVottFqtePXVV0VNTY247rrrfP6y\nOyFs63/llVfEypUrRUJCgpgxY4a46aabxE8//eTtMu0qKSkRkiSJxMREq0sE/WX926t/165dfrP+\njx49KpKTk0ViYqJISEgQTz75pBBC+M3676l+Z9e/JISfXAJARERu5bOHjIiIyLMYCEREBICBQERE\n7RgIREQEgIFAHvb+++9DoVDgm2++6bFNeno6Dh48aDP+H//4B+6//36nlhcdHY3a2lqn63SHvLw8\nvPHGGx5f7pkzZ5Cfn+/x5ZL/YSCQR+Xn5+OGG27odQPlyjtCfenO0jVr1mDlypUeX+7333+PLVu2\n2J1mNBo9XA35MgYCeUxjYyNKS0uRm5uLbdu2Wca3tLQgKysLU6dOxS233IKWlhbLtNdeew1xcXGY\nPXs2Pv/8c8v48+fP49Zbb0VaWhrS0tIs02pqarBw4UJMnz4d9913X48P9goLC8N//dd/Yfr06Viw\nYAH279+PefPmYfLkyfjggw8AmJ/JM3fuXMyaNQuzZs3CF198AcB8s9XcuXORnJyMhIQE7Nu3DyaT\nCffccw8SEhIwY8YMPPPMMzbLzMnJwdNPPw3AvBf08MMPY/bs2YiLi8Nnn31mt85NmzZhxowZSEpK\nwiOPPAIA+O6777B48WKkpKRg7ty5lr2te+65Bw888ACuvvpqTJ48Ge+99x4A4OGHH0ZJSQmSk5Px\nzDPPYPPmzcjMzMR1112HBQsWoLm5GatWrcLs2bMxc+ZM7Ny5sw9/TRqU3H7HBFG7N998U6xZs0YI\nIcQ111wjDh48KIQQ4umnnxarV68WQphvsFGpVOLgwYPixx9/FFFRUeLChQtCr9eLq6++Wtx///1C\nCCFWrFghPvvsMyGEEGfOnBHx8fFCCCHuv/9+8dhjjwkhhPjwww+FJEl2H0EuSZIoLCwUQgixbNky\nsWDBAmE0GsWRI0dEUlKSEEKI5uZm0draKoQQ4ttvvxUpKSlCCCGeeuop8fjjjwshhDCZTKKhoUEc\nOHBALFiwwDL/S5cu2Syz66OI09PTxW9/+1shhPkGzOuvv96m/a5du8RVV10lWlpahBDCclPUtdde\nKyoqKoQQQuzfv19ce+21Qggh7r77bnH77bcLIYQ4ceKEiImJEUIIUVxcLG644QbLfF977TWh1Wot\n83vkkUfEm2++aVnGFVdcYXmUMg0tbntjGlF3+fn5+PWvfw0AuO2225Cfn4+ZM2eipKQEDzzwAABY\n/oUthEBpaSnS09MxevRoAMAdd9yBb7/9FgBQVFSEkydPWubd0NCApqYmlJSUYPv27QCAJUuW2H0c\nNgAEBAQgIyPDssygoCAolUpMnz4dlZWVAMyPEV63bh2OHDkCpVKJiooKAEBaWhpWrVoFg8GAm2++\nGYmJiZg8eTJOnz6NX/3qV1i6dCkWLlzocH3ccsstAICZM2daltnV7t27sWrVKgQFBQEARo4cicbG\nRnzxxRe47bbbLO30ej0A8+GxjkcrxMfHW57MKbrtJUmShAULFmDkyJEAgI8//hgffPABnnrqKQBA\nW1sbdDod4uLiHP4GGlwYCOQRtbW12LNnD7766itIkgRZlqFQKPA///M/AOw/s7378X8hhGVcR2AE\nBATYfM/evLpTq9WWfoVCYZmPQqGwHFf/61//igkTJuCNN96ALMuWDfM111yDkpIS/POf/8Q999yD\n3/zmN1i5ciWOHDmCjz76CC+++CLefvttvPLKK73WEBgYCABQKpU9Hsvv/ltMJhNGjhyJ8vJyu+27\nro/e1kNoaKjV8P/93/8hNja213pp8OM5BPKId999F3fddRcqKyvx/fffo6qqCtHR0SgpKcHcuXMt\nJz2/+uorHD16FJIkYfbs2fj0009RW1sLg8GAd955xzK/hQsX4rnnnrMMHzlyBACs5lVQUICLFy/2\nu+b6+nqMHz8eAPD6669DlmUAQFVVFSIiIpCdnY3s7GwcOnQINTU1kGUZt9xyCx577DEcOnTI7jz7\nElYdFixYgNdee81yTuXixYsYPnw4LrvsMrz77ruW+R09erTX+QwbNszyoEV7NWRkZFity57ChgY/\nBgJ5xNatW7Fs2TKrccuXL8fWrVuxdu1aNDY2YurUqdiwYQNSUlIAmN/ClZOTgzlz5uBnP/uZ5YUf\nAPDcc8/hwIEDSExMxLRp05CXlwcA2LBhA/bu3Yvp06dj+/btmDRpkt16uu99dB3u6P/FL36BzZs3\nIykpCd988w3CwsIAAHv27EFSUhJmzpyJt99+G+vXr0d1dTXmz5+P5ORkrFy5Ek888USfltvb+IyM\nDGRmZiIlJQXJycmWE9JvvfUWXnnlFSQlJWH69OlWJ4Ht/Y7ExEQolUokJSXhmWeesbmK69FHH4XB\nYMCMGTMwffp0bNiwwW6NNPjx4XZERASAewhERNSOgUBERAAYCERE1I6BQEREABgIRETUjoFAREQA\ngP8PKB2w9Bs2WKAAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x85607d0>"
]
}
],
"prompt_number": 125
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This affects all the modes because the mass is not being added at a nodal point."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(modes2[:,:,0].T); grid(); title('Mode 1');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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+9A2yWbyYFiyoQl+uXycyMyOKiVGFec2PBw+IvvuOqFMnoh49iDZtIkpNVbVV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\n4eHheQn4f9HsybEjp5qDAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x8e2e050>"
]
}
],
"prompt_number": 126
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(modes2[:,:,1].T); grid(); title('Mode 2');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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kxmDIkSH4zPkzLHFdUr3cL0RsaccPPzCB++UXpgQCV63kicU4m5WFk5mZ8MnL\nQ+/mzTHO0BDD9PXRsnFjQX1WGrqYUJpYipK4EpQ8fCbuz34ueVQCNS01aFpqQtNKE5qWmvD28kZP\nq57osL+DrA/f/HyMi4pCkJMTzJpUUuz8yROWmO3PP+XKYf3N1W8Q+SQSFyZeqP6bsoK5fBmYP59l\naBVSacuH54pRKPx+KpYGLfr+Sf4YfXw01r6/FtMcp1VvgMBAtoEqJYVtqho3DqjiSpiXyS4vx5ms\nLHhmZsI3Px/9W7TAOENDDNfXV4hlI0oXoTC0EE/vPWWC/uzpvTSpFI2NGlcQdk1LTTSxbAJNS02o\n61Qc+9rla2i2uBnafNsGRtOMZL9fm5iIs1lZ8HF0rHwlkJ8fMHo0s3oELk8tl5TD7YAbRrQfge96\nfyeoD0UyfvyL/XTVhYuUYuH3U7E0WNE/d/8cZp6diYOjDmKI9ZCqdxwVxbzqkBCWDG369Bd1ZKtI\nhkiE08+E/nZBAQbp6WGcoSGG6ulBWw6hFz0RoTCkEEUhRSgMLkRhcCEkTyXQ7qqNprZNK4p7uyZQ\n1ajem1RxZDHC+oXB8YYjtGy1AFTD39+8mRUh9vMDBH5qScxPhPNOZ1ycdBHOrZ0F9aEoUlPZtM3N\nm0CHDm8/n8OpLzRI0d8duhvLvJfhjPsZdDPpVrUOExKYyF++zNIvzpsHVGZpvIbUsjKcembd3Ckq\nwpBnQv+Bnh60BExylmeXozCkUCbuhSGFkORL0KxrM2g7a0O7qza0nbXRpF0ThaYrTtuThuTNyXAK\ndIJa02r4+0Tsad/SUq4Up8cjj2OZ9zLcmXsHWo21BPejCLZtY1M5164pN9kph6NIGpToExFW31iN\nfWH7cHny5aqVNMzIYKtwjh5lRu5XX1V5U1W6SIS/njyBZ2YmoouLMVxfH+MMDTFITw9NqmEFleeW\ns6f3l0S+PLsc2k5M2J9/NbFoAhVVYepDRBCLc1BamoiyskSUlSXJfi4tTURQUCamTr2CJk3METM5\nBmpN1WCzy0bWvkr+fnY24OjICq8Mqcanq/8w7fQ0aKhpYOeInYL7UAQSCZujXrSI7fquKtyOUCz8\nfiqWWt+RW1NIpBLMvzQfAckB8JvlJ8uhUylFRcDatWyZxtSpwL17gKHhW8cRE+Fidjb2pqfjel4e\nPjQwwNI2bTCgRQs0rqLQl2eXI+96HvKu5SH3Wi7KksrQrAt7gjcYZYB2q9tB01qzWgIvlZaitDTp\ntYLOvicnuPfuAAAgAElEQVRBVbUxNDTaoEmTNtDQMEOTJm3QrJkjmjRpg9jY/YiOdkeXLjfRfkd7\nhHQNQcbRDLSa2AoA0Lt5c3xpagr36OjK/X19fWbxuLuz6l/GxlWO/2W2DdkGxx2OOH3vNEZ1GCWo\nD0Wgpgbs2MHKBg8bBujpKS0UDkep1Lkn/ZLyEkw8NRGFZYU4NeEUdDTe8KROBBw7xqqm9+vHlhq2\neXuRlAdPn2JvejoOpqfDvEkTzDI2xnhDwyp59OJCMfJv5stEviSuBM1dm0O3vy5a9G+BZo7NoKJW\nNYEvL8/F06fRKC6OQnFxFJ4+jUJxcTTE4hw0bmzyTNArCruGBvtZXV37DbeFEBn5IZo2bQ9Ly/Uo\nCivC3YF30eVWFzRtzwqtV9nfX7ECuHWLrd8XMPkNAH5Jfhh9fDTuzL2D1tqtBfWhKBYsYOWJPTyU\nGgaHoxDqvb2TU5KDkcdGok3zNtg/aj8aq71hEvHuXfY/uKiIGbaurm8co1giwYnMTOxNS8ODkhJM\nadUKM42MYKv1Zq9ZUiJBgV8Bcq/lIu9aHoojiqHdTRst+reAbn9daLtoQ7XRm8VQLM5DcXH0S8LO\nviSSImhp2aFpUztoaXWEllZHNG1qBw0NU6hUcaljcXExUlNTkZaWhtTUVKSmpqK8vBzz509DeHh3\ntG//O/T1hyPlzxSk7UyDk78TVJuwvqvk74vFQP/+zOL5/vsqxfQ6VvqshF+SHy5PvqzUZZz5+YCd\nHcsxJ+f2DA5H6dRr0U/MS8QHRz7AYMvBWD9ofeXCkJPDNladPAn8+CPLaV/J5CoR4XZhIfakpcEz\nMxOuzZtjppERhuvrV7pkUSqSojCoUCbyhUGF0LLXkom8Tk8dqGm+fjyJpAhFRREVhJ2Je8EzYbd7\nJuxM4DU0zCqduC0uLpYJ+cuC/t+fRSIRWrdujdatW8PY2BitW7fGtWvXMHDgQCxfPgZRUWPh5BQE\nDQ1TRI+PRqOWjdD+9xfzI775+RgbGYngrl0r9/eTkgBnZ+DMGaCHsPoEYqkYffb1wXi78fiyp7Dk\nbori77/Z1E9ICPC2fXPcg1Ys/H4qlnrt6bvudcWi7ovwVa9XUy8DYDNxu3Yxu+Gjj4CYmEqN2UyR\nCIcyMrA3PR1lUilmGhkh0sUFrTVen66hJL4E2eeykXMpB/m38qFppYkW/VvA7BszNO/THOrar94m\nqbQcxcWRKCy8jYKC2ygsvI2SkkcVhL1Fi4Evift/0h9LpUhKSkJsbCzi4uJk3+Pi4pCUlCQT8+dC\n/vy7vb297OfWrVujefPmFd44pFLg1Kmz+OqrBXBzc4ODwxeIifkYjo4+sNltg2CnYGR6ZsJwHJvz\n6N28Ob40M3uzv29mxvyQiROZvy8gZ7G6qjqOjDmC7ru7Y4DFANi3kj/lhVA++ohl4NyyBfj6a6WF\nweEohTrzpH/o7iFMtp/8+hN8fZmVo63NrByHV9MnS4hwJScHe9LT4ZWbi5H6+phlbIz3/iOKAEAS\nQkFgAbLPZSP7XDZET0TQH6YP/WH60O2ni0b6FR//iAilpY9k4l5QcBvFxXfRpIk5tLW7QUenG7S1\nu0FLqzNUVV+0lUgkSE5OriDoz39+9OgR9PT0YG1tDSsrK9l3KysrtGnTBrq6urK4y8qAzEy2OOnJ\nk1e/v/xzVhZ7et24MRzLlw9EUNBt5OXNRbNmXWFh8TMKgwsRPjQcTgFO0LRgW1SlRBgWEQGHZs2w\nxsKi8n+ozz9nA/z1l+B1jwfCDuA3v98QNCcImo0EbJFVEA8fstU8oaFVmgbicOok9dreeW0Yqals\nkvZ57UR391fEJlMkwq60NPyZmgrjxo0xy9gY7i1bovl/JmXFhWLkXsllQn8xG41bNYb+CH3oj9CH\nTjedCpOvIlEmCguDKjzFq6pqVhB4be2uUFdnk8zFxcWIjIxEREQEYmJiZMIeHx8PfX39CqL+/Lul\npSWaNtVCVhbw+DHbWpCQwH5OS6so5MXFbDFSy5ZAq1Zv/m5oCFy6xJKNTZu2GdeueeLff48jPLw7\nbGz2Qk9vEJK3JCPjcAa6+HaRbfrKFIngFBICj/btMbQyf7+khCnlwoXMVhMAEcH9pDtaabXC1iHV\nrJSjYFavBoKDWR0HDqc+0nBEXyRiu0LXrQM++YTly2nWrEKbkMJCbEtJwZmsLIwxMMACU1M4/uec\n0sRS2dN8vl8+dHroQH+EPgxGGKCJOfOviaQoLo5Cfv515Of7oqDgNsrLs6Gj4/JM5LtDW9sFGhqt\nIZVK8ejRI4SHh8u+IiIikJKSgg4dOsDe3h62trawtraGtbU12rWzQHGxlkzMnwv7y8caGoC5OdC2\n7YvvrVtXFHNd3eotnPHx8cGZM2549IhQWjoEXbs6YcmSQYiO/hhdu4aicWMjRI2OQpN2TWC1yUrW\nrkrr92NigPfeY2/EdnZVD+olckty4bDDATuG78BQ66GC+lAEZWXsQ+PatcCHH77+HO5BKxZ+PxVL\nwxD9S5eAL74ArK1Z9Spra9l55VIpTmZlYWtyMpLLyvC5iQlmGxvLsliSlFAYVIjsc9nIOpcFUaoI\nekP1YDDCAC0GtYC6jjqIJCgqCkd+/nXk5V1Hfv5NqKvronnzvtDV7QMdnR7Q1GyPnJxcREREyIQ9\nPDwcUVFRMDAwgL29PTp37gx7e3vY2dlDTc0aDx+q4949Zhs8F/bERKBpUybmLwv7y8c1UZDLx8cH\nvXq5wdUV+PDDQuzYYYs9e/bAxiYAeXnX4eBwFeJcKUKcQmC1xQoGH77IhrkmMRHn3pafZ/duVs8y\nMFBYFjMAPgk+mHhyIsI+DUNLrZaC+lAEPj6sEmZU1CvPFc9e5yKlSPj9VCz1W/Tj4ljJvpgY9pQ/\nbJjs9QyRCB6pqfBITUX7pk2xwMQEIw0MoK6iAqlIirxrecj0zET2+Wyo66vDYIQBs2166ACqEhQW\nhj4T+OvIz7+Fxo2NoKvbF82b90Xz5n2QllaOoKAghISEyES+oKBAJuz29vYwN3eEunonpKZq4949\ntv/r/n3g0SP2ZG5jw/K6WFlVFPXXCUlt8egRW2zz448hWLVqOIKDbyMzcxp0dd1gbr4c+f75iBwV\nia63u6JJW/Zk/9zft3/T+n0iZrUZGAC//y44vu//9z0in0TirPtZhaafqC7TprFPVb/9prQQOBxB\n1G/R19dnSym+/JJ5HgBuFxRgW0oKzmdn4yNDQ8w3MYF9s2aQiqTI9cpF5olMZJ3NQlObpjAcZwiD\nDw2g0U4NhYXBL4m8P5o0aSMT+dLSDrh7NwFBQUGyr8aNG8PFxQVOTi4wNu4BdfVOyM1tiQcPVGUC\n//QpE/Xn4v6yyAt82K0VPD3ZtIi7+1r4+1/GhQuHEBbWDXZ2R6Gr64bE3xKRdSoLjjccZfsNnvv7\nu21sMLiyrat5eUCXLsDGjSxPjwBEEhF67umJ2V1m4zOXz4Reotw8eQJ06sQybyugjg6HU2vUb9FP\nSgJMTSGSSnEiMxNbk5PxpLwcn5uYYKaREXRJDblXXxJ626Zo+VFL6I/RRbluJHJzvZCX54OCgkBo\nalpBV7cvAGfExWnizp0HMoEvLi6Gs7Mz7OzcoKvbF1JpJzx+3BwRES+yN3To8KrAt25dfxJ1/fcj\n9OefAxkZhOzsAXBz64sFC3ri/v2Z6No1FI3UDRExIgJaHbVgue7Fk713bi4mxcQg1NkZRpVl2vT3\nB0aNAoKCBC+BuZ91H657XXFzxk3YGtoK6kMR7NoF7NvHFoq97GpxO0Kx8PupWOq16KeWlmJHaip2\npqWho5YWFpiYYGizFsi/msusm3PZ0OqoBYOPDKA9ohDFja8jN/cq8vK8oaFhBk1NNyQmmuLePQlC\nQ6Nw+/ZtpKamwsGhO8zNh0Jb2xUikQ2SknQRHq4CsZg91b38ZWcHvGWDbr3gv/+xSkuBnj2B8ePz\nsW2bLY4cOYK2ba+iqCgUnTtfhDhbguAuwWjv0R76Q1+s3FkeHw//ggL8a28P1cre8X79Fbh4EfD2\nrnba6ufsDNmJP4P/RMCsAGGlLxWAVAr06cOsnk8+efF7LlKKhd9PxVKvRV/35k24t2yJz/WNYXSr\nDJknmEev1VkLeu6N0GhAOArhg9zcq5BKy1BW1guxsUYIDy9DYGAYIiOjYGnZD2ZmQ6Gp2R1Pn1oh\nMbE54uNVYG39qsAbG9efJ3dFEBvL0g789JM/fvppHEJDg5CaOh76+sPRps13yLuZh+iPotE1uCs0\nTJnwionQLywMw/X18W1lT/JSKTBoENC7N7BypaDYiAijj49Ge/32WDdwncArlJ+ICGDAACAyknn8\nHE5dp16LfsLJdDw9lYPsC9lo2qURtKckAV2DUVB+DQUFMUhPt0dsbCuEh5cgMDAGRUXGsLAYBy2t\nPigqao9Hj5pDS0vlFXG3sRFcB6TBcewY29A8cuQqRET44Z9/duLOnW7o1OkUmjd3xeOfHyPn3xw4\nXnOEijp7R0wsLYVLSAjOdO6MHpUtNUpLA5yc2Katvn0FxZb1NAsOOxxwcNRBDLAYIPQS5WbJEiA9\nHTh4UGkhcDhVpl6LfvBHJ6AxOhJiqwCkPLmFuDhjPHhgiLAwEe7cUUOLFgPQosUAiEQdkZpqCCMj\nFTg5qcDJCbIvA+XW4a4zvOkj9Jw5QFGRFElJfTFs2FDMmdMJsbHz4ewcCnU1PYR/EA6dbjpot/pF\nqcTTWVn4Mi4Od5ydKy8LeekSMHcucOcOS8ssgCsPr2DW2VkImxsG/abC+pCX4mJm8+3fzxK3cjtC\nsfD7qVjqtej/8IMBYmKMEBJihowMCxgYDAKRE7KzjdC2rQpcXNRk4u7oKCj9yzvDm/5jPX3KNtVO\nnZqDDRvs4OnpCSOjf1BSEotOnc6g/Ek5gp2C0WF/B+gNfLFyZ35sLJ6IRDhuZ1f58sqvvgLi4tgW\nV4He2Zf/fomk/CSc+OiE0pZxnj3Lnvjv3gX8/blIKRIu+opFiOiD5OTSpUtkY2NDVlZWtGbNmtee\ns2DBArKysiJ7e3sKDQ195XUA1KJFPDVqJCJr66c0bZqEtm4l8vUlKiyUN0LOf4mOJjIwIPr9dx8y\nMzOjJ09SKTi4GyUmbiQiopz/5dAt41tUllYma1MikZD97du0MyWl8o7Lyoi6diXatk1wbCXlJdT5\nj860J3SP4D4UwYcfEv34o1JD4HDeihAJl0v0xWIxWVpaUnx8PIlEInJwcKDo6OgK51y4cIGGDBlC\nREQBAQHUvXv3V4MAKDCQ6OlTeaLhVIf9+4lsbYkWLfqehg8fTsXFD8nX15Dy8wOJiOjRskcUNiCM\npGKprE10UREZ+PpSZFFR5R3HxrJ3lLAwwbFFZESQwToDis2OFdyHvDx+TKSvzy6Hw6mrCBF9uapZ\n3L59G1ZWVjA3N0ejRo3g7u6OM2fOVDjn7NmzmDZtGgCge/fuyMvLQ0ZGxit9detWtzc51Sd8fHze\nes60aYCLC5CT8xMyMzOxY8dptG//J6Kj3SEW58F8uTmkIikS1yTK2thqaWGthQUmREejRCJ5fcdW\nVix9xoQJzCAXQKeWnbD8veWYdGoSyiXlgvqQlzZtWM2Yjz/2gfIN0IZDVf42OTWLXPn0U1JSYGZm\nJjs2NTVFYGDgW89JTk5Gq1atKpw3ffp0mJubAwB0dXXh6Ogo8/6e/6Hw46odh4WFVen83393g4uL\nGvr1+w4//TQDvXv/C339oTh8+EO0bbsSvY72QohzCCJ1IqHVWQtubm6YYWSEI//+iwn37uHsswrj\nr/Rvagq0bQu3hQuBPXsEXU8n6gQ9TT38eONHDFAZoJT7uXChG/74A1ixwgf9+9edf19+/O4e+/j4\nYP/+/QAg08tqI89HC09PT5o9e7bs+NChQzR//vwK5wwfPpx8fX1lxwMGDKCQkJAK58gZBkcOwsOZ\nG7N16xUyNzen7Ow0CgrqQsnJ24mIKOtcFvmZ+ZEoSyRrk19eThb+/nTiyZPKOy4oILKyIjp2THBs\naYVpZLTeiG4+vim4D3nx8yNq3ZooL09pIXA4lSJEO+Wyd0xMTJCUlCQ7TkpKgqmp6RvPSU5OhomJ\niTzDchRI587AL78AO3cOxJAhYzBnzuewtf0LCQkrUVh4B/rD9WE4zhD3Zt6TrRLQUVfHX3Z2mPfg\nARJKS1/fsbY2W7e/cCEQHy8oNqNmRtg5fCem/DMF+aX5Qi9RLnr2BEaMAJYuVcrwHI7CkUv0nZ2d\nERsbi4SEBIhEIhw/fhwjR46scM7IkSNx8NlOl4CAAOjq6r5i7XAUy/OPg1Vl9mwm/mVl65CQkID9\n+6/CymoroqPHQywuhMUaC4hSRUjZmiJr46KjgyVt2mBidDTKpdLXd9y163NjHCgX5s2PsBmBD6w+\nwPxL8wW1lxcfHx/8+isryRwUpJQQGhTV/dvkKB65RF9dXR3bt2/H4MGDYWdnhwkTJsDW1hYeHh7w\n8PAAAAwdOhQWFhawsrLC3Llz8ccffygkcI7iUFEBduwAbtxQw+TJF7Bq1SqkpNhAV7cfHjyYC5VG\nKrD7yw6PVz9GYUihrN1iU1PoqKtjRUJC5Z0vWsRqGS9fLji+DYM2ICglCMcijgnuQx5atGBpl+fO\nBcRipYTA4SgOxbtM1aeOhPHOExrK/P1Nm86TlZUV5eSk0+3bnSg1dRcREWUcz6AAywAqzy+Xtcko\nK6PWt27R1ZycyjvOyGDG+NWrgmMLSQ0hw3WGlJCbILgPeZBKifr1I9qyRSnDczivRYh21pkduXUg\nDA5YTZTduwFn5wUoLMzE7t3LcfduXzg4XEOzZp1xf+59SAoksD1qK9sx65Wbi2kxMbjj7IyWjStJ\ndOTlxdaJ3rkjOJvZWt+1uBh3EdemXoOaqprQSxTM/fssr1xYGMCnpTh1ASHaKZe9w6mbyOObzpvH\nltqrqW3CvXv3cPjwDVhabkB09HhIJEWw2myF4shipO9Jl7V5v0ULTDMywrR79yCt7A/w/feBqVOB\n6dNZZk4BfN3ra6hABetu1V4mzpfvpY0N8NlnrJonRxjc01c+XPQ5FVBRYQVFrl5Vx4wZl7Bs2TKk\npXWGjk53xMbOh5qmGuyO2+HRd49QHPVi89Uqc3PkicXYmJxceec//gjk5ABbtgiKTU1VDYdGH8Km\ngE0ITg0W1Ie8/PADe9K/eFEpw3M48qNgi0kQdSQMzksEBzN/f+PGs8/8/VQKDLSltLT9RESUuieV\nAu0CSVwslrWJLykhQ19fup2fX3nHjx4RGRoS/WevRnX4K+Ivar+tPRWVvSEdRA3y779E7doRFRcr\nZXgOR4YQ7eSePqdSnvv7XbvOR1FRFnbvXoq7d/vD0fEGmjbtgJjJMVBrqgabXTayNp6Zmfj24UPc\ncXaGTmVpmI8fB5YtA0JC2Hp+AUw7PQ1N1JvAY7iHoPby8vHHQLt2bI8Dh6MsuKfPAaA433TePMDa\nGgA2P/P3b8HC4ldER4+HVFqC9jvaI88nD0/+eiJrM87QEAP19DD3wYPK/xgnTGC1CecLX3u/bcg2\nXH14FWfunXn7yXJQ2b3cuJHZYFFRNTp8g4N7+sqHiz6nUlRU2JP+9evqmDr1ub/vBC0te8TFLYK6\ntjrsjtshdkEsSuJKZO02WVoiorgYe9PTK+9861YgMBA4fFhQbDoaOjg85jDmnp+LtMI0QX3Ig7Ex\nqw752WfgCdk49QvFOkzCqCNhcCrhzh3m769ff46srKwoOzuZAgKsKT39CBERJW1JouCuwSQplcja\nRBUVkb6vL4W/qSDC847lyF+83Hs5DTo0iCRSydtPVjBiMZGLC9HevbU+NIdDRNzT59QgHh7M43dx\nWYDi4kzs2vUtwsMHoUuXW9DUtEbU6Cg0adcEVpusZG0OpKdjTWIigrp2RTO1StbVb9vGCtLeuiWo\nmLFYKkbvvb3xcaePsajHIqGXJ5jQUGDIEGbz8HKdnNqGe/ocADXjm37yCdCpEyCVsvX7R44Ewtz8\nR0RHTwBRGWz22iDzVCayzmbJ2kwzMkIPHR189iZ/f/585pUIzGimrqqOI2OOYPXN1YjIiBDUx5t4\n2710cmKTut9+q/ChGyTc01c+XPQ5VUJFhT3t+/urY9Ik5u9nZHSHpqYV4uK+QiO9RrA7Zof7c+6j\nNOlF5s3t1tYILSzEvsr8fRUVYO9elpHz338FxWapZ4l176/DpFOTUCquJOtnDfLjjyz0mzdrfWgO\np9pwe4dTLcLDgQEDgCVLLmDnzi8QGHgNDx64wdJyLQwNx+Hxr4+RcyEHjj6OUFFnaRqii4vxXlgY\nvB0c0LlZs9d37OMDTJzI/BIjo2rHRUQY7zkepjqm2DR4kxxXKAxPT2DFCpZlQoBLxeEIgts7nBrH\n3h5YswbYv38Y+vT5APPmfQM7u7/w4ME8lJQ8Qptv20C1qSoSVibI2thpaWGDpSXGR0ejqLIyi25u\nwKxZLD+PgDQNKioq8BjuAc9oT1x5eEXYxcnB2LGAuTlbysnh1GW46DdAato3nTmTpcoXizchJiYG\nR4+GoG3bpczfhwi2h2yRtjcNuV65sjZV8vdXrACKioANGwTFpaephwOjDmDGmRnIepr19gZVoKr3\nUkUF2L4dWL9ecM2YdwLu6SsfLvqcaqOiAvz5JxAcrI6PP76MZcuW4cmTPtDQMMGjR9+hcavGsD1k\ni5gpMShLKZO1e6u/r64OHD3KktcLrFjSv11/TOw8EXPOzal1y7BdO+Crr9jcNHcrOXUWBS0XlYs6\nEganmkRGsmX2a9deICsrK8rKSiB//7aUmXmaiIgSfkqgUNdQkoiquX7/xAkiS0uiN+XweQOl5aXk\nuMORdoXsEtReHsrKiGxtiTw9a31ozjuIEO3kE7kcuThwgHn8PXsuxNOnT+DhsQiRkaPQtettaDRu\ng4jhEdCy04LlessXbaqyfn/uXGb1HD7MPlpUk+jMaPTd3xe3Zt5Ce/32Qi9PEDduAJMmAdHRglML\ncThVgk/kcgDUrm86bRorHl5auhHR0TE4duwuzMy+RnS0Owhi2B6yRaZnJjJPZb5oY2SEnm/z9zdt\nAu7eZcs5BWBnaIeVfVdi0qlJEElEgvoAhN3L994DBg6Uq0Jkg4V7+ooj6XG2oHZc9Dlys307EBGh\njvHj/8WyZcuQnT0A6up6iI//Ho30G8Hubzs8+PQBnsY+fdHG2hp3iooq9/ebNgVOnAC++44lsBfA\nPJd5aK3dGt95fSeovTysW8emJ0JDa31ozjuAVEpwcrwtrLFiHSZh1JEwOHIQE8P8/TVrLpC1tTVl\nZcWTv785PXlygoiIkn9Pptv2t0n89EX+/aiiIjJ4m79/7Bjz9/PyBMWV/TSb2m5qS6djTgtqLw97\n9rDcPGLx28/lcKpDb+d9pNE4UJB28id9jkLo0AHYvBnYu3coXF0/wOeffwc7uxN48OAzFBfHoPVn\nraHVUQuxn8fK2lRp/b67O/DBB8CMGYKWxOhp6uH4uOP45PwnSMhLEHh1wpg+HdDQYDuZORxFsfK7\ns7gVMhgTBwvbFMJFvwGiLN900iSgb1+guJj5+0eOBMHCYg2iosZCIimCzU4bFAQUIG3vi1TIU6vi\n72/YACQnM59fAN1Nu+M71+8wwXNCtf19ee6lqipb2rpiBfCmLNPvEtzTlw8/3wf4aZ0LRvT4DRM3\nzhTUBxd9jkLZsgV48EAd48ZdxYoVK/D4cUc0b+6K+/dnQVVLFR1PdsSjbx+hKKxI1ua5v19p/n0N\nDebvr10L+PoKiuuLHl/AqJkRvvWq3cxonToBs2ezgjR8gRpHHgoLyzBwYD7szA+j+xJ1WKgOEtaR\nUE8pOzub3n//fbK2tqaBAwdSbm7ua8+bMWMGtWzZkjp16lRpX3KEwamD3L/P/P1Nm66TqakppaTE\nU3BwV0pM3EBEROlH0ynAMoDKc8tlbaq0fv/CBSITE6L0dEFxPff3/4n5R1B7oZSUsLX7R4/W6rCc\nBoZlm79IV/sMzfq//iQqF9N77wnTTsFq+80339DatWuJiGjNmjX07bffvva8GzduUGhoKBf9d4y/\n/2bFw7/++lfq06cPFRQ8oFu3WlFu7nUiInrw+QOKGBVBUqlU1uZAWhrZBAZS4ZtmPpcuJerfX/Ds\naEBSABmuM6RHOY8EtRfK7dtELVsSpabW6rCcBsLHo4+Qmtp9mjX+A0orTKMtW4h69apl0bexsaH0\nZ09caWlpZGNjU+m58fHxXPRrEW9vb2WHQERES5YQvf++lD74YDgtWrSIsrMv061bram0NIUkpRIK\ndgmmxPWJFdrMiImhydHRFd4MKiAWM9H/v/8THNdGv43kstOFysRlbz1Xkffyhx+IRowgquzS3gXq\nyt9mfeLgHj9SUXlCUwZ8Qtce/o8ePCDS1yd68ECYdqoL9ZcyMjLQqlUrAECrVq2QkZEhtCsAwPTp\n02Fubg4A0NXVhaOjI9zc3AC8mPzhx1U7Dnu2rl3Z8fzyixuGDFGBpuYCnDgxAy4uLnB1/RQHDw6G\npeUm9DrRGyHdQnC30V00s28GNzc3bLe2Rsddu/BtdDTWjR37av9qavCZPx+YOxduvXoBQ4ZUOz7H\nUkecTDqJb72+xabBm2rtfixf7gYXF2DpUh8MGqT8fx9+XPePH8dnY8aceNi3+x0dvm4LSlCFq/t0\nWFoCR46YQxBvekd4//33qVOnTq98nTlzhnR1dSuc26JFi0r74U/67y5ZWczmWbs2gQwMDOjOnVAK\nDx9GsbGL2OsXs8jPxI/K0l88dVfJ3795k/klCQmC4sp5mkPmm83pVPQpQe2FEhJCZGhIlJxcq8Ny\n6iFisZT0ml8ls1YeNPmXviSWiGn9eqL33iOSPEtnJUQ75bJ30tLSiIgoNTWV2zucSnle/3zNmgtk\nYWFB6ekPyd/fgtLT2czmo/97RHf63SGpuJr+/vr1RN26EZWWCoorMDlQKf7+ihVEQ4e+2zYP5+30\n7L7lorEAACAASURBVHqImmj40vRpvSijKINiYpit8/Dhi3OEaKfgJZsjR47EgQMHAAAHDhzAqFGj\nhHbFUTDPPx7WFRwd2VLOnTuHYvBgd0yf/jlsbf9GXNxCFBdHwXylOVRUVRC//EUi+qlGRujdvDmm\n37tX+fr9xYuB1q1ZPmMBdDPphh/6/PDG9fs1cS9/+AFITQX27VN413Weuva3WVdZtuQ8AkL7YdrA\nPzB95S/Q02iJadNYaU4LCzk7F/oulJ2dTQMGDHhlyWZKSgoNHTpUdp67uzsZGxtT48aNydTUlPbu\n3ftKX3KEwXkNdXWybPFiokGDJPTee/1o2bJllJZ2gAIC2lN5eR6VZZSRn6kfZZ3Pkp1fKpFQj5AQ\n+ulNFk5uLkvTIHA9pFQqpQ+PfUiLLi167es1dS/v3mWffh4/rpHu6yx19W+zLuHr/YBUVNJprOsX\ntMZrFRERrVlDNGDAC1vnOUK0s06oLRf9d4PycrbwZuHCIjI1NaUzZ87Q/fufUUTEaJJKpZTnm0e+\nLX2pJL5E1ialtJRM/PzobGZm5R0/94+iowXFpSx/f/VqooEDuc3DeUF+fik10QglB6ufadLm/iSR\nSmR1K1737MNFn1PnycwkMjcn+uWXB2RoaEgxMREUHNyNHj9mez4SNyZSsHMwSUpfPNL45+eToa8v\nxRQXV97xnj1sB9SbJn/fwHN//2HOw7efrCDKy4m6diXy8Ki1ITl1nHamp0hPx5MmfNaRMoszSSRi\nfyM7d77+fC76HCKq+x+hQ0LYk8vy5X+TnZ0dPXkSTbduGVFOzv9IKpVSxJgIuv/Z/Qpt9qSmUvuA\nAMotL6+kVyKaMYNo0iTBj86b/TeT805nKi1/MTFc0/cyMpJNzsXH1+gwdYa6/repTMZ/eJzU1KJo\nwZhh5PvYl4iIfvqJaNCgyv+khWgnz73DqXWcnICNG4GjR8fByWkA5s1bjg4dDiEmZhJEohR02NsB\nuV65yDjyYu/HTGNjDNTTw6ToaEgqm9hlif0Fp7Vc2H0hTHVMscRriaD2QujYEfjmG2DWLEAqrbVh\nOXWM/Tv9cOJsP0wfsB1mi3rDtY0r7t5lCyB27xZUPK5SeLlEjtL44gvg3j0JsrNdMX78WEyYIEFW\n1mk4Ol7H08hy3B1wFw7XHNCsczMAQLlUioHh4XDV0cHPlS1hiI0FXF2BixcBZ+dqx5RbkgunnU7Y\nMGgDxtiOkefyqoxYDPTuDUyZAnz+ea0MyalDPIzLgk2HIvR12IFWs0Nw+NN/IS5XRffuwMKFLKt4\nZQjSTqEfRRRJHQmDU8uIRER9+xItXJhHRkZGdPXqVYqIGEX3788jIqL0I+nkb+5PZRkvNm49KSuj\ntv7+9HdGRuUde3qyiYPsbEFxKcPff74GOy6u1obk1AHKy6Wkq+NN5sbbafgXVpRVzFavrVhBNGzY\n251KIdpZJ9SWi75iqU++aUYGUZs2RKtWhVOrVq0oLi6cAgKsKS3tIBGxjVshvUIqTOyGFBSQga8v\nhb1p0vbLL9n/mv+ucasiz/39K15XBLUXwoYNRH36CA65XlCf/jZrg24Of5FmE2/67GNX8kv0I6IX\nu7ZTUt7eXoh2ck+fo1RatgQ8PYFt2zpj6tRfMWHCDFhZHcPDh4tRVHQX5qvMoWGsgfuf3Jd9jHXS\n1sZWKyuMjoxEdnn56zteuxbIzWXfBbCw+0KY6Zjhz+A/BV5Z9Vm0iPn627bV2pAcJfLd4osICu+F\nuYP2wfLzUehp1hNlZazi2saNbN9hjVDtt4kaoI6EwVEi+/YRtW8vpVGjptGMGTMoLe0IBQRYkkiU\nQ+IiMQU5BdHjNRV3Mn0TF0f979yh8so+AycnExkbE507Jyim3JJcare5HXlGeQpqL4TnGRTv33/7\nuZz6y4ljoaSi8oTGv/cFjd8zRJZVdulSog8/rPoCNCHaySdyOXWGBQuAhw/FePy4CxYunI8BA+6j\nqOgu7O0voTyVENojFNbbrWEwygAAICHC0PBw2GlpYZOV1es7DQgARowAvLwAB4dqxxScGoyhR4bi\n6pSrcDCqfnshbN0KHD8O3LgBqKnVypCcWiQyPA2OXcrRu/OfUB9yDCeW30ELzRYICgKGDwfu3gWM\njKrWlxDt5PZOA6S+5jfZuBEoKlLHgAE+WLZsGTIzx0JNrRkePPgUjU0ao+M/HXF/zn1ZqUU1FRX8\nZWeHc9nZOFhZqcUePYDff2fCn5pa7Zj+v73zDo+i+t74u6mEmpAOCUVKCIQUOiIShICi9OpXASmK\nCChKt4EiEqqCoP5QkKIELIQOCkKAJAQiBEJCQiCkk977Znfe3x+DwZgi2Wwq9/M885Ddmbn3zOXu\nOzPnnntuTlgOvnrhK4z0GIn47Pj/PkELzJ8P6OnJC803NOpr39QWaWkF6NM3AR1tDsCknwfWzv8F\nJkYmKCgApk+XQzQfV/A1RYi+oM6gry8vhevpaYo5c05g0qQpMDHZhJycm4iOdkfz3s3RaXsn3Bp9\nC8oEOUGaib4+jjg4YFF4OPyzssoueNIk4M03ZeHPza20XZMdJmNOzzkY6TESucrKn19ZdHTkZGzu\n7kBISLVXJ6gh1Gqia+dLaGIUgucG/YxX3t6I3q17AwBWrpTnbEyeXAOGVNohVA3UETMEdQQ/Pzl6\n4Z13vmGPHj2YkhJGX19bJiYeIElGrIrgtb7XqM5/FOZyKCmJNr6+jC8sZzUsSSKnT5cdphostShJ\nEqd5TuPYA2OplmomvObrr+XM0RVNQhbUH5y7/cpGhhf4/sSRXOe9rvh7X1/SyopMSqp8mZpop3jS\nF9Q5+vYF1q4FTp+eg27dnsb06e/C3t4Td+8uQGbmZbT9uC0atW+E0JmP0i6PNTfHTCsrTAgOhrKs\nqa0KBbBjB5CRASxfXmmbFAoFdry0A6n5qVjx54qqXuJjMWcO0KwZsHFjjVQnqEamjDuEWyHd8c7w\nH5D8P3MseXoJACA/X47W2bYNMDevGVuE6DdAGoLfdNYswM1Ngbi4LSgsJFas+B52dj8gOHgcCgoi\nYLfLDvn38hG9Jrr4nJXt2sFMXx9v37tXdqEGBsChQ8CRI/IN4DH4Z1sa6hni0KRDOBRyCN9f/74q\nl/dY6OgAO3cCmzYBQUHVXl2N0BD6ZmX5fNWf+Pnw05jlthXBI6OwfeS3UDzMq/Dhh3Jakocrg9YI\nQvQFdZYvvwSaNdOBqaknfHx8sWtXMNq2/Qi3br0ISS8LDkcc8GDHAyT/mgwA0FEosLdLF1zMyMD/\nlTdo27IlcOIE8PHHwJkzlbbJtLEpjr98HB+c+wDnIs5V5fIei7Ztgc8/lwf5ypuSIKi7HPO8hQ8/\n7Y6xT29AyKAz2PfqIejr6gMAvL0BDw/5Kb9GqbwXSfvUETMEdZDcXLJfP3LevCza2trSw8ODd+8u\nZEDAYKrVhcy6nkVvM29m/ZVVfM6d3Fyae3vzUkZG+QVfuCAPHAQHa2TX+YjztNhgwZDkEI3OrwyS\nJE8ufqfsdV4EdZSQ20nU1Y3gAIcVfHZxK0akRxTvS0ggbW3Jo0erVocm2lkn1FaIvqAikpPJTp3I\nDz6Ipbm5Ob28zjEwcBRDQmZQkiQm/ZZEXxtfFsQ9Sol8KjWV1j4+jKlo/dy9e+VV2yvK41MBu67v\nYoctHZicW8ECL1oiLU1ugzIWnhPUQTIzlWxi5M+ONps4+o2n6BfjV7yvsJAcMEDOr1NVhOgLSDbM\n/Cbh4fLk2k8+CaCFhQWDgq7R378HIyPXkCQj10Tyr15/UZX7KDLHPSqKPf/6izkVRet89JH8KpGX\nV+bu/2rLFWdXcMDOASVy8FcXt2/LLyd+fv99bF2lIfbNf6NSSWxlcYotWxzkW6/25i/Bv5TYP2cO\nOWaMdnIsaaKdwqcvqBc89RRw9Cjw1VfOeP31XRg5cgIsLHbhwYP/Q1LSQbRZ0QaN7Roj9LVQUJIj\nepba2qJ7kyYYX15EDwB88gnQrp2cv1aDhPafPfcZrJtZY/ax2dU+q9zeXs6tPmECEF8z88QEGtC/\n169IzWiOOcN+Qps54zGh64Tifd9+C1y6BOzdKw/U1wpVv9dUnTpihqAecPIkaWlJLliwlb1792ZC\ngh+9vc2ZkeFDdb6a1/pfY8TKiOLjiySJowIDOTk4mKryEprk55P9+5MffqiRTbnKXPbe0Zufen2q\n0fmV5dNP5ZeTijxXgtph+pRD1NG5xyWjZnL2oRnFOXVI8uJF0sKCvHtXe/Vpop11Qm2F6Asqw/ff\nk+3bS5w8+W2OHDmSiYnH6ONjxby8cBYmFPJy28tM9Hjkp89TqTgoIIBv3blT4kdYgqQk2b+/e7dG\nNsVnx7PtF225P3C/RudXBrWaHDeOnDlTLKpel9i09jwVigTOGjafL+5wpVKlLN4XHS27J0+f1m6d\nQvQFJJ8Mv+nKlWSPHmq6ur7EefPmMSZmG69csaNSmcbsm9n0NvNmpl9m8fEZRUV09vfnyooWow0O\nlp3mXl7FX1WmLQMTAmm+3pw+0T6Vv6BKkp1NOjiQX31V7VVplYbaN38/FUqFIoGj+7/LZ9d0Znp+\nevG+vDyyRw9y/Xrt16uJdgqfvqBesnIl4OKiA339Q7hwwRcHDxagZcsRCA4eh8YOBrDbaYegcUEo\niCkAALTQ08NpR0f8lJiIr2Jjyy60a1dg/345V09YWKVt6m7ZHXvG7MH4n8fjfvr9qlzef9K0qTzH\nbPVq4Amc71SnCA9PxYsj9dDHfhsyB/yC3XNPw7iRMQCABF5/HejSBVi8uJYN/RtN7zCpqakcOnQo\nO3XqRDc3N6anp5c6Jjo6mq6uruzatSu7devGLVu2lFlWFcwQPMEoleQLL5CTJ2ezdWsbHjx44GEo\n52uUJIlR66Po7+zPooxHyWsi8vNp4+vLHxMSyi94xw45PjIlRSO7tl3ZRvtt9iWe9qqLM2fkvC0V\nvcAIqo+cnCI2a3yZ7Vtt4dg5HXg55nKJ/Rs2yE/55QSHVRlNtFNjtV2yZAnXrZOTBrm7u3PZsmWl\njomPj2dAQABJMjs7m507d+bt27dLGyFEX6Ah2dlkz57km2/G09zcnBcunHkYyvkZJUli2PwwXnv6\nGlXZj8I2b+Xk0MLbmycrEvUlS8hnn9V4tPTtU2/Tba9bCb9udbF5M+nkRObkVHtVgn8gSaSt9XEa\nN/uNb03tVyo08/Rp+YYcFVVOAVqgRkXfzs6OCQ+fluLj42lnZ/ef54wePZpnz54tbYQQfa3SUP2m\n5ZGQQD71FLlw4S1aWlry1q1L9PVtw8RED0pqiaGzQxngGlAiht83I4Nm3t70KW/WrlpNjhnD88OG\naTRaqlKr+OJPL3LOsTnlDx5rCUkip04lJ0+u+wO7DalvDuj9Mw30/bh84liuvbS2xL67d+VInYsX\nq9cGTbRTT1O3UGJiIiwtLQEAlpaWSExMrPD4yMhIBAQEoG/fvmXuf+2119CuXTsAgLGxMZydneHq\n6grgUZIm8fnxPt+4caNO2VPdn0NCvLBqFbBkiSsmT96DYcMmYdOmpZCkt2Fo2AYPXi5EtHs0FGMV\n6H6kOy76XQQA7HN0xNigIKzNysJTRkaly//xR6BHD3jNnAlMn15p+zzGe+CZH57BvK/nYVK3SdV2\n/RcueOGVV4APP3TFunVAv37V297isxfWrvbB5Wuv4N2XPsOt7vlYVPRI106e9MJbbwGrVrli4EDt\n1u/l5YXdu3cDQLFeVpqK7ghDhw6lg4NDqe3IkSM0NjYucayJiUm55WRnZ7Nnz5709PTU2t1KIPg3\nvr6kmRk5a9Y37NOnD2NiPOnjY8mcnFuUiiQGTQxi4EuBVBc+mgq5PyGBrX19GV6e0/XBA9LOjly9\nWiObojKi2GpTK/4c9LNG51eGmBg5LPDEiWqv6olm5itHqFDEcvbw0qGZarW8ZMPrr9fMW5cm2lkl\n9058fDxJ8sGDB+W6d5RKJYcNG8YvvviifCOE6Au0xOHDpLW1xDFj3uOYMWP44MFP9PGxYk7OLaqV\nat4afYtB44MoFT36RW6LjWUHP7/yF2CJjyft7eU4UQ1+yQHxAbTaaMV9N/dpeFWPj7e3HHUaGlrt\nVT2RzJ52WBb8YQvYd12nUoP1K1fKeXXK60rapkZFf8mSJXR3dydJrl27tsyBXEmSOHXqVC5cuLBi\nI4Toa5WG5DfVhK+/Jjt2lDhgwGguWLCACQn7Hwl/gZo3n7/J4P8FU1I9EvBVERF08vdn+r+WqSpu\ny8REOTD+/fc1Ev7gpGDabLbhN/7fVOXSHosdO+SXk4qSjNYW9blvvvHaYSoUcZw5bD77bejCuKy4\nEvsPHZIzZz58Fq4RalT0U1NTOWTIkFIhm3FxcRwxYgRJ8tKlS1QoFHRycqKzszOdnZ156tQprRgu\nKJ/6/MPSFsuXk717F9HRsR8XL15cLPzZ2YFU5akYMDiAITNCKKllAZckifPDwjjw+nXm/SNBW4m2\nTE6Ww2SWLNFI+MPTwtn+y/Zc710Ns3T+xdy55EsvaSeplzapr33zzVmeVCge8LWh8/nsFhem5JaM\n/Lp1S3Yt+vvXrF2aaKfi4Ym1ikKhqPZkVYInCxKYNg1ITVUiMXEgnnmmH95/vx/Cw9+Do+MfMFJ0\nReDzgWjSvQk6be8EhUIBicSrISHIUatxyMEBeg9XNypBWhrg5gY8+yywebO8DGMliM2KxdC9QzHZ\nYTJWDVpVvIKStlEqgaFDZTM/+6xaqnhiWPDGEWz/vg+mDlmDxPE38fOME2hu2Lx4f1oa0KePPGFw\n6tSatU0T7RSiL2iwKJXyMnRqdRFSU4fCxcUeq1YNwv3778HR8Xc0krripttNtHi6BTps7gCFQgGl\nJGF0UBAsDQywy84OOmWJcno6MHy4vJjv1q2VFv6k3CQM2zcMz7V/DpuGbao24U9KAnr3ltfYnTix\nWqpo8Lzz5mF8taMfXh28Brmv3sOPrx6Ckb5R8X6VChgxAnBwkJ8BahpNtFOkYWiA/B3i9aRjYAD8\n9hvQtKk+mjb9E4GB9/D++2fQvv1mBAYOR4HObTiedkSGVwYi3o8ASRjo6ODXbt0QlpeHxeHhOH/+\nfOmCTUzkpRavXQPmzq10SmaLJhY4P/08fGN88cbxN6CW1Fq64n/VYyEvCfzWW8DNm9VSRaWpT33z\n3bdkwf+f6xpwVgIOTDtaQvABYNky+a1y/fpaMlIDhOgLGjQGBnI6HRsbPejo/I5795KwdOlJtGu3\nCYGBw1GoHwKnM05IPZaKqNVRAIAmuro43r07zqSnY39SUtkFt2gB/P47EBwMvPFGpYXfxMgEZ6ae\nwb20e5jqORVF6upZALdnT2DLFmDMGCAlpVqqaJAsmncYW77tjymD1qDFggLsnnKgeG3bv9m3Dzh8\nGDhwANDTeMZTzSPcO4InAkkC5s0D/P3VaNZsEiws9LB58yhERS2Go+PvMMjtghuDbsBqphXaLG0D\nAHhQWIhnAgKwxNYWc1u3LrvgnBxg5EigTRtg1y5AV7dSduUX5WPCLxOgr6OPAxMOoJFeo6peapks\nXQr4+wPHjwNNmlRLFQ2GpW8fxsZt/THp2dVov6wRPn9+QykXnLc3MHYscP687NqpLYR7RyAoBx0d\n4OuvAVdXXaSm/oK0ND0sWPAb2rTZiMDAYVA2CYXTn06I3xGP2K1yFs5Whob4w8kJ62NisDoysuwf\nV9OmwIkTQFycPHKsUlXKLiN9I3hO9oSBrgFGeoxErjJXG5dbirVr5fvSc8/Jvn5B2Sxf6ImN257G\nhIGr4bzSCmtf2FhK8D09ZcH/8cfaFXxNEaLfAKlPftOaRKEANmwAxo3TQXT0j8jLM8Gbb3rAxmYj\nAgOHo6jFHTj96YTYzbF4sOMBACD2yhVc7tEDh1NS8EZYGFRlCX/jxsCxY0BqKvDKK0BR5Vw1BroG\n8BjvAZvmNhj+43BkFmRq43JLoKsL7N4tBx4NGADcu6f1Kh6Lutw3Vyw8hPVbB2DcwNUYvK4Llg/+\nsNQx27bJb4ynT8tj+fURIfqCJwqFAli1Cpg9W4G7d78H2Ravv74PrVtvQGDgMKhM78DprBOiVkch\nYU8CAMDKwABezs6ILSzE6Fu3kKMuY+DVyEh28ObmAlOmyKFDlUBXRxc7R+2Ei7ULntv7HFLytO+A\nVyjk8M3Fi4GBA4ErV7ReRb3lw/c8sW7rMxjzzGqM2dIbc/vNL7FfkuRB223bAB8feayk3qKVGQJV\npI6YIXjC2LaNtLWVOHLkIg4ePJj37++hj48ls7NvMDcklz7WPiWWXVSq1ZwZEsKef/3FhPLm2RcU\nyMlXRo3SKC2zJElccXYFu27vWmrGpzY5dkyeTHTkSLVVUW/4cNEhKhRJHD1gAQ8HHyq1v6CAfPll\n8umnNV5iodrQRDvrhNoK0RfUFj/8IOfqGTXqQw4cOJDh4buLhT/nVg59LH2Y9GtS8fGSJHFVRATb\nX77M0NzcsgstLJQXsR0xQl50XQM+v/g5O2zpwIj0CI3OfxyuXJHzvX9T/Zkh6iyrFv9KhSKJIwcs\n4Nl7Z0rtT08nXV3JsWOrbyGUqiBEX0Cy/k51ry0OHCAtLSWOGbOG/fv35927j4T/xI4T9LH2YfSG\n6BJ58Xc+eEBLH5/y8/ErleSkSeSwYRqrxVa/rbTdbMvQ5OrLnnb3Ltmxo8YphSpNXeqbny79hQpF\nEl/sv4CXo31L7Y+OltMtLVhA/iMzR51CiL6AZN36YdUXjh4lzc0ljhu3mb169WJo6C76+Fjy5Mnv\nmR+VT39nf96edpvq/EfJbE6lptLc25uHkpLKLrSoiPzf/8ghQ8jy3gr+g53Xd9J6ozVvJtzU6PzH\nISmJ7NtXXoilurND1pW+uWaZLPgjnn6bN+NvlNofGEja2JAbN9bthWmE6AsEVeCPP2ThnzDhWzo7\nO/P27e8fPvEHUJWjYtD4IF7rd42F8Y+U8VpWFlv5+PCr2NiyC1WpyBkz5ERtGuY7Phh0kBYbLHjs\nzjGNzn8ccnPlYYihQ8nMzGqrpk4wf+oPVCgS+Xz/dxiWElZq/59/yumpPTxqwbhKIkRfIKgiFy/+\nLfx76ODgwKCg7+jtbcakpEOU1BIjVkXQt40vs65nFZ8TkZ9PuytXuOTeParLeiyUJNlxbmZG7t2r\nkV0XIi+w/ZftOc1zGtPy0jS9vApRqeTsnI6OZHn3sPqMWqVmb/tvqFDEcvTgNxmdEV3qmB9/lAW/\njryQ/CdC9AUk684rdH3l6lXZxz9x4s9s06YNQ0OP09fXluHh71OSVEz6JYneZt5M/PlRZE+qUskB\n169zSnAwC8rLZ3zzJtmlC/naaxqtYp5dmM15J+ax9abWPH7nuKaXVyGSRK5dS7ZpQwYFab/82uqb\nkcERtDDxpKHBVc5/+23mF5UcYK/u664uNNFOEacvEPyL3r2BP/5QwNt7Itq3n4Phw+eB/A5ZWb4I\nDBwB49E6cPzDEeGLwxG5KhKUiJb6+jjr5IQiEsMDA5FR1sxcR0c5FwIJ9OoFBAZWyq6mBk2xbcQ2\n7Bu7DwtOLcBrh19DRkGGlq5aRqEAli8H1qyRZ+9euKDV4muF7z/fBTuXTECRj4MnE/DVli0l0l2o\n1cD8+YCHB+DrC3TrVovG1gTVcPOpNHXEDIGgBCEh8kpIM2YE0NTUjFu3buHdu+/x8uV2zMqSffvX\n+l9j0PggqnLk8A61JHHh3bvsdvUqoyoK19y7V3b3fPutRiOF2YXZfOvEW7TZbMMTYdWzKO7Zs7Kr\n48CBaim+2pFUKr7itoIKxQO62K1lTl7pt6vcXHlaRX0dy9BEO+uE2grRF9RV7t+XfdwvvphFB4en\nOXnyZIaH/0BvbzPGx++mukDNkOkh9Hf2Z37UI5HfHB1NG19f3sjOLr/w0FC58EmTNF7b8M/7f7Ld\nl+342uHXSq3Xqg1u3qwfUSz/JizIl73t1lKhiOfUce5lHpOcTPbrVzNRS9WFJtop3DsNkLqc36S+\nERXlBT8/wNa2GfLyLqGwsBtGjHCHgcEOREWtQXj02+i0sz0sX7XE9X7Xkekr581519YWmzt0gNvN\nmzibnl524XZ2ci4EMzOgRw/Z9VNJnmv/HALfDISRnhG6f9Mdp+6eqsrllsLRUXZ5/PAD8O67siuk\nKlR331RLamxftxCugyNwI/xF7P42AHt/W1bquPBw4OmnZRfWnj1yCu4nhmq4+VSaOmJGg0EM5GqP\nf7blwYOyu+PVV6/Q1NSMO3d+zcDAUbx27WkWFMQx5WQKvc29Gb/70crYF9LTaeHtza0xMWVH9vzN\nr7/KhW/erPEj9d9P/TMOz9D6U//fM1OHDJEjnDR96q/OvhnyIJDvjJpAI8PLbNniCO/fKR2dk5ND\nbtnScGYia6KddUJthegL6gv37pE9e5JDhmSwY8fenDVrJkNDP6aPTyump19kzu0c+nX0471F9yip\nZGW8k5vLZ65fZ/9r1xhUUdTO/ftknz7yiuYaJnnJKsjim8ffpM1mG566e0qjMsqjsFAegujYUXaL\nHDpUN2aqFqmL+PXBpXx54Hzq6ETT2f4bKpVFJY5JTCQ/+kgeRhk3To7QaggI0RcIaoCCAvKdd8i2\nbdUcMuQDOjk58cqV7+jtbcGYmK0sTCnkjSE3ePOFmyzKkMVHLUn8Ji6OZt7e/Pj+/fLDOgsLycWL\n5RHkixc1tvFs+Fm2/aItZx6ZyYx8zcYLykOlkl9MevcmO3cmd+zQOMVQlQlMCOTCuV35TPdPqVAk\ncvYru0rsv3tXnntgbEzOmUPeuVM7dlYXQvQFJIV7R5tU1JaenqSFhcQxY7xpamrO/fu38epVR96+\n/SqV+dkMmxfGK12uMDfsUQqG2IICjrl1i12uXOGligZvT5wgLS3J1as1fpzOKsjinGNzaLvZlqfv\nntaojIqQJNLLS84rZ2VFrllDpv3HvDFt9c1CVSE/O7mCnw7vybZW31NP9w7373xU9tWr5MSJdKA1\nzgAAE2xJREFUpKkp+cEHZEKCVqqtcwjRF5AUoq9N/qstIyNlV8eAAem0tXXhO+/M540bU+jv78S8\nvHDGfRtHbwtvJnsml0jY9ltSElv5+HDunTvMKCoqu/DYWPLZZ2VHenx82cc8BmfCz7DtF2053XM6\nr8ZeLWGHtggMJKdNI01MyHfflZOVlYU2+ublmMsc90FHrnz+VTYxOscWzc7w3p0YShJ56pQ89mBr\nS37xBZmV9d/l1WdqVPRTU1M5dOhQdurUiW5ubkxPLz1wlJ+fzz59+tDJyYn29vZcvnx52UYI0RfU\nY5RKculSsnVrFfv3X8p+/frxypVP6O1twZSUk8y4lMEr9ld4w+0Gc4If+fTTi4r4RmgobXx9eTg5\nuezCi4rIjz8mra3J7ds1TtyWWZDJledXsuPWjuy4tSM/PPchg5OCNSqrIqKjyUWLZPGfOlW+GWiD\noMQgrjy/kk5f2PH98RacOnQpdXTC2d1uH3NyVNy7l+zeXd727ZP/T54EalT0lyxZwnXr1pEk3d3d\nuWzZsjKPy33YSYuKiti3b19eunSptBFC9AUNgJMn5fQNw4Z50cLCir/+upE+Pq0YGbmaqsIixnwZ\nQ28zb4a9HUZl2iNVupCezs5+fhwfFMQH5S28cuWKPIvIwoL85BONB3olSaJ/nD/f+/09tt7Umo7f\nOHLtpbVaz9ufni6nNbCyIl94Qc5lU9kXjL+Fvuv2rnRYbc1j0wbwgNtouvZYSYUiidMm7ufmzfJT\n/XPPkadP16+5BNpAE+1UPDyx0nTp0gUXLlyApaUlEhIS4OrqitDQ0HKPz8vLw6BBg7Bnzx507dq1\nxD5NVnQXlI+XlxdcXV1r24wGQWXbMi4OePllID8/DTExgzFz5mCMHXsVenq66NBhAxoV9kDkR5FI\n9kxG+0/aw/p1ayh0FSiQJKyJisL/PXiANe3bY5a1NXT+tSA3ACAkBNi0CTh0CJg6VQ6eb9dOo2uT\nKOFS1CV4BHngt5Df0Nm0M152eBkTu06EZVNLjcr8NwUF8gLiGzYALVoAI0Z44a23XFHWpQHAnbTb\nOBr+C47e+xnZRVmY0XgoZl3Mxo2kPPzatBeOnh2IQmUbjB+ZiDMXn8WQIcCSJXJWiycRTbRTY9E3\nMTFB+sNJJyTRsmXL4s//RJIk9OjRA+Hh4Zg7dy7Wr19fpuHTp09Hu4e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fjkuXLtW2SQ2G\n8uajCB6fuXPnIiIiAjdu3IC1tTUWLVpU2ybVO3JycjB+/Hhs2bIFzZo1K7HvcfporYp+69atERMT\nU/w5JiYGNjY2tWhR/cfa2hoAYG5ujrFjxwq/fhX5ez4KgHLnowgeHwsLi2Jhmj17tuiflaSoqAjj\nx4/H1KlTMWbMGACV76O1Kvq9evXC3bt3ERkZCaVSiYMHD2LUqFG1aVK9Ji8vD9nZ2QCA3Nxc/PHH\nHyUiJwSVZ9SoUdizZw8AYM+ePcU/NIFmxMfHF//t6ekp+mclIIlZs2aha9euWLhwYfH3le6jlU7c\noGVOnjzJzp07s0OHDvz8889r25x6zf379+nk5EQnJyd269ZNtGclmTJlCq2tramvr08bGxvu2rWL\nqampHDJkCDt16kQ3Nzemp6fXtpn1hn+3586dOzl16lR2796djo6OHD16NBMSEmrbzHrDpUuXqFAo\n6OTkRGdnZzo7O/PUqVOV7qN1Yo1cgUAgENQMYuUsgUAgeIIQoi8QCARPEEL0BQKB4AlCiL5AIBA8\nQQjRFwgEgicIIfoCgUDwBPH/VeBt5+sskJkAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x8047750>"
]
}
],
"prompt_number": 127
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(modes2[:,:,2].T); grid(); title('Mode 3');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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7ZmZyq+mPHZORwlWACRO4jWPGeUwlHu8D+d2QTjaDSp97hwiYMoWb3a9VS9ba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\n",
"text": [
"<matplotlib.figure.Figure at 0x82b3c50>"
]
}
],
"prompt_number": 128
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"These definitely show that the mass is effectively \"pinning\" the string as it gets larger."
]
}
],
"metadata": {}
}
]
}
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