{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Beat phenomenon" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "init_cell": true }, "outputs": [], "source": [ "import vibration_toolbox as vtb\n", "\n", "import matplotlib.pyplot as plt\n", "from ipywidgets import interact, interactive, widgets\n", "from IPython.display import Audio, display\n", "\n", "# %matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook we will investigate a phenomena that occurs when the driving frequency becomes close to the system’s natural frequency. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For zero initial conditions, the response is given by the equation:\n", "\n", "\\begin{equation}\n", "x(t) = \\frac{2f_0}{\\omega^2_n - \\omega^2} sin\\Big(\\frac{\\omega_n - \\omega}{2} t\\Big) sin\\Big(\\frac{\\omega_n + \\omega}{2}t\\Big)\n", "\\end{equation}\n", "\n", "Since $(\\omega_n - \\omega)$ is small, $(\\omega_n + \\omega)$ is large in comparison and $sin[(\\omega_n - \\omega)/2]t$ oscillates with a longer period than $sin[(\\omega_n + \\omega)/2]t$. \n", "The result is a rapid oscillation with slowly varying amplitude that is called a **beat**.\n", "\n", "The system defined in the function bellow has a a natural frequency $\\omega_n = 1000 \\ rad/s$. \n", "\n", "You can change the excitation frequency moving the slide 'wdr' and hear the resulting sound.\n", "\n", "When you get close to the natural frequency you will be able to recognize the beats." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "scrolled": false }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "5a7e3a2416a142a8bfe5e9e4e35059a9", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type interactive.

\n", "

\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "interactive(children=(FloatSlider(value=1100.0, description='wdr', max=1100.1, min=900.1, step=1.0), Output()), _dom_classes=('widget-interact',))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "@interact(wdr=widgets.FloatSlider(min=900.1, max=1100.1, step=1, value=1100))\n", "def f(wdr):\n", " t, a = vtb.forced_analytical(m=1, k=10**6, x0=0, v0=0, wdr=wdr, F0=200, tf=5)\n", " display(Audio(data=a, rate=1/0.000125))\n", " plt.plot(t, a, alpha=0.5)\n", " plt.show()\n", " " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "9d6833e10c314ddaa17649db9fa889a8", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type interactive.

\n", "

\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "interactive(children=(FloatSlider(value=999.1, description='wdr', max=1100.1, min=900.1, step=1.0), Output()), _dom_classes=('widget-interact',))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "w = interactive(f,wdr = (900.1,1100.1,1));\n", "display(w);" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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AjH2DGQBvWn94enp64kDK1NTU2Gf7xsv8/DzK5RW02y2IogRRnIySKMsy5ubmTC8QpzKslEqliTLsm5nFYhHA0EYrCCsTGZ6cgnPZz52IogS9UMFCtehYD79NptXV1Ym/sX4WhBWUSv7qYI8sWS6XcbOVx8njw7Lm5uYm7tshkZPBS+9dQrE4+YztB3PKZdH2uYxGu2WWFUROTvWw37+6rEGWC45ystfDivGMrTpmx17XILK+U1+GJEmOchr/jfHPxvfzpRqmp4aNCiInp3oD44fGBGHZUU5WnN9J4NNmDo/fP5wz2uUkSRL27NljfrbfByZlba3rX75/yVVOXoiihI3e9nMI+k4Ck+23lnF1WXOVU7vdwvT0NIBgcrIOpk5QmYyMjd6RR9CaZeP3nNt90msAXgSwqCjK86OyXqapqxU/m3e7y2dzjfYQ14cUPsm8MiwBwEVGWd2coNno5Lm38eaVcB5GBt0+n7rdWacLQRF1XhBSvPbeaHV7i9P7Tssbn7gHHOSl29TnEFRVfdHh2imf+77XRiuMie9FwQB8HjZtuT1OnUhGcJLqs08LzQZrBluiODluJ/GbyjwQBMHz/m+v8NmMpA0x/B7F7M0r9kmYY/s7AUEQuKU6vE05E6eRpRdvXqfzMLLn7mUFTx2jievDwnvJKV8BC7wCDvr1YWFJ5YDgd0qUV47ZK/Vowlg74ZVQ43pE4bWjJpfLcQ8mF5bfXQt3QNGPOxvJbO9Vju7cNMliWHiz8s5x4QSvk+6pHBD8knJHFbM+SgxvDydaDIK08fATp10y93q9xJpAguYrICWOhPMkdBjIwU3HvHTbD52B3rJoW1B4yTmVA8JOhkcHFySPshs8sqf9lnLjFgD+7n324RhYmAiSnCeGh46dDxlOwwqPkB+/YaBjYYIv+uEX4ZUXqRwQEpg3hZiwLyvvZDGfrbO3EX9Kacri1eQoIqmGhUWb49jMJOG6yz4EjW7zNGXRsOajY1mCHIbwSi7hBSuTSlh3Rd6JU3hEpKSdJfGScxwmAhIGgwGTNid1QHDTMRrd5mW6o8UtD4JBliCHISTJJWi9SOxcZLTc/eXFuv+XHHBLIsJqoOIRo4l2L4dXEhFWUUE/Y5y28uKdJpM203rD2WE1wFx2eYdoEuQkNd6VnxkqS5ATMawzgbGKX8MjBWFGMFgdZGLtrsgqBSzrwZ3Fxm1GNGQDggusDx5tMvJcYh2iuJdQ8wBLeJ5YpsHPLBBXeazDVCfVBMWSuMJgsyaVAwJJjBHWUQzjDgnglkTELQFHGFh2cCy8LAw5v38zmeEYzn3EVsfevd7gljiFhtcvszNBOelY2AQ5dYbnBz6OIL+ylaQmyNmR8EoukWTcIh6GTdjjBMvVCwtziiFn1rb6JJNE3XbzDgqDU/iWsAlyaHKA2Ik653lSE+Rk7HBYulCyNA2wNGWxPGi4W0wDUdJk6IHWZ/j8WZ632GSYcTBOHcsGhAhgbcNm6QHFsrN87RI708DZj+hySFthmUGMZz5kGnqMXWFZrqraDE7CG4TNY+0Ey0OLLDfi48x4l8oBQZYnY67zhLWXRZhUhPaY6Ty4eIedHZU2hzTAR843E2p+MlZUrNrM2suOFRduT+pYFLodJSQHMnn1YakcEEjjgLBaurFeAIapFk28F1KSZk3hEe+F9WqPmY6NimHV5qR6BjntU0Wh21HSJdiLy2IZMYT0pWYVn4dFrCArYcwpTklEGgw31ZKIVc6sNrzfYRylVHWY8Ybht58OTSmsBixWJrsodIxn8qcgsNKxDwgSYSU2QY6iKM9imDv5pKqqPyC5H+Da86Nijqmq+ue0dQ3KleVNPHQgnEublY8/4xNOm5b6ZvI8UnjR6vQhi8mb/1ypb+KBe+h17ALHrHU03N7YXbN3L9q9ZOpYEKhqryjKSQBQVfUsgDXjs9f9ANfOADg7yqS2OPrMBCN5tx+sTCBJyHSWRP903pDKOU5Y7QX3R0nlk9bmKMyImW6zg3Y4ew7DWT0ALAGwd9pO90mvLVrKWxp9jhSnDaww8MqoRAtLjw0DFpuR1zgk7Hn7Gn34ZR52dVY6ltSYPK9cYHv4DmCjY7ca7M8NvMcg2xxrb7Gg0A4IMwCsvcocwX2ia6qqvmjJs3wSwG8p62rSYxwyYCfgdJCFdQA/ALi+St+Zs3LttMqZxT4OS/dJXiRNt3kMVDdtB93CHNL6kMBOHxQWp/5Jk1XxkjP1HgJvRuak86qqnrdebzQapneBJEkQRRGt1lBRcrkcKpXKWBTEWq2G9fV1aJoGXdfR63XR6/XMzRlBEJDL5czd+1xuGGK2Xq9PlGEwNTWFdrttbmoZS1dDQfP5PMrlMjRtu5MsFApjCizLMrrdrultYiwFDYHn8zmIoohOpztWhrVe1WoVzWbTLKNYLELXdXQ6HbNtuq5PtGW8XjI6nY65xJckEbquoz+aseTzeQiCgG63a3k+420pFApoNBqoF4fPsFwuo9PpmM+UVE6NkZyGz0cikpM1+qPxjHVdh6ZpZhlG+93k1Gw2x+phlXWlUsHq2oZZL1I5jT+f8WcsiiIGg4FZL0EQUCwWsbm57Ydur4dd1qVSCb1ez6yXruvodru+cup0tiyyltDv96GPzE6CkEc+nzfr5fU+GdjfBVmWkc/nzXp5ycnALmv7M87lcpAkCWtra6gXumY9rLKtVCrmO278BrAta+MZr1t0jFRORtu8ZG3Uw01OhlxEUYQsy5bnk0O1WsXy8spYvdzkpOs6Go0Gcb9HCu2AsAZgdvTvGQD2k0lu90mvAcAZpw3l6enpiTjodn9ku21xfn4e5fIKWq0WRFGCKE768trjjE/vmYUkbC+k5ufnx+6XSqWJMqrVqvlvrdNDuVweu2//LIqTYrCHO7fXtZUv4/Dsdjl+dtSVlRXMzs6OXbPXo1TyVwdJGq+HvYwrG8BXH553vQ/4y+mThj72dyRyKpdF2+cyWq2WKR9RlCZkZ5UTMBxIrdi/X++2J9rjJyeSZzyzZxaiRcfsOmWvh/15tbt983darRYkSfKVU6k0/tn+fQDoiFM4MLNdF6f3abzMyXdhUvcn5WTFWdbjnz9e6eMrFh2TZXlMt+1yBCZlfWV9MPbbYd4FJ1lbnwnJ3ob9d9f04tg1Nzm1Wi1MT08DIOv3DKyTHidoTUYvYdu2vwjgLAAoijLjcZ/0GhRFed7iccRsU9lJ+d2gDbJ2nVOMk6Duj04dMw9YhflmQRA5k/Cry+FyUfhBu8dkPdnKss2s3aVZYU+UE5VuR8E/XLhL9D3Wum1ANSAYZpxRZ71mMeucc7tPem30779QFOWyoij0O4IWDFNKmvCbGexGWMs5h+TnXs10e2dDmhqTl5yp9xAsG7/Wa6d87vteG7mg7qGtHy2X725ioTa5BCXlU045W2k3XuNK4u0Hz8BeWqeHshxe5XltKt9Ya2GuEt51ktc5lwu3N/D72B/675OanpJnfoxWp4+SHN4lNGyKXFbs7FMUEUCbTjDuPAhuvPUp00UXMzYYJ2exEnXMelJo8yJcqSczUfyvGeZBYAmP/N8GrE6ex0UqB4Q0HmQJm0RkJ5NGOaexzZlusyOVA0ISk4iEIYh5xe569tEtfuE01rTw5ihWeYGBSTlfoQgrHPeBIVJY6zaNCe9Djjpm3YgPmiDnDsdwGjSm3CCxkLIEORkT3KboPHnmUn6F0FPCif/03i2GNRmHZj/n0t3ds3EZhLsUaSZ5hq34h4vhdexH7/LTMZpT9moCTJrZgLCDGTAPrB0/SW1RUsNBp5XdKI4kvM+pHBDsh5r8CJtqr8lxgxQAbgVI1mI9xMc7RR9N9iiWHW9QOXvBI76SFafk8SRs2nSMZZuBcMmYAP46dtlimrEfUN2pXAmwgmUtZ4NUDgjG8XFS3gvpKfQ6Zy+LV1TyZbM1TMU6Ry+LJBFUzl6wyo3hxvs3wtnbf2XTMZZtBoCffhAuLwLLBPZ+WHV7J3M5yP6DniXIYUbQ2UvY8NVJMjMYsV2A9CSK30ntDFtX+2Z3UtocZS2sup0WeMk5lQNCUJZCbiiyCm3MmjrFRiEpYRQ2igE0qVniwm54JzUxTlhTUxDC6FhY828Qknogj4RUDghBk0sEsdVbSdIKweq3/De/4+dlYfBZiNDarAdQJzn/gkN8fhZcDblHods6xaQkyPkxR28xgzujQSeITz5Pd2uDIKbcsEgOATFZkMoBIYM/YQbDKDLLJSF7XQYbwlhNopik9XawCSuVA0IUSUSisuWSeqdEfRjvRogor58sh/dOcsJJzmFm4kk1ATjpGA/dTmpiICPBUxDdvkzhAUdKmFAiQXWs1882lWMlaECsqLwsfnctmbGS7N4vJATysoiQ1y7yCXtNy3JEAQrfZZAakgd//3Fw8x9v9+GwvEpxmJMlqRwQ8nn+YYzttl1ekC6BBSEZtuUoYSXnfkSyDLqqdPo6D91OiueSG7tBt4OasnI5Pl13KgcEpwxlftwKuEl6hbH5ww3SRDlGFqmkLv954CbnoC/fxYg8eW4GdF5w8n4Lo9t+BD2Ho3WiPefilCEtboJ6MwU9zJnYTWVFUZ5VFOWMoijfJ71Pem10/SRtHe1Yc6GSEnRJ9+qFaMwMpB28kac3qSGgeeAm5zD7G1EQ1DTlZJYLo9t+BA0XHYUnjxVrDuqkcIez2y3rA4gGVAOC0VmPktms2Ttvp/uk10Z/fwbAD2nqyIqoTEAZ/ElCzBgneAYcjJJd0oxUQrtCeA6AYbNYAmDPe+x0n/SaMUAsUdaRCSzDMrMmyIb3z0NsxIXldgAz26U70a1cXrtEvuEdpYktyPOKmiD7CL+McBP+VoN8tRf2gGkYgiSganWSY8alHRBmAKxYPs8R3Ce9xo3dlkSEZNMzjiQiQWLDf3CTvZnBTc5BOt4oY/KwgJduJ3XW/0l9k1i3SffbWBDEY241RP6QYjFLkMMM3j75UXtlkBy2CppEhAVBbM880hqykHNSN+HddIyXbkcR8iEMG+0esW6vJDSPeJDEOAbtNh85025VrwGYHf17BoB9Le52n/SaK41GA+32cKYnSRJEUUSrNVw+5nI5VCoVbGxsmyFqtRrW19ehaRp0XUev10Wv1zPNLYIgIJfLodfrjcoYhpjd2tpWomv1dZSw/Xlqagrtdhv9/rDTMGZnFz9rQNM05HI5SJKETmf7bwqFwthLK8syut2u+YIboQeMA0b5fA6iKI5tFtrL+PlHt/DkoZJZRrFYhK7r5u8KggBd11Gv183IkPYyCgUZnU7HdGWUJBG6rqM/6gjy+TwEQTA3s4bPx15GAZ3OllnGu1e7+OKhovlMveT06e1Vl+cjBZaTUYau69A0baIMURSwsbFh/k4+n0e5XEazuT2rM/Tlr35zE62uzkRO9mcsiiIGg4GpP/l8DjeXG5AH22UY9TCoVqtoNpv4pK5B07QJOem6jm63G0hOkiSh3++bQeIEIY98Po9ud/sZv/LxZzi1f3tWaq+X9V3QNC2QnNxkbX/GTu/Te9f6eGxuD+r1oZmqUqmY77jxG8BwoLy9ss5MTiRlLC8vm/pSKpXQ6/VMuYiiCFmWoWka/vrNW2h1+4HkJOWHfSBpv0cK7YDwEoDTo38vAjgLAIqizKiquuZ2P8A1V6anpyfioE9NTY19ti+f5+fnUS6vQNM0iKIEUZQmyrXHGS+Xtx/Rlp7H4YX5sfulUmmijMFKF+Vy2fxsdwW03nO6P6wHbN8Zr6u1jLrWw9yct5WtXq+b7XerR6nkrw6S5F6PYRnjn2dmZibKcJKTV72CyskoQ9M0syx7GdVqFdVqdeya3X1xfn4eOWkFZcmoB52cAP9n3BmIODA/PVEPK4VCAZcaQLk8aT8fDhJSYDnZvz+8tt24utbD/PxBz3oZ74JVliRysuIsa9i+I058ttbFyQ21Wq2O1YtWTiRl+L2Txt8MxBUYP0cqp36njenpoZ6Q9HsG1kmPE1QmI1VVzwOmN9Ca8RnAObf7pNdGn58FcHr0f2YUCuGSS1xfJTvlSJOqMQzLTf+lcLVaHctDmySCngInxUvOSTUF3Vwj2yR1C8EQVrf9IHWq2IghzId9YHeCl455wVPHeO0VUZ9uUFX1RYdrp3wgHu7DAAAgAElEQVTuk157GcDLtHW00+l0iGYAdt6+uoavKwu+34t6QCCh2WzitevRe0q1u30UJe+TpLc5JT33kvNbn67iy/fPO96Lkzc+WcFTBPVy2xgPq9us+EUEkT7trDbWcc/CXs/vBD1YygKeOtbt8NkPSeWmchqPFAwGA2icU3o6QXJ+I8ymGgleP60lyNWPJXHrdhwbtyROFfZEQlFAomNhHVB4naVJ5YCwGyFJehM2rwMNb3yy4vudMEHKaHmfIBzD1QSu9OJkjcA9Mo4B4R2C9KNRnr8xINGxpXqyTlmnckDgEe8lbvxexLjivZD4Y/Py9aeV8/W1nTcg8NTtqKKrBuXGhv9MfDWh50k+CzlJc3ICYEEqBwSacwJNH7NLFKkDnfALwNaNIAeEEzzOF5DiJ2e/+x+ETHxPi9/G7KpHx8zzDMwVn9lsHGYZwPt5xI2vjt0MF1o8y6nMEMOfOAy/9onz/ws1nhSNfuknr9bTE9TOwE/OLR8vEL/Bnxe/veId9uCch/mDRrf98MuLcIPQQ4o1PNtMy5bP/tjmVri693tZgpxE4Jdx63pCI2mutZI5U49rVgkAzRhXL1745aNOapKXOMN8eOlYnKes45pUhCWVAwJNEpGk+vL78asr8WW9+sTD1BA01n4Q/OT8kw8+c70XRe5dN8LalYFokj+5EYdzADBs87UV94lYlDGM7Pzsw9uu92gmQ0I+S5DDjN24qQx4d2JxttkrNnyYHMek+LW57nGgj5crLG94yznOFZ0boiiivumuY3Hmv/Aa3NsUOpZtKjOENonIpssy8E7M4YvfueZue+aROIWU1z32XYJmigoCTZtfuxRvHmW3kMh+4Z55yznO2bYbnU4Xr3gciPNaocYJzX5jJzuYlhzc7IJ+tl/euIWQjuPY/k7BzfbM05RFwrqLp9HtmPNyuPnNx2liSzpuOhZVatYgZANCCNzsguc+iseGauAW04hHrgEWJCGk8pWEHj77qYuOxXHAyoqb+SWJKwcgGaY/Lo4mnLaKUjkg0AaGiuusAQlOs5F3rq3GnhTIKdAX7zMKJG2+6OCum4QVVT2kjsUl53evxzcgGG120rG1VvxnFJxWVbQ6VizwOWiaygGBd4KcOHHygqo3O7G3+ddLk/sIZz9y98BgAUmbnVZPV5aTaXMmIQo5O+lYnC6nRpuddOwnH/DVMRLOO6TT/IRSx9pbfMzTqRwQWNCwvQBJOS350a3xGW8SZrvAMFKsnTi9P7z4DUH8pSiw71UlJefyB7b9lSTrWNiVFm+c6poEsgEhJG9dHe80vHzao8Q+S0rquYmo04x6YXeljCMIoBNvXhnXMd4rKlLsAQvD5ASOgiTpmH0vg/ZwIa/TJqkcEFgkEfndtfFZUlI6ETt/NxqoeCVOCYI1WmYUroCkbX7N4habpE7kHdsskiRJTRxy/o+/uxn5b1qxttm6ck+Sw8DrS2x1rMhpr4h6QFAU5VlFUc4oivJ90vs011jA2oc3Cd4yVqxZt4yDMbz8loNgTZ7y/73DvxMhbbPVxnuRIDprHJDqWFRyvmNJahTn/gEw3uZzH2+vov767RtxVMcRq45dYOBuupXEcwiKopwEAFVVzwJYMz573ae5RlNXK6wmgZdGnUfSXO5eevMagHFzURImvlEfEArS5q1RNNi/ffcWp9qEwzAt2M1HbkQl53/366sAkmGStLY5idkKDQyz0Y/fY6FjyYx2+hwAozdcAnCG4D7NtUTxN6Ol8i8vxnuq1Ym+PsD/8ctP4q7GBJ8ubxIlDomaf//WjUTmWX75resAgDeWkrHRbUVPqI7dXGvhPZ/IrHHw0ptXXaMcJAXawCczAKyaOkdwn+YaEySJXbyXf/WzC8zKYsm/Pndx7DPLNtPwV+ejW8YHafPt9Tb+zS8uc6xNeILoWJRy/h9tOhYX9jYbK+SkUW928OKrS0zKymIZMUTXk2Xzj4Kszekga3M60DntW9JOJ9YAzI7+PQPAfjLE7T7NNQBAo9FAuz3c2JIkCaIootUabqbmcjlUKhVsbGz75NdqNayvr+Mb95XxN+81IQhd9Ho904daEATkcjn0RokncjlAlmVsbW1v3hQKhbGDP7IsjZUhigIAoDeyR+dyOUiSNLbpNVmGjG63a3oe2MvI53MQRXEsaJm9jEJBRqfTMW2poihiMBiYiUPy+Rz6fR39vkZchiSJ0HUd/ZHi5fN5CIKAbrdreT72MgrodLYsZUjo9/vmCysIeeTzeXS74Z9xEDkN66/tKDkFLcMuJ13Xkc93d5Sc3MoglVO32zN1e6fIifZ9yss5NBoN4n6PFNoB4SUAp0f/XgRwFgAURZlRVXXN7T7lNQDA9PQ0KpXKWGWmpqbGPtuP8c/Pz2N+HihJAn58YQOiOLnskuVxt71yWbR9Lo99di4Dtu/4lTG8//zTi+aScrKM8d+xl1EqeYtS07SJvyEt4+kTe/HqhaGHkH2pOlnG+Genpa0ksXjGwzIePzyDd66tOZZhbTNLOXmXMfydP/7Svfi3r38aWE5OdQ1ShqZpkCTJVU6GjkUtJ78ynnloH3724e1Qcsrn82N1CSInez0MrM/4oQM1fOhwop32nQTCv095vYPp6WkAZP2eQbPp7eFEZTJSVfU8ACiKcgbAmvEZwDm3+zTXaOpqZd90iVVRTJkqiHjoQI1L2XmKhBqn7t2Df/bUUXaVYcQLX1vE15W9rvdp2kzDdx69B3OVeGIK+bWZp47R8MjB6dA6xlPOf/b1Y/jWQ/u4lR+WLy3u4VIu9Q6UqqovOlw75XM/9DUWyLKMZ08dMj04ksA/ffIIAOBrJ/Y6zkZoEQQh1N/dMz0MojU7Ff/BNjtl2Vt9w7aZlhMLVQDA9544iP8QsS+8V5v/q1GHy0vHwkKrYzzlXJTi0SE/Hjgww6XcVG4qa5qGw7Nl/y9GyL7a8KXgpYCGrTIo1tnR3mq8EVOtPHnfrPnv//LkIcfvhG0zLUYay6PzUz7fZI9Xm/eMOtykdXLfeeQe899hBgVecv6CRce+98RBLr8RlnaLTxywVA4ISefYQsX/SxFhNX1888GFGGsyzqmj20vmI3PJGdw/f3TW/0sJ4NCe5JhNZ8rbg8C3Hk6OecYqy3sTpGNfOsbMA3+CVA4IudxwBnd/QjrerxyfH/v8zIPsX4ocg2hY99T4xGAPQ0H0n+WyaHNQnlwcHxAW90a7SnBr81dtOvbdR/dHUJvghNExXnKWxe3uMReHMrlw6t493OqTygGhWh3aeJMym7t/7/jAVJLZL+llObi55+kT4xu2SXop7DjNeMO0mRZJGH+lTh7hs/nnhlubj++rjn2eKiTjoKJ9MhRGx6KS84GZZEyIJCFv9mGsSeWAYPjlGptZcbMngg3bMIlTHj88uXF1MAGmhscOT09c++rxSW+juJMCAYh8r8qtzdMlPidbaTnlMGAu1IJ18DzkbN0/MHDSsbgIcrYgCKkcEHYCPFYJQck7TNa83Dyj4tSRyZd1rhK/F9SJfXxmbbwoSPG//nkHJfvaifh17GEH19wkOFV87tDkZIgl8WtEynHb3PviIr+NI1Kclu8L1fhXVdNlh0NUQvyqzPtlDYvbKiUJOubEoT3xb+BaN7oNkqBjvM+QxN/CGKjVth/q7z0Qr+fMN102kB/cz3a2GTT5etJcE8MQdcL5/S4myGciPNjk1OanbXZ6gwfuiXdFM89oxh21nONk32hCZu3DWJLKAcEa6+NIzOcR3PyuSbxogtDpBLOzOu0fJJ3j+8Y354O2mRbRZQbpNlDwwKnNCy6eO34H+3jDakCKUs5xu4QbJjZrH8a0fC6lJhxrCrtaQjfbWBM0ccqjHuaPOO31ThvKBl+5f3wmnISkQEC0G7pJaTMJD+53n+UG0THWbXbaUDZ40uNelPBK9ZrKAcGK4LRzmoGKh1viE4ejdaW08sA97p2Ik903Ku7zOJXstnJIO1469tih+Faoxz1WAftiPIsTxZmWVGqqPaJgUmG5SckyoUacp1xnHDaU3eCVRMQJJWZ7vEHQNj9+JJmmwQMz5DrGWs5OTgtJwKpjvPqwVA4I9kTkTi5mUeB3BP30veyWp0YsdxZEcW7CjSB2b5Zt9sPPHm7f3+CFvc32w4V2nkjoXlEQF0/Wcma9f8cKxeLWbO/DWJHKAcFI2mEQVyTPPT4mDuvReVqCZJWShN1hRosyk5bfCduoNpbtbfbbv4jLlZLlOZu0ZEyz6pi9D2NFKgcEO3F51JzwmTXGdTgtqXFu9hAs5ZPqW/94TPsux3zsznGFsLBGOE0SJA4A9nhVu4lUDgh2m2Ncm35RxgYSArSRpJNguXohZZYg6Yz1hQ7SZt5E5bxgb3NS40+RTHbyhHVnKWeSsBm1Yvx7DLz2x6ifpKIozyqKckZRlO+T3ie9Nrp+kraOdpxS7O12gmSVmiMwoX1Dif5A3xcJZmZWT4yoMqYFjb3Dk7iyxAVlfsr/mX3nUbJVBMs2f4Eg4OWxvdGfRbAH1uPVh1E9SaOzVlX1LIA1e+ftdJ/02ujvzwD4IU0dnWhxSi7BAy+/+yAYCdNJIFkxxZGDgCRshvWEdZA20/DIgeSErAjT5jicKpxiGNkhDT7JUs5uh/isxGHKfWj/uI7x6sNoh9bnAKyN/r0E4AzBfdJrxgCxRFnHREKqVNOl+IO2OSFm5zdMqsVkrjhJ65WEwIBOSDtktRMF5UI0gxDtE58BsGL5bN/Rc7pPeo0bTnbVqKN4fvcRso1bVhvepKZkUo+rnRDrKCrzudehNCtfvt85phBLrG3+R4Qbt1FveJPqGOmkKaHbJExZtOkYr72hZE5tCGg0Gmi32wCGGyyiKJrLqFwuh0qlMhbvo1armTHEdV1Hq9VCu902fZjzvR46nY7pzpXLAbIsY2tr29+3UCiMxV6XZQm9Xg+6PjxGLo78l3u9vlkPSZLGfIaNMtrNBuoDDZVKBZqmma5zRqAu43cEQUCv10Wn050oY/uzjE6nYx7hF0URg8Fgu235HPJ5AZqm+ZZRKA9Qr9dRKpXQ6/XMfLWiKEKWZbOMXC6Hfr9vK6OATmfLrIckSej3+2bbBCGPfD5vLvGDPuN6vQ5ZlpHP503ZO8m6KAIr6xoGgwE0TaOS03Y9ZHS7XTNkgLWM5eVlCIKAYrGIzc1N82+sOgcAJSGHVkvzlJMoioFkLUkidF1Hv6+bbel2u+h2u2hvNLCst1CtVsfqUavVsLGxYbalXC6j3W4zk9OwDAG5XM7xfTowBdTr9YnnMzU1NfZOGvrkJyddH5h66SUnkmdcr9dRrVbRbDbNMorFInRdN39XEAQI0LGhtUPLKZ/PQxAE8/0aPh97Gdvv0/LyMsrlstlH6bqORqMRqN8jwXdAUBTleYfLS4a9H4CxCzMDYNn2Pbf7pNdcmZ6eRqUyvrkzNTU+itqjIM7PD2doRodXKm2fhixUupAvr0OWx2cv5bJo+zxuOxfFyd1+WxETG0DlchlHDiyYs+xicdJuac2IJIp3J37HXo9SyVuUmqZN/I1TGafu34/5efdDVta/EYRlhzLGPzt5Q0hSuGdsyA/AhOytsn7sMPDGJ+NtDisnr/tGGdZ6WXXKXmdR60w8HydoZK1pGiRJgiRJOHJgn+kNZq0HAMzNjS/CnXQwrJysOL1PTxzb1jF7vezPT5YLvnLK5XJjdXGTk1ddy+Uy8rmcWR+/CKpPHtPxq8vj3VTQdxKYfD/c3iejXsb9er2O6enhvgJpvwcAzWbTsz6+NVZV9UWP2y8BOD369yKAswCgKMqMqqprbvcDXIuMasSuZEk1uQTJM/344Rm8c23N/4sMCBKm/OS9e/DGJyv+X4yYqGMtxeEaTIJXrCA7D+6v4aNbfLKD2fnmg+Q69uih6YkBYTdApTGqqp4HTG+gNeMzgHNu90mvjT4/C+D06P8ZERDENhml7TYLQrh7CKJjUZ6aT+peRJS6T72H4LSCUFX1lM990msvA3iZto52eCWX4MWD+6v46BZd/HMeSUSeOLIHb1+NZoUQJBZQYTQzjiJxShJSiloJ2+bFvVNYurvp/8WIOX3vLN693vD8Dis5L86T61gxwnhHTqe6swQ5DHHbZIkqZ2rQbGiKR8hnUngkIo8yzn+QgGPGDJRHm+0E6UQA/nGzjDYHTbUYV4BHP0gij7KSc5DzBSTnKFix3yHya5CN4iCkckBwI7LwAgH9qzOf/wQTUDRR6Rhp2AeDpIa4yIiWbECwcMYlvzFrnvIJe23nYIDY8DSwzuMcJySB8FhQC3go7VsR5Vf2C61u5+gc/+QrALuT90mgHNGJ5akIT0anckCwu2kZRNWJBI0wyWJ5Ksv+bTsyG02nEJQws+pjCxWiNtMSdGbN29PIaLNXNjInolq5BEl8QwoLOYfx+osqKZKTjrn1YbSkckAwDjXZ2c3LZpL46bKYzPYXQrhPFkSBW8x4GnirWBLbbIWH+ZNFm6dChIaI063XrQ+jJZUDgluGpd3s2micIPUi6AYpEE04hu8Qhvmw8vjhGaI20xAmhhHvhDS820xLGB3zy3HBos3feih4foZT9/IP+eG20uOVDTCVA8JOxB7+lgdhTFMLEXhm7ZkKbhKIYvZGGsNopxBFAvkwOrYvgvDiYTzmoki1GeSgKAtSOSDYj9PvBGiVTxD4KK8UQccb1GPGgFebDeJKP+kFTZtLcvLaAwCij1ceCzkn1VrsNrHh1YclUwM445VQ417Ocf4fPxIueuk3AoRucILX/siBCHIFh03zyHtP6Av3hUulyNNrLJfLhU4j+ntKNB5QQTk86/28WMg5qaFk3MxSvBIhpXJA8NqQ4eEFYSVssvWg7o12/Dbewib9SPJGPO8N1rCdyCGfDo6GXq+HvdVws8cK57wOtZAHGf10LOkb6TS46Vi2qRwRvGOnJNHMAAByQuu1GwnjNRWEsCY23kN7KaGz8IxtUtkLeM04Hj3IJiGNG/eFPABEOxP3+/NvEyZTiZoZirMhT93HV5Zh+dwhfvXK5cIfMuMdjuEZTofyaBepNCFYvnKcv5edE7xW5qkcEOyx9K3w9k6JMgaKFb9NqFmKA1OHZ/ntuxyl8OQ5spDMAYHnKnGYQCiZZjyajvfgHnczG+0G6zEKT559BHm+eeDVh9GQygHBmlEoLVizXbGGp7UprPkDAFpa8qJ38oannOPEy5RL22aa8TOuLTRefVgqB4SdCs+ZeNhNZQD4hkLnAeXF54+GP/yzL+TmKglPhvQwSjr3cPQao1l98/SAOn1veFny9BgL68VGQzYgREhYLwsD3i6xYeEZn6csh/d84ekBxbPjpGGWMh6XPZl7UiAJgx0WmskQT/NcVEEtraRyQNhpCXJYEEWymKSRRjkXS3QDVVL3H7zIdJsd1I7Ho/SWawBOqqr6A5L7Aa49PyrmmKqqf05bV4P19fWJ5N5WvvHAAn7+8R1WP2dyJkDOViceOTCNX16sh/rbra2tiQTeBlGF8Y0aXklEAOAIpfnui4tz+PUS+5y8Tx6km1U+ejC8jnnB01nDS7d3Ml4b6X59WFiopKQoykkAUFX1LIA147PX/QDXzgA4O0qtuTj6HAm8Tt/SmhlolrZePLh/986kj87z6ShEyp10Xua/uRBxn6zwOrH7GEdX27ihnRy4EceZJdpffA7DWT0ALAGwd9pO90mvLVrKWxp9zsjIyMjgBK3JaAbAiuWzPYiK032iazbz00kAL1kLbjQa5vFtSZIgiiJarRaA4WZipVIZc82q1WqmCUHXdbRaLbTbbTOM7NB/O492uw1dH6DV0iDL8phLW6FQGMvfKssSer2eGX5XHAWg6/X6Zj0kSUKnMyxjfXUF09PTY6aMSqUCTdOg67r5G8B2nlhBEFAsFrG5OXSh1DRtoh6FgoxOp4PBKAqwKIoYDAZm2/L5HAQhD03THNuyv1jF1tYWms0mBqNCSqUSer0eut2uWaYsy2YZuVwO1WrVbIs86KClC+h0tsx6SJKEfr9vtk0Q8sjn8+h2e6My4PmMTyyUPeXkJ2td13GslsOlz7qB5OQsaxndbtd8PsbvucnJWg+DarVqPuN8Xx/JbFxOoiii0+m61sMua0kSoes6+v3RM87PQtM0VzkZ9drY2DDbUi6X0el0zBAQW1vtQHIaPp/xd0EQBORyObPMe4o1bG1tub6TwDDpi1XW9nehu9VGThAn5DQYDMz22uVkl7X9GR/fO2y7m5wAoFgsQtd183ftslb25PDJ3X4gOeXzeQiCYL5fw2c8/kw7nY6rnHRdR6PRCNTvkcA3eAkDRuak86qqnrden56enjicYc8iZN9sMmxuq6urKJVKKJUmbXRGmaXSKgCgXB5/RHZbpShOLtHt52REcVjG3r17x+phUCxOmpKq1fFsTEZdy+UVx3qUSt6ibLdbE39jfD5+ZJhvgGRzzl6G0ZYvKgJevXAXpdL4fUmafD6SNP6A3J7xF04c9JWTgZOsV1dX8bljCzi3tBlITvZ62O/fM1005eMmJ2s93Oopy2twwl7XILIWBAHlctlVTgZzc+NzN+v3C4WhjpHKya3ewPahsfsP3zMq2/mdNHCStfGMv/5wHq9dqk/ISRDyKBa3/85+f1iP8c9GXb/0wCHIsuwpJzeMus7PAz+7vBn4nQQm3w+jjEN7SpBl2VVOq6urmJ4epiMl7fcAoNlsetbHt8aWjV0rS4a9H4DhLDsDwL5L5naf9BoAnGG5oQzwSy6RZJKeOIUHvOScZD+cTLd3B34u07zk7DsgjDZ13XgJwOnRvxcBnAUARVFmVFVdc7tPek1RlOctHkdnRoNQqnn88AzeueY8s4yTo3NlvMq4zIWYwgL4ETaE+U7h+L4KLt72nknGwYl9Fbx2ia0H1FwlmblRosjG5gTVprJhxhl5AK1ZzDrn3O6TXhv9+y8URbmsKMoqTT3tkCwHaeKbOMHqZOujh6ZD/Z3IObvTXIW9LzitVxUv/3RlH5vk6ot72R4Ce3JxlkmbP380maew3Q5A0ug2zcFHnvhl4+Ol29RPw2kFoarqKZ/7vtdGq4F4hknQxTfJ2N2wOgHN+iR1LtHGrIydQCpPKlt38t04vsBmFmhwhJHfuVvSbT8MLws7UeTRjQsSOcfJ/XvZrkIPz5aYtJkmKqkTvPOBu+n2boaXbqdyQCDhxD62L+uhPWwGBNYHh74aUzx3P+ar7JbEtOlHefHgfraTjqTq2JfvT6aOsRyo4sqLwJpUDggk+UiTnBoyDDutPSyyihlyTmrLeciEV65dGnjrXtjyWYbToAnTHur3spzK7NiNcU/8cDoPANBlJLPDciP+GANziiHnpEYm5UESdZs2H7iVQw7xfdx0248TjJwDAOd68YSXnFM5IPgdzkg6YeLgWE93WqkW2Q0IXz5mP6genicO07t2GnJmuU+SVA8cA1a6zTIGFEsde/rE3olrbrrtx0MMY3ix1DESj0RefVgqB4SdTlKTlbNcNic1DDPvFKtJQRaSqWMCQ71Iqhk1Th1Lh3bHDOvDLzwzp9HAKxprkthXS2bsfdZmMV4RPGmZSui5AZbEaeJM5YBAmlyClXcK6xSTDx8IvtR1OsjCeqDiFTo5LDySiNw7x/Yw2deVSRNIGL42MqWwanMYHXNiL0NvMcB50rHbEuSQeIvxSpCTygGBNPqfV2LvIIiMyjEIs9R18lsOe6Zhp8AzQQ4rWMW8N0wprNrMymQXhY4l/bwJD3jpdioHBFL2MgrHUGO4qcaSownNn8uDB+5h6/PPigVGM+iphA7u9zMOAZNk/MJN7ASyAcGDBUaeA0l9WR/nkMWKRXyeJxfZe/I8dSyZB4dY6VhSV3usTE9WWLg3f4mhR5zBbjiclsoBwR5LPw3I9oDw4OPJw2IfgcWhNGBczrmUaHrSdJuHJ49sM8E66bZvGRw8eYQIvZZ4yTklr8k41sxhO5Wg+xtGZibeHGOwQjgww+aQj1XOZQYDFcuDTLxgqdssXTxZYj+0GEa3eRwkKxfodYx09cOrD0vlgGCkdCRBpHwpeJ1g/L0H9gX6vpGGjzcsThjvn2bzzKxyFhls3n7+vtiC73pidRENott+fPPBZMaAsu9LhNFtHrk2CgxCzH9pkcyUxVLOVlI5IAShINE9Il6HTBIYsgZAcg/7sIBXeGnaSQcvHUtqOO3drGNxL8qod6IURXkWw1SZJ43sZn73A1w7MyrmGZZpNIP4LX/txAJ+/N6t0L/1OIMQDE4EjWxpTyJCO9DtBFj7p7MOC23w1P1zePVC+Exgp49ur1xYtjlMiBQrrNy2/eCd/ClKaoQ6xuvsBVWvoCjKScBMZrNmfPa6H+DaGQB/NLp20l52VNCe2GR9kMmA1quEdGm6m/hcyGxzBrxm4rR7E6xMbHZoveO+epzNobudxCMH6XSM1bmUsND++nMYzuoBYAnAGYL7RNdUVT2rquoLo2uLlvSc1AQ5yLJbVqf2JCK7edltYJdz1CGKSWFZryQd0orqeScpQU5U/XlSE+TMAFixfLZPO53uk14DACiK8n0ALyAmWLlAJg2WkR7tPEGRhP4PPrefYU3G+QKjvNasSeo5FVoeYJwAyArNau/3OerYk/eFX3knwasr8ZqoquoPFEX5oaIov1VV1VhFoNFooN1uAxjGQxdFEa1WC8Bw9lupVLCxsWGWU6vVzOPevV4PrVYL7XYb/f5wdiHLMvL5vFmmtQzDxatQKIyNzLIsodfrQdeHXg6GLdOYseRyObTb7bFQtdZ6AEN/Yk3TTK8BwzZo/I4gCCgWi9jc3JwoQ9Q7WG/3UCjI6HQ6MJwtRFHEYDAw22acNxhzVdN7qNe361GtVtFsNk2PjVKphF6vZ7r0iaIIWZbNMnK5HKrV6lhbarUaNjY2UB60oWkaJElCv9832yYIeeTzeXS7vVEZw+e+tbUdvrgq51Cvb9vTp6amiOVkfz69XqpNp94AAA1DSURBVA/1en2sDE3THOUkSdJYGGW7rB8+tAcrKyuh5OT2jIvFInRdR6fTgaZpyOdzEEURnc62G6W9HnZZS5KIRqNhyknXdWiaRiQnox7lchmdTge9Xm9U5vb7NOi20e7pE3LyexcEQcBWS0ODQE4Gdlnbn3E+n0e5XEaz2cQUtqBpGgqFgtnmYT1kdLtds212WefzOVSlwZiOBZGT0TYvWQ/rNSknXdfR7+tmWwRBMOWWywGP3Ts/US83OfV6PTQajUD9Hgm+A4KiKM87XF4y7P0AjGnXDIBl2/fc7vtes+wrnMfQjPQ8AHPTenp6euJwxtTUuL3evvEyPz88SdhqtVAqlVAqTdpe7WUWCgWUy9uLF3tiClGc3ASynpMpFosoFsdd3Ix6WL9jp1odn13Z6zo/P4/jB3v46Nb66L63KHu97lhdZVmeqAfJRpW9/fYy5ubm0BbKKF/bHqztSNL4QaJyebvulXIRlcK4DEjlZK+XIWdrGVZZ2s8zieL4M7S29cBsFbOzkysMEjl51XP7t7brZdcp+zO3y3p6enu2bLSZRE5evwEM36ej97Tx6bI2+o7783Gqd6VSIZKTFSdZ259xsVhER2yhfL09+lwY+227HIFxWdemypgqjK+Qw7wLbrI2ZOn3TgLj78e+6TLm58d1zE1OVt0m7fcA/zwKvjVWVfVFj9svATg9+vcigLMAoCjKzGg273if8NoZAMa+wQyAN/3qSsrm5qaj4rlxdL6MK/XgB0FIEl3Q8NXj8+aA4Een03UcvHhwgCJ8L8sQDEHl7MVJCjMYCffOlc2ONwh2HWPZZmAYqff//NUVZuWxwnp4MahuJ9VE98QR8nMurOVsQGUgNzZ6Rx5Ba5aN33Nu90mvAXgRwKKxQlFV9WWautIwOxXOxYtlpignWEdRZcVu3LBmcbDNiz1T4UKRk7ophiWse3JSN/CTzK7YQ3BaQaiqesrnvu+10QrDa3USGQ/tr+H8p6uB/+4IpR+3H1LI02lOaQjTwuLeKSzd3fT/YsQ8tL+Gd66u+X/RBm8dK4b08X/q/vS5NRvsny7iVqMddzVCsTtdaHwImlwibJIPXgeZDIIEp7PaFaMISTwfIvnOg4y9Upzk/CilnzgvwubktYdWZ504JWwAxCjCjRuroyCHtKKQ/+kI8m5nCXIYshMSp7DG6hESxQnSe0IclgprmnPDSc7lXZ6CMSm6LUYQW8WYqAXxyQ9rmgtCtchfx7IEORmOhMk/EEWn+NUQseF5b9wC4fLV8oidv5MIo2NR5NcOk36UVygZK2FWe0nJpZANCJzgFebADqusbqwJcwSf98ZtWGbKycx4V46g0wWA2Qhm1WEIs7+RhI1bJ2Y4m5dJSeYbyBm7XzMJXwwY+4fniVsrJ+8lc1UrFKJ9qZPw4oWRsxMsQnqT8FTAlch3HpnUMVZttnKKUMcMopoMGb8TtW7zYDGgjvGQM5DSAcHvcIYTQfMazEU0cyfNUGacsqQNvrWTcJPz/oBmo6gCjgU1Z81XJzvCMLrtR1ATI8+wKE5YT5gnhfmAjihBJ1A85AykdEAIk1AjqKdRiUGGLpYYTaaN+MmLhRr7AdRNzknNrxzU9uyUkCWqREhePBaBnd4KaZODTgRo4H0olZecUzkghCForuAkmEycCOveGIYnF8lfis9H4KpnEMR3PwqPEYPdomNR7jkECVhozRvBm8V58o34PQnao0rlgOAUO2gnQ3KuwCm+C2+OL5DbOXnM3ljImSZ6ZRzw0u0ozhWE4fhChVi3WeXqJiHIYE26D2iFl5xTOSCEzUdKmkHqscPRmmVIFCoOU0IQMxuPMB8s8s4e3xfNhrLBQcJOy03mvHLtJnXvaaFWJNbtKM+gBAnf8sA9wfdcspzKDAm7CfWV+8lsz48ditaGSuJ62u/3cV+AZexuwEvOpDM4OWJXWFJ/dLczG7w2WElNjWHOLNBihMtOGqRuwWEOivKScyoHhLAsEL4UUXkYGZC6+UW92UdKUA8uFpB2vGFDN4SF1KzBO3CiHVIde+JwdHb6IMShY6R7FkkKBpnKAUEQkuUBFAX5fA73UuaHDsMzD+3z/c43H/T/Thi85EwS0yZMPKa4iVu3D89G3/F+44T/Ps8ZTjrmxaMH/SdgYQcqXnJO5YDAc1M5qkM5dvwUXhTFyGe7ANm+C68ggF5yJjlb8JWEJon30jGeuk0SJTeO2e7x/f4dL+9Ak06Q9AVBD/0ZZJvKDLGmvgvK0ye8TQ3/6JF7QpdNwyMHvTempuV4lqUkpg1e7pM0cgaAo5xDS7vhd2L5u4+6n4KnbbMXT/iYHMPEiWJBrucf3C6OyRAJYff1eMmZekBQFOVZRVHOKIryfdL7pNcs9xzLjoPHfWyk983Fs3HrNzP79oPJdJ+M8lyEHb9k63HZdv28xuIaqPw6VZ7J62kg9Q7kgd8EMUn7BwDlgGDJe3wWwJrx2es+6TVLGWcAPENTT5b4zWbjnIl4HQgqh8x8xYJ//uX7XO/9Z48fiLAm43gdHorzRLefOSvOTsRLx+y5GaLknz55xPXetx6OZ9UOACf2uZ/fCHKoLipoe4nnABhpnpYwzIPsd5/0Gjdok0t82cX91Espo+DZU4dc71kTsUfNtMdJTJY5lO34ydkrumrc4YjdTJNeMgb4JU4x+N7Jg47Xowh37UatVvNcafLUMT+8JpA04S2SmiBnBsCK5bPdLuF0n/QaFEU5OVo1MIU2ucTnXdzJ4jR/AO7Jw//s68diT5zyoEPAs288sMD1N0na/C++Orl6yeWc4wRFyUmXhOuHfTzFeMvZbRXwX3/5KNff9cJos5OOkXi58cbt2dCEe09rgpzkrakwXLJ/27YM/cPH4jN9WPkTWwd3cKYUOEYOD7798OSLGUWyEj+cNr3/7OvHYqjJOLlcDr9nGzD9VgdR8adPL459PjBTjH0ABZx1LAknrGfKk2a2/+Yb8euYE75rKUVRnne4vGTY+7Hdac8AWLZ9z+2+7zW/1UGj0UC7PUxkLUkSRFFEq9UCMHyZKpUKNjY2zO/XajVzVO31emi1Wmi32+YpR1mWkc/nzTL9yliQgTPKLH76wS18W5nFTL6NjY3hEXojpV8+n0e5XB4LVWstAwAqlQo0TTOPohv5YY0yBEFAsVgc8yqwl1GtVtFsNs0j/P/48b34q3duQZkv4uThElZXV6HrOur1OnEZpVIJvV4P3W4XwNBtVZZlaJpmPp9qtTpWRq1Ww8bGhllGuVxGp9NBr9cDAPzx6QX87Qd1COjjGWUWy8vLns8YAKampkLLqdfroV6vT5Rhf8b/7NQ83r7Vwsc3VvEHj+zFxtoqchHIqVgsQtd189SpvYyDJeC7D+/Ff3jrKr770DxKuoatLcFTTr1eD5qmUcmJ5H36J6cP4P95fQknD9fwyP4y9fvkJGv7M3Z7nww5A8CfPnUIf/XWNeRzA3zrgTnz93jKiaSM5586iFfUu7h8t4nvfW4BreYG+hTvU6/XQ6PRCNTvkZCjiXEz2vw9rarqiyNPoLOqqp5XFGVGVdU1p/ujPyW5ZkxDZgG8AOBPVVU9P/rd6ltvvbVeqYSLM7O1tRUoMfduIGtzOsjanA7CtrnZbOLUqVM1VVU3nO5TmYwsHfQZAGvGZwDn3O4HuPayqqovj8pjalvglVwiyWRtTgdZm9MBrzZTb7+rqvqiw7VTPveJrlmuO94LSxKSiERN1uZ0kLU5HWQJcjIyMjIyuJLKAaFUij4AV9xkbU4HWZvTAa82p3JAMLwp0kTW5nSQtTkd8GpzKgcEw0UvTWRtTgdZm9MBrzbHd6abEppof5ubm7sur7IfWZvTQdbmdBC2zX795k4dEJpPP/0036AtGRkZGbsTV59VqoNpGRkZGRm7h1TuIaQRe2jyjIzdQpLypex0Ujcg+CX02Y2MToD/MO56RImiKM+P/vuLuOsSBSOdPpOW9hokLV8Kbwz5usSYoyZVA4JfQp/dyqi9S3HXIypGncTZ0Sn3xdHnXcuofX80kvPJtOh1SnleUZTL4PQ+p2pAQMSJeDJiYxHbsl3CdqDEXYmqqmdVVX1h9HHRElNsV8MrX0rC+VNVVY/xavdO9TIKi19Cn4xdgC0u1kkAL8VVlygZmUFf8P3i7iGR+VI4Y6x4T6qq+gPWhadthZCRIkamk/NpmTGPOogXFEWJP/MQZ1K6OoCqqj8YtXuOhyk0bQOCX0KfjN3FGVVV/zzuSvBGURTrvsESAC4bjgljceQg8jyA2TTsm4ycJJ4dfVwGB1No2gaEl7D9EBexnZxnVzNSotMWZdr1KIryvLGk3u2byhjul1gnOrvegYBnvpQE81ts91nHRp+ZkrqDaaMZxRKGm29M8yxkJAOLm+0Khh3lH+1m88LIRPSPRx9PWTaYM3YZo/5rBcP+i/keQuoGhIyMjIwMZ9JmMsrIyMjIcCEbEDIyMjIyAGQDQkZGRkbGiGxAyMjIyMgAkA0IGRkZGRkjsgEhIyMjIwNANiBkZGRkZIzIBoSMjIyMDADA/w8LXC3nT/8XOgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "w = f(wdr=10)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "64e80ceb132647f79d708e8fbd6f05d8", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type interactive.

\n", "

\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "interactive(children=(IntSlider(value=10, description='wdr', max=30, min=-10), Output()), _dom_classes=('widget-interact',))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "@interact\n", "def f2(wdr=10):\n", " t, a = vtb.forced_analytical(m=1, k=10**6, x0=0, v0=0, wdr=wdr, F0=200, tf=5)\n", " # display(Audio(data=a, rate=1/0.000125))\n", " plt.plot(t, a, alpha=0.5)\n", " plt.show()\n", " return" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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