modélisation d'une onde.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: matplotlib in c:\\cours\\drap\\wpy32-3680\\python-3.6.8\\lib\\site-packages (3.0.3)\n",
      "Requirement already satisfied: numpy>=1.10.0 in c:\\cours\\drap\\wpy32-3680\\python-3.6.8\\lib\\site-packages (from matplotlib) (1.16.2+mkl)\n",
      "Requirement already satisfied: cycler>=0.10 in c:\\cours\\drap\\wpy32-3680\\python-3.6.8\\lib\\site-packages (from matplotlib) (0.10.0)\n",
      "Requirement already satisfied: python-dateutil>=2.1 in c:\\cours\\drap\\wpy32-3680\\python-3.6.8\\lib\\site-packages (from matplotlib) (2.8.0)\n",
      "Requirement already satisfied: kiwisolver>=1.0.1 in c:\\cours\\drap\\wpy32-3680\\python-3.6.8\\lib\\site-packages (from matplotlib) (1.0.1)\n",
      "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in c:\\cours\\drap\\wpy32-3680\\python-3.6.8\\lib\\site-packages (from matplotlib) (2.3.1)\n",
      "Requirement already satisfied: six in c:\\cours\\drap\\wpy32-3680\\python-3.6.8\\lib\\site-packages (from cycler>=0.10->matplotlib) (1.12.0)\n",
      "Requirement already satisfied: setuptools in c:\\cours\\drap\\wpy32-3680\\python-3.6.8\\lib\\site-packages (from kiwisolver>=1.0.1->matplotlib) (40.8.0)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "You are using pip version 19.0.3, however version 19.2.3 is available.\n",
      "You should consider upgrading via the 'python -m pip install --upgrade pip' command.\n"
     ]
    }
   ],
   "source": [
    "pip install matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Modélisation de la déformation à un instant donné."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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    },
    {
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896y6+uF8Ni3MIzMlgcdtOnGdoqd/kJ/vPsOmBVOZkzv5qtfzvrICuvoGee5QbD+GtvOUm8MNnWzZWIzLdXXDriTEuXjXspm8fLTZlu7amlQiwGOVdczJTeWGcTQoj+T9Kwvo7B3k+cOx+5zFhYv9vHC4iXtWFkxo7Kmk+DjeuWwmLxw5T9vFfgsjjCwvHG6ivWeAj21464N547G6KIvC7BTbStdO8VhlHVmpibxz2cSGA3r/ygIGPYbfvX7OosiCp0nF4Zo6e9l7uo07l8yc8IBxa4uzyc+cFNNVYM8fPs+gx1gyhtf7VxYwMGR48o3wn7hO8UxVI9OmJLOqMGtC6xER7i4roKK2jdOtFy2KLrJc6h/i5aNN3HLtNJLi4ya0rpK8NJbPyuCxyrqw96rTpOJwzx1sxBi4bfH0Ca/L5RLuXlHAzlNu6tp6LIgu8mw92Mjs7BSumTFlwuuaP20KS/LTedyGE9cJOnsH2H6ihc2Lpl91VU2g9yzPxyXwm32xWeh55XgzPf1D3L5o4uc6eKsUTzV380aYH3zWpOJwz1Q1Mn9aGiV5V19fHei9ZfmIeEeRjTXu7j52Vbu5ffF0y4YJf9/KAo6d76IqBrvDvni4if4hD7cvseYiOC09mRvm5fHEvnrbusPaaWtVIzmTE1ldnG3J+m5fMoOUxLiwt/tpUnGwxo5LVJ65wO0W3KX4zcyYdLk7rCfGusP+4fB5hjyG2xaNvxvxaO5YMiNmu8NuPdjIzIxJLCu4uh6JI3lfWQFNnX28djK2etX19A/y8rEmbr12OnEW3PUBTE6K57ZF03n6QHh71WlScbBnD3ob1DdbdDvsd9eSGTR09HIwxp5Z2VrVSHFuKgumWzeHx5TkBG6aP5UXjjTFVJLu6BngtZMt3GbhXR/A2+bnkZYUH3OdSV4+2kzvgMeSau5Ady2dycX+obB2fdek4mDPVDWwcPoUiifQVXMkN87PwyXw8tEmS9frZC1dfeyucXP7ImsvguDtXtzS1RdTSfr5I+cZGDLcZnGBJzHexcZ5ubx8rDmmkvTWqkZy05JYOcEOD8OtKsoiLSmel46E71zXpOJQ9Rd6eONsu2X11YGyUhMpm53FizaPZhpOfzjUiMfAbYutq/ryu3FeHnEu4aUYStJbqxopyJrE4vyxRyMer5sXTKWlq4+qGEnS3X2DvHK8mdsWWVf15ZcY7+L6MCdpTSoO9Zyv6svqkqDfpoV5HG3spP5CbPQCe6aqkdK8ycybZv30tRkpiZTNzuTFMJYG7XThYj87T7Vy26IZIZkX/YZ5ud4kHSP78+WjTfQNWl/15Xfzwqm0dvdxoD48vcA0qTjUMwcbWTQzndnZqSFZ/00LpgLYPvdCODR39rLndFvITlqATQumcux8V0wk6ReOeJ/1sbIDSSB/ko6VO7+tvmd9Voxz8Mhg3TA3vHfSmlQcqLmzlwN17dxy7bSQbWNO7mSKc1Jj4sT947FmjIFbrw1hUlkYO0n6xSPN5GdOsuRZn9HcvNCbpKP9earegSG2n2zhHddMteRZn5GkpySwsjCTl46E59jUpOJA233dKW+YN7FhWcayaeFUdte46eodCOl27LbtRAvT05OZO9XaDg+BinJSmZMb/Um6f9DDrupWbpiXG5KqL78376Sje3/uPd1G74CHG+Zd3eCRwdq0YCrHm7o46w59krZ7jvpbROS4iJwSkS+O8PlHRKRFRPb7Xh+3I85w23aihdy0JBZOD11JELwH2sCQYfuJ6H0mYGDIw46TrVw/N7QXQXgzSXdGcZKuPNNGT/8Q188N7UWwKCeVkrzJvBTld37bjreQGO9idbG1vb6Gu9l3Jx2OQo9tSUVE4oAfALcCC4F7RWThCIs+ZoxZ6nv9OKxB2mDIY3jtZAsbS0N/EVw+K4OMlISoLl3vr2unq29wXLM7Xq03k7Q981iEw7YTLSTECWvnWPPU95XctCAv6pP0thMtrC7KGnMO+omane1N0i8fi+KkAqwCThljaowx/cCvgbtsjMcRDp7roL1ngI1zc0K+rfg4F2+bl8crx5ujdliM7SdaiHMJ60pCvz+Xz8okMyUhqttVtp9oZcXszAmN8BysmxdMZdATvUm6of0SJ5u72Vga+gIPeAs9FTVtdFwKbZK2M6nMBALHtqj3vTfce0SkSkSeEJGC0VYmIltEpFJEKltaIvcg3Ha8BRG4LlwH2sKptPcMsO/MhbBsL9y2nWhhWUEG6ZMSQr6tOJfwtvlT+eOx6EzSTZ29HG3sDHnVl9+yWZlkpSZGbddif7K8PsRtp343L8xj0GPYFuIkbWdSGaluZ/jTOU8DhcaYxcBLwM9GW5kx5hFjTJkxpiw3Nzx/pFDYdqKZxfkZZKUmhmV7G0pziHNJVI611NrdR1V9R1iqvvxunJ9Lx6WBqHy6/vJFMEz7M84lXD83lx2nWqNyFGh/B5JSiwaLHcvSgkzSJyXwWhQnlXog8M4jH2gIXMAY4zbG+Kcu+xGwIkyx2aKjZ4D9de1hvQhOSU5gcX46O6ujL6ns8CXKcJUEwTtnDcCuanfYthku/g4kVo6dNpZ1c7Jp7e7neFNX2LYZDoNDHnacCk8HEr84l7C2OJudIU7SdiaVvUCpiBSJSCJwD/BU4AIiEvhgwZ3A0TDGF3Y7TrXiMXB9GNpTAm0oyeFAXXvUNYhuP9FCVmoi186wfiiR0WRP9vba2xFld35DHsOOU61h6UASaL2vLSza9uf+una6egfZGMYCJMD60hwaOno5HcKuxbYlFWPMIPAZ4Hm8yeJxY8xhEfm6iNzpW+xzInJYRA4AnwM+Yk+04bHtRDNTkuNZkm/dUOLBWF+Sg8fA7igqXXs8hu0nW7iuNCdkD5WNZkNpDvvOXAjrcOOhVlXfTnvPQFjv+gBmZEyiODeVnWEcZTcctvk6kKwPQweSQOt9vfZCOWqxrc+pGGOeNcbMNcbMMcZ80/fel40xT/l+vt8Yc40xZokx5kZjzDE74w0lY7wNaNeV5hIfF94/y7JZGSQnuKKqyuZIYyet3f1hrUr0Wzcnm/4hD5Vn2sK+7VDZdsLXgSTMF0GA9XNyqKhtYyCKOj+EswNJoKKcVGakJ7MrWpOKetPxpi6aOvtsuQgmxcexqig7rHMuhJq/h0u4etEFWlWURUKcRN3+XJKfQWaYOpAEWl+SQ0//EPvDPC1uqLi7vdMk2HGui3jvjnZVuxkK0ajFmlQcwl9nvKE0/CVBgA0l2Zxq7qaps9eW7Vttx8lWFkyfQm5aUti3nZIYz/JZmVFTZdPZO8CBunaus+nYXFucjUuip11lV7UbY+w719eX5NBxaYDDDaHpoahJxSF217iZnZ3CjIxJtmx/3RzvAR4NF8LegSH2nb1wuSeWHdaX5HC4oZMLF/tti8Eqe2vb8Bhs25/pKQksmpkeFccmQHmNm8lJ8SyaGb4OJIHWlXj/jjtPhaa6W5OKAwx5DBW1bbZeBBdOn0JmSkJUVNnsr2unf9ATlqFERrO+JAdjvBeQSLe7xk1inIvls0MzNHsw1pfksL+une6+QdtisMruGjcrCzPD3nbql5eWzLypaSFL0ppUHOBIQyddvYO2XgRdvqFMdp1yR/yDZuXVblzibduwy5L8dCYnxUdFki6vcfs6c8TZFsOGkhwGPYY9tZGdpJs6e6lpuWjruQ7euxXvCMnW91DUpOIA5TXeC4+ddyrg7WVzvrOX6paLtsYxUeU1bq6ZkR72njWB4uNcrCnOivgqm46eAQ43dNp+EVw+O5OkeBc7TkZ2Utntu3NdW2xPe4rfhpIc+gY9vB6C4ZnGTCoikiEinxORfxeR7/tflkcSw8qr3RTnppI3JdnWODaURH67Su/AEPvPttt+EQRvlc0Zd09ETzRVUettVLa7wJOcEMfKwix2RfjID+XVbqYkx7MwhBOcBWN1cTZxrtD0UAzmTuVZoBA4COwLeCkLDA552Hva3kZlv1nZKRRkTYropLLvzAX6hzyO2J/+JB3JF8LyGjdJ8S6WzgrvA7kjWV+Sw7HzXbR09Y29sEOV17hZVeS9oNtpclI8SwsyQnKuBzN+dbIx5vOWb1kB3qHuu/vsbU8JtKYomxePNuHxmLA/iW6F8mo3cS5hpY3tKX4leZPJmZxIRU0b7185y+5wrkp5tZuywkyS4u1rT/Fb45vIak9tG7ctDt3U0KHS0H6JM+4ePry20O5QAPiHW+aTFG99C0gwa/yFiHxCRKaLSJb/ZXkkMcrfO2iNA0rW4L0tbu8ZiNgB/Mpr3CyamR6W+T7GIiKsKsqiorYtIjs/tF3s59j5Lkfc9QFcOzOdlMQ4KiK0sb682t+e4oz9uaooiyUF1t+BBpNU+oHvAOW8WfVVaXkkMaq82s3cqZPJmRz+h/RGstpXwq+IwK6wF/sGOVDnjPYUvzXF2Zxrv0T9hUt2hzJu/mPAKfszIc5FWWHW5cbuSFNe4yYzJYH508I3yrMdgkkqnwdKjDGFxpgi36s41IHFgv5BD5UOaU/xK8hKYWbGJCpqI2/cqsozFxj0GEftz9VF3lgi8UJYXuMmJTGOxWEe4PRKVhdlcaKpG3d35LWrlFe7WV2UHZHVyuMRTFI5DERu9xUHq6pv59LAkGNKgn5rirMjssqmvNpNvEsoK7TvIb3hSvMmk5mSwO6ayEvS3vaULBJsekhvJIHtKpGkrq2Hc+2XHHeuh0IwR8sQsF9EHtYuxdby17GuKnLWgba6OIu2i/2cbO62O5RxKa9xs6Qgg5RE+9tT/FwuYXVRdsS1A7R09XGyufvyRdwpFs3MYFJCXMTdSV9uT9GkAsCTwDeBXWiXYkvtrnUzf1pa2KYODtaaCKyy6e4b5NC5DkdVffmtLs6i/sIl6i9Ezg2/Pwk6bX8mxrtYMTszoo5N8J5L2amJYZs62E5jJhVjzM9GeoUjuGjWP+hh35kLjun1FaggaxIz0pOpiKAqm8rTbQx5DKsdVrKGN9tVIml/VtS0kZIYx7U2DXp4JauLsjh2viuiBuusqG1jdXFWWGfNtItzKktjzMFz7fQOeC73tnISEWF1cbbvaerIaFepqG0j3iWssHHQw9HMn5ZG+qSEiKoCq6h1s2J2pqPaU/zW+KqQ9pyOjCTtb09Z7bBq7lBx3hETI/wNt3YOengla4qzaO3up7olMtpVKmrcLMpPd1R7ip/L9ebzKpGg7WI/J5q6HXkXDbA4P52keFfE3Pn5/+5OvIsOBVuTiojcIiLHReSUiHxxhM+TROQx3+cVIlIY/ihDo6K2jdK8yWQ75PmU4fylqvIIOHF7+gepqu9wdElwdVEWZ9w9NHY4/3kV/0jATryLBu9MpctnRU67SkWNm4yUBObmRffzKX7BDCg5V0R+JCIviMgf/a+JblhE4oAfALcCC4F7RWThsMU+BlwwxpQA3wX+daLbdYLBIQ/7Trc5uuQyOzuFqVOSIuIhyDfOtjPo0PYUP3+pPxJK1xW1bSQnuBz1fMpwa4qzOXq+k46eAbtDGdOe022sKsyK+udT/IK5U/kN8DrwJeDvA14TtQo4ZYypMcb0A78G7hq2zF2Av1PAE8BNEkRLVyjmCLDS4YZOLvYPObpkLSIR87xKRY13/pQyB7an+C2YPoW05PiIKF1X1LSxfFYmiSEYF8oqq4uzMMb57SrnO3o54+5htUOrEkMhmKNm0BjzQ2PMHmPMPv/Lgm3PBOoCfq/3vTfiMsaYQaADGPGvIyJbRKRSRCrPu0Mz97JVKhxeveC3uiiblq4+alqdPb/K7to2rp2ZTlqyffOnjCXOJawqdH67SkfPAEfPdzq6wAOwtCCDxHiX4++kI+Vct1IwSeVpEfl0CAaUHOmOY3iROJhlvG8a84gxpswYUyYJzmyn8KuoaaMox/75U8bif/DNyVU2vQND7K9rZ1Wh80/aNcXZ1LZepKmz1+5QRrX3dBvGOLcDiV9yQhzLCjIcn6R317SRlhzPgun2zp8STsEklfvwVncFPvxoxYCS9UBBwO/5QMNoy4hIPJAOjHkUdfcNMeRxZpXNkMew53RbRJRcinJSyU1LcnSVjX8++kioXvC3+Th5f1bUeuejX+aA+VPGsro4m8MNHXT2OrddpaLWzcrCLNvnTwl7P0NWAAAgAElEQVSnYB5+LBrhZcWAknuBUhEpEpFE4B7gqWHLPIU3qQG8F/ijCaKC32MMRxs7LQjRekcbvfPRO7lR2U9EWF2U5ejnVSpq2hAhIu5UFk6fQlpSvKNL1xW1bSwtsHc++mCtKc7CY7wPvjpRc5d3PvpIKEBaKZjeXyki8iURecT3e6mI3D7RDfvaSD4DPA8cBR43xhwWka+LyJ2+xf4LyBaRU3hHS35Lt+PROLU0eLnPusPrrP3WFGfT1NnHGbczhxipqHUzf9oU0lOc257iFx/noqzQuV1hu3oHOHSuIyIKPIC3M0Gcy7GDde65/HxKZJzrVgmm+uu/8c6pss73ez3wT1Zs3BjzrDFmrjFmjjHmm773vmyMecr3c68x5m5jTIkxZpUxpiaY9SbGuRxbGqyocXuHQcmYZHcoQVnj4Cqb/kEPr5+9EFElwTXF2dS0XKS5y3ntKpVnLuAxkVPgSU6IY2lBhmMb6ytq2khNjONam+ejD7dgksocY8y3gQEAY8wlRm5Ad4zUpHj21LbhcVi7isdj2Hu6LWJOWoA5ub4pcR2YpKvqvUPdOG0k3Svxl1qdOHR7RY13qJvls53fnuK3ujiLQw2ddDmwXaWi1s2KwiziHTjUTSgFNfOjiEzC1+tKROYAjp4hZ3JSHB2XBjh23llT4h5v6uJCz4Bjh78YibddJZuKGue1q/jvnpw2dcCVXDtjCqmJcY6889vtwKkDxrK6KJshj6HyzAW7Q/kT7u4+31A3kVPgsUowSeUrwB+AAhH5JfAy8IWQRjVBqb75yZ02gF+kzqmwujiLho5e6tqcNcRIeY0zpw64knjflLhO66bd3TfIQYdOHXAly2dnkBAnjtuf/naeSNufVgim99eLwLuBjwCPAmXGmFdDG9bEJMS5KMia5LjSYHmNm1m+6Xojif/OareDknTf4JB3KuYIS9DgTdInm7tpddCUuHtrvVMHRNr+TEmMZ3F+hgPP9VYmJ8WzyIFTB4RaUJV9xhi3MWarMeYZY0xrqIOywuqibEe1qwx5DBU17ogsuZTmTSYrNdFRpcH9Z9vpG/RE5P5c48B2lfIa7/Mpy2c5d6ib0awpzuLguQ4u9g3aHcpl5dVuVhZmxlx7CkTx0Peri7K40DPgmClxjzZ20tk7yJo5kVfHKuIdYsRJpcHyGjcikdNTKdCimemkJMY5qtdSebWbpQUZTEp0/vMpw/nbVfY5pF2lubOX6paLEdV2aqVRk4qIPBvJQ81frrJxyIl7uT2lOMfmSK7OmuIszrU7Z0rc8mo3C6dHxvMpwyXE+afEdcadSselAQ43dFye/CrSrJidSbxLnHOu10Rm26lVrnSn8lPgBRF5QEQi7swt8LVdOOlAK8pJZVq6s8f7Gs3qy0na/gth78AQb5xtj8iqL781xdkcb+rC7YB2lT21bXhM5DYqpybFsyg/3THn+u4aN2nJ8VwzI/baU+AKScUY8ziwDJgCVIrI34nI5/2vsEU4AevmZFNe47Z9HLDBIQ97atsi+nZ43tQ0slMT2XXK/ia1189coH/IE9ElwXVz/JOg2X8hLK92kxgfGeN9jWb9nBwO1Hc44nmV8mo3q4tia7yvQGO1qQwAF4EkIG3Yy/HWl+TQ3jPAkQZ7xwE73NBJd99gRF8EXS5h7Zxsdpxqtf15ld2++VNWRtCT9MMtmplOWlI8Ox2QpHfXuFkxKzMixvsazbqSbF9nGHvvpBs7LnHa3RPRBciJulKbyi3AfiAFWG6M+Yox5mv+V9ginIB1Jd4/7A6bT1x/aTTSH4TaUJJDc1cfp2zu/FBe42bRzHSmOHj+lLHEx7lY40vSdmrv6efo+c6ILvCAdxyw5ASX7fszUp9Fs9KV7lQeAO42xnzRGOOM1tlxyktLZt7UNHZV23+gleRNJi8tMttT/NaXeDsZ2Fm6vtTvnT8lUhuVA20oyaGu7RJnbRysc3eNd/6USL8IJifEsbIwyxHnekZKAgumxdZ4X4Gu1KZynTHmcDiDCYX1JTnsqW2zbYrhgSEPe0+3RWwjaKCCrBRmZ6ew45R97QCVZ9oYGDJRsT/X++6kd9p4Idxd42ZSQhxLHDwffbDWl+RwoqmbZhsnQSuv8banxMp89COJ2udU/NaXZNM36OF1m/qwV9V30NM/FPElQb91c3KoqHEzOOSxZfvl1W7iXcLKCJg/ZSxzciczdUqSrVU25dVuygqdPR99sDb476RtStJ1bT3UX7gUFQWeiYj8I2kMq4uziXOJbQfajpOtiBA1DXcbSnLo6huk6lyHLdvfcaqVpQUZl8d3i2Qiwvo5OZRXu20Z+aGps5fjTV2smxOZz04Nt3D6FDJSEthp0520v3DgryaOVVGfVCYnxbOsIMO2KpttJ5pZnJ8RUYMeXsnaOdmIwM6T4U/S7u4+Dp7r4Pq5uWHfdqisL8mh7aK3sTzctp9oAYia/elyCevmZLPTph6K2463MCM9mZK8yWHftpNEfVIBWFeSw8H6djouhbcPe0fPAPvr2rm+NHpKLlmpiSycPsWWKhtvd2bYGCUXQbC388P2k63kpiWxYHpEPCEQlPUlOTR29FLTejGs2x0Y8rDzVCsb5+YiErvtKRAjSWVDSQ4eE/4hW3acasVj4Pp50XMRBO/+fONsOz394R3Ab9vxFrJSE6Nq5Ndp6cnMyU0Ne5XNkMfw2skWNpZG10Vwva8qL9wP6e6va6erbzBq7vomwpakIiJZIvKiiJz0/Tvi0KgiMiQi+32vp652e0sLMkhJjAt7aXDbiWamJMdHRc+aQOtLcugf8rD3dPg6P3g8hu0nW7iuNCfqetZs8PVQ7BsMXw/Fqvp22nsGoq7AMzvbOzxTuO+ktx1vIc4lrIvx9hSw707li8DLxphSvJN+fXGU5S4ZY5b6Xnde7cYS412sKsoK64FmjGHbiRauK82NuuGvVxZmkRjnCmuSPtLYSWt3f1SWBNeX5HDJN55ZuGw70YIIXBdlF0ERYUOJt/NDOIdn2naiheWzMkifFLkP5FrFrqvdXcDPfD//DHhnqDe4oSSHmpaL1LWF50GzE03dNHX2sXFudJ20AJMS41gxO5Ntx1vCts1tvkbl60qjL6msmePtoej/P4bD9hMtLM7PIDNKOpAEWl+aQ2fvIPvrwnMn3errQLIxCo/Nq2FXUplqjGkE8P2bN8pyySJSKSK7ReSKiUdEtviWrWxpeevJedOCqQC8fLRpYpEHaduJZiC6GpUD3bQgj+NNXWFL0ttOtHDNjCnkpiWFZXvhNCU5gVWFWWE7Ntt7+r0dSKL02Ly+NJd4l/DS0eawbG+HrydktFUlXq2QJRUReUlEDo3wumscq5lljCkDPgB8T0TmjLagMeYRY0yZMaYsN/etf9yinFRK8iaH7UDbdqKFeVPTmJ4eWVMHB+vmhd4k/VIYLoSdvQO8fuZC1F4EATYtnMqJpm7OuEPfa+lyB5Io3Z/pKQmsKsripSPhKkB6O5BcG6ND3Q8XsqRijNlkjLl2hNfvgSYRmQ7g+3fEK70xpsH3bw3wKt6h+K/apgVT2V3jpjPEw2P39A+yt/ZCVJdcZmenUpo3OSxJZdcpN4MeE7UXQYBNC7w36+Eo9Gw73kL6pASW5EfvRXDTgqmcbO7mdIi7Fns8hu0nWtgYhR1IrpZd1V9PAff5fr4P+P3wBUQkU0SSfD/nAOuBIxPZ6KYFeQx6TMjbAnbXuOkf8kT1RRC8VYoVNW0hT9LbT7YwOSme5bMjb/70YF1O0iEuXRvj7UW3oTQn6jqQBNq0IDx30kcaO3Ff7I/qAuR42XVUfQu4WUROAjf7fkdEykTkx75lFuCdHOwA8ArwLWPMhJLKslmZZKUmhrzu+tXjLUxKiKOsMHovggA3Lwx9kjbGu/51c7JJiOKLIHirwPacbqOjJ3RJ+tj5Lpo6+7g+yhuVZ2WnMHfqZF4O8Z3fq8e964/GDiRXy5az1BjjNsbcZIwp9f3b5nu/0hjzcd/Pu4wxi4wxS3z//tdEtxvnEt42P48/HmtmIEQDIno8hhcON7G+JIek+Mid9CgYSwsyyU5NDGlp8HBDJ+faL/G2+aP15YgemxZMZchjePVE6C6Ezx8+jwjcEAMl600LQp+knz/cxJL8dHImR18HkqsV3UW/EWxaMJXO3kEqQ/Tg3utnL3C+s5c7lkwPyfqdxJ+kXwlhkn6mqpF4l/COa6aFZP1OsrQgg5zJiSFtV9la1ciqwizypkT23D7B2LQwtEn6jPsiB891cPviGSFZf6SKuaRyXWkOiXGukJWun6lqJCnedbkLc7S7yZek9562fhpXYwzPVDWwviQnKp+nGC7OJdw4L49Xj4cmSR8/38XJ5m5uXxz9BR6ApfneJP1iiNqpnqlqBODWRdFf4BmPmEsqqUnxrCvJ5qWjTZaPZDrkMTx7sJEb5+UxOQqGZg/GdaU5JMa7QlJ3XVXfQf2FSzFzEQRv6bqrd5C9tdYn6a1VDbgEbrk2Nvany3cnve1EC/2D1ifprVWNLJuVQX5miuXrjmQxl1TAWwV2xt1DdYu1c63vPd1Gc1cft8XQRTA1KZ71c0KTpJ+paiAhTnj7wtgpCfqT9IsW30kbY3jmYCNrirOj8gHS0Wxa4EvSFt9J17R0c6SxU6u+RhCzSUUEnjrQaOl6t1Y1kpzgiolG5UBvv2YaZ9w9HLRw4i5jDFurGrmuNJf0lNgZTyklMZ6NpTk8e7DR0tk1j53voqblYkwVeAA2lOYwKSGOpw80WLreZw96rx2bterrLWIyqUxLT2ZDSQ5PVNZZNujckMfw3KFGbpo/NSpmJRyPzYumkxTv4vHKOsvW+UZdOw0dvTFV9eX3nuX5NHX28ZqFE6E9U9VAnEu4JQY6PARKSYxn86LpPH2gwdKpGp6paqRsdmbUjpgxETGZVADev7KAho5ey0barahx09rdH3MlQYD0SQlsXjSd3+9voHfAmuHbnznQSGKci00LY6PDQ6CbFkwlOzWRx/Zak6T9d33r5mSTHYNdX9+/soCL/UNsrbKmZuJUcxfHznfF5LkejJhNKjcvnEpGSgKPWVS6fuZgIymJcdw4L7aqvvzeV1ZAV+8gzx2a+Inr8XV42Dg3lynJsVP15ZcY7+Jdy2by0tEmWrv7Jry+ww2dnHb3cNui2LwIrizMpDgn1bI76a1V3md9Nsfo/hxLzCaVpPg43rl0Ji8ebuLCxf4Jrat/0MMfDp3npgVTmZQY3Q88jmZNcRazs1MsKV1XnomdZ31G876VBQx6DE++cW7C63q6qiFmnvUZiYhwd1kBe09foGaCnXOMMTxd1cDKwiymxsCzPlcjZpMKeEvX/UMentw/sRP36QMNtF3s593LZ1oUWeQREe5ekc/umrYJj7T70121pCXHx8yzPiOZOzWNpQUZPLa3bkK96nr6B3lsbx1vm58XE8/6jOY9y2cS5xIer6yf0Hp2nnJzqrmb9y7Ptyiy6BPTSWXhjCksmpk+oRPXGMMj22uYNzWNG6J8AMmxvHdFAS6B30zgxD3depHnDp3nz9bMjplnfUbz/pUFnGzuZn/d1c8I+fjeOtp7Bvjk9cUWRhZ58qYkc+O8XH77ev2EetU9vL2a3LQk7lqmXYlHE9NJBbzVDMfOd3HoXOdVff/VEy0cb+riExuLEYntoa+npSdz/dxcnthXf9W96n68o4YEl4uPriu0NrgIdPvi6UxKiLvqtoDBIQ8/3lHLitmZrJidZXF0ked9ZQW0dPXx6lUOgHq4oYPXTrby0fWFUT+u30TEfFK5c8kMkuJd/GrP2av6/iPbapg2JZk7l2jJBbwn7vnOXl45Nv4n7N3dffymsp53LpsRE2NTjSUtOcHXHbaRrquYXuC5Q+epv3CJLRtj+y7F78b5eeRMTuLRqzzXf7S9htTEOD64erbFkUWXmE8q6ZMSeM+KfH5TWcep5vE14lXVt1Ne4+ZjG4pIjI/5XQl4u8PmZ07iO88fH3c1w8/Kz9A36NGLYICPri+ku2+QB185Na7vGWN4eHs1xTmp3BzDbVOBEuJcfGjNbF4+1syecQ6DU3+hh6erGrl31SzSJ8Vej8Tx0Csh8Pmb5zIpIY5/2jq+6Voe3l5DWlI896wqCFFkkScx3sUDmxdwvKmLR8fRE+xS/xC/KD/NpgV5lOSlhS7ACHPtzHTeuyKf/95xelyzGJZXuzl0rpNPbCzWGQkDbNlYzPT0ZL729OFxVdH+ZMdpBPjzDUWhCy5KaFIBciYn8VebSnn1eEvQ1TZn3T08d7CRD66ZTVoMPktxJbdcO401xVn8+wvHae8Jrrv245V1XOgZ4JPXzwlxdJHnC++YR0Kc8M1njwb9nYe215AzOYl3LYvdHokjmZQYx/2bF3C4oZMn9gVX6Gnv6efXe89y55IZzMjQJ+jHoknF58NrCynOSeUbW4+MOaJp/6CHv3l8P0nxcXx0fWF4AowgIsKXb7+GjksDfO+lk2MuX93Szb89f5xVhVmURfGUwVcrb0oyn3lbKS8eaWJHEEO3PLb3LNtPtPCJ64pITtAG5eHuWDydstmZfOf542O2VXk8hi88UeWtlo3xHnTB0qTikxjv4ku3L6Cm5SI/Lz99xWW/8cwR9p25wHfuXqwPQI1i4Ywp3LtqFr/YfYaTTV2jLtfdN8gnf7GPhHgX371nacz3oBvNn28oZFZWCl9/5vAV26r217Xzf548zHWlOXz8Or0IjkRE+Mod1+C+2M+Df7xyW9V/vnqKF4408Y+bFzB/2pQwRRjZbEkqInK3iBwWEY+IlF1huVtE5LiInBKRL4Y6rhvn5XH93Fy+99JJtp8Yudvh45V1/GL3GT65sViHvR7D52+eS2piHH/92H4a2i+95XNjDH/3+AFqWy/y4AeWMVOrFkaVFB/HA7ct4ERTN19+6vCId9MtXX186hf7yJuSxPfvWUactqWMalF+OnevyOcnO2tHHcH4lWPN/N8XT/DOpTP4c62RCJpddyqHgHcD20dbQETigB8AtwILgXtFZGEogxIRvvmua5mRkcx9/72H77544nJjnjGGXada+dKTh1hfks3fv2NeKEOJCtmTk/j39y3ldOtFbvv+a7x6/M32qr7BIb730kn+cPg89986n3VzcmyMNDK8feFUtmws5lcVZ3nfw+WcC0jUFy7285e/fJ32S/08/KEVMf30fLDuv3UBi/Mz+Oyjb/CV3x+ib9A7GKoxhkPnOvjcr99gwbQp/Mu7F+sd9DiI1RMrjWvjIq8Cf2eMqRzhs7XAV40x7/D9fj+AMeZfxlpvWVmZqax8yyqD1tM/yJeePMT/vn6OtcXZZE1OvDwK8cyMSTz92Q1k6UkbtJqWbj79y9c53tTFe5bn09hxicrTF+gb9HDnkhn8h1Z7jctzBxv5whNVxMUJdyyeQeWZCxxt9D68+733L+Wd2jgftIEhD//63DF+vKOWxfnplOROZle1m/OdvWSkJPD0ZzZQkBUbMzuKyD5jzKg1R0Gvx8FJ5b3ALcaYj/t+/xCw2hjzmVHWtQXYAjBr1qwVZ86cmVBsxhge21vH154+QvqkBNbOyWbtnGw2LZiqCeUqXOof4su/P8RvX69n3rQprC327s8b5+USH6dNe+NV23qRz/zqdU41d7NidiZri7O5YV4ei/LT7Q4tIv3h0Hn+4bdVxLuENXOyWVvsPdenpcdOm6njk4qIvASMNCzqA8aY3/uWeZXRk8rdwDuGJZVVxpjPjrXtid6pBBoc8hDnEi1JW2RwyKNJxCLGGIY8RvenRYY8BpcQs+e6VUklZCP2GWM2TXAV9UDgU4X5gLVzggZBT1hr6f60jogQHxebF8BQ0I4N1nDyGb4XKBWRIhFJBO4BnrI5JqWUUldgV5fid4lIPbAW2Coiz/venyEizwIYYwaBzwDPA0eBx40xh+2IVymlVHBsmbDCGPM74HcjvN8AbA74/Vng2TCGppRSagKcXP2llFIqwmhSUUopZRlNKkoppSyjSUUppZRlNKkopZSyjCYVpZRSltGkopRSyjKaVJRSSllGk4pSSinLaFJRSillGU0qSimlLKNJRSmllGU0qSillLKMJhWllFKW0aSilFLKMppUlFJKWUaTilJKKctoUlFKKWUZu+aov1tEDouIR0TKrrDcaRE5KCL7RaQynDEqpZQaP1vmqAcOAe8GHg5i2RuNMa0hjkcppZQFbEkqxpijACJix+aVUkqFiNPbVAzwgojsE5EtdgejlFLqykJ2pyIiLwHTRvjoAWPM74NczXpjTIOI5AEvisgxY8z2Uba3BdgCMGvWrKuKWSml1MSELKkYYzZZsI4G37/NIvI7YBUwYlIxxjwCPAJQVlZmJrptpZRS4+fY6i8RSRWRNP/PwNvxNvArpZRyKLu6FL9LROqBtcBWEXne9/4MEXnWt9hUYIeIHAD2AFuNMX+wI16llFLBsav31++A343wfgOw2fdzDbAkzKEppZSaAMdWfymllIo8mlSUUkpZRpOKUkopy2hSUUopZRlNKkoppSyjSUUppZRlNKkopZSyjCYVpZRSltGkopRSyjKaVJRSSllGk4pSSinLaFJRSillGU0qSimlLKNJRSmllGU0qSillLKMJhWllFKW0aSilFLKMppUlFJKWUaTilJKKcvYklRE5DsickxEqkTkdyKSMcpyt4jIcRE5JSJfDHecSimlxseuO5UXgWuNMYuBE8D9wxcQkTjgB8CtwELgXhFZGNYolVJKjYstScUY84IxZtD3624gf4TFVgGnjDE1xph+4NfAXeGKUSml1PjF2x0A8OfAYyO8PxOoC/i9Hlg92kpEZAuwxfdrn4gcsizC0MgBWu0OIggap7U0TmtpnNaZZ8VKQpZUROQlYNoIHz1gjPm9b5kHgEHglyOtYoT3zGjbM8Y8AjziW2+lMaZs3EGHUSTECBqn1TROa2mc1hGRSivWE7KkYozZdKXPReQ+4HbgJmPMSMmiHigI+D0faLAuQqWUUlazq/fXLcA/AHcaY3pGWWwvUCoiRSKSCNwDPBWuGJVSSo2fXb2/HgTSgBdFZL+IPAQgIjNE5FkAX0P+Z4DngaPA48aYw0Gu/5EQxGy1SIgRNE6raZzW0jitY0mMMnLNk1JKKTV++kS9Ukopy2hSUUopZZmISipjDdsiIkki8pjv8woRKQz47H7f+8dF5B02x/l5ETniG6bmZRGZHfDZkK+dab+IhLRjQhBxfkREWgLi+XjAZ/eJyEnf6z6b4/xuQIwnRKQ94LOw7E8R+YmINI/2fJR4fd/3f6gSkeUBn4VzX44V5wd98VWJyC4RWRLw2WkROejbl5Z0P51AnDeISEfA3/bLAZ+FZXinIGL8+4D4DvmOxSzfZ+HclwUi8oqIHBWRwyLyVyMsY93xaYyJiBcQB1QDxUAicABYOGyZTwMP+X6+B3jM9/NC3/JJQJFvPXE2xnkjkOL7+S/8cfp+73bQ/vwI8OAI380Canz/Zvp+zrQrzmHLfxb4iQ37cyOwHDg0yuebgefwPn+1BqgI974MMs51/u3jHSKpIuCz00COQ/bnDcAzEz1eQhnjsGXvAP5o076cDiz3/ZyGd2is4ee6ZcdnJN2pBDNsy13Az3w/PwHcJCLie//Xxpg+Y0wtcMq3PlviNMa8Yt7sSj3aMDWhNpFhcN4BvGiMaTPGXMA7ltstDonzXuDREMUyKmPMdqDtCovcBfzceO0GMkRkOuHdl2PGaYzZ5YsD7Ds2g9mfownb8E7jjNGW4xLAGNNojHnd93MX3t60M4ctZtnxGUlJZaRhW4bvmMvLGG+X5A4gO8jvhjPOQB/DW0LwSxaRShHZLSLvDEWAPsHG+R7f7fATIuJ/GNWR+9NXjVgE/DHg7XDtz7GM9v8I574cr+HHpgFeEJF94h0WyW5rReSAiDwnItf43nPc/hSRFLwX4t8GvG3LvhRvk8AyoGLYR5Ydn04Y+ytYwQzbMtoy4xryZYKC3paI/BlQBlwf8PYsY0yDiBQDfxSRg8aYapvifBp41BjTJyKfwnsX+LYgv2uV8WzrHuAJY8xQwHvh2p9jccKxGTQRuRFvUtkQ8PZ6377Mw/uM2TFfad0OrwOzjTHdIrIZeBIoxZn78w5gpzEm8K4m7PtSRCbjTWx/bYzpHP7xCF+5quMzku5Ughm25fIyIhIPpOO9PQ3nkC9BbUtENgEP4B1VoM//vjGmwfdvDfAq3lKFLXEaY9wBsf0IWBHsd8MZZ4B7GFbFEMb9OZbR/h+OG45IRBYDPwbuMsa4/e8H7Mtm4HeErgp5TMaYTmNMt+/nZ4EEEcnBgfuTKx+XYdmXIpKAN6H80hjzvyMsYt3xGY6GIosam+LxNhIV8WYD3DXDlvlL/rSh/nHfz9fwpw31NYSuoT6YOJfhbUwsHfZ+JpDk+zkHOEnoGhmDiXN6wM/vAnabNxvvan3xZvp+zrIrTt9y8/A2food+9O3jUJGb1i+jT9tCN0T7n0ZZJyz8LY5rhv2fiqQFvDzLuAWG+Oc5v9b470gn/Xt26COl3DE6PvcX7BNtWtf+vbLz4HvXWEZy47PkB0QIdo5m/H2XKjGO9oxwNfxlvYBkoHf+E6KPUBxwHcf8H3vOHCrzXG+BDQB+32vp3zvrwMO+k6Eg8DHbI7zX4DDvnheAeYHfPfPffv5FPBRO+P0/f5V4FvDvhe2/Ym3JNoIDOAt3X0M+BTwKd/ngnfSuWpfLGU27cux4vwxcCHg2Kz0vV/s248HfMfEAzbH+ZmAY3M3AUlwpOPFjhh9y3wEbyehwO+Fe19uwFtlVRXwd90cquNTh2lRSillmUhqU1FKKeVwmlSUUkpZRpOKUkopy2hSUUopZRlNKkoppSyjSUWpIPhGeq0NGGU20/f77LG+q1Qs0aSiVBCMMXXAD4Fv+d76FvCIMeaMfVEp5Tz6nIpSQfINdbEP+AnwCWCZ8Y6EOynoN9oAAAF2SURBVHy5PwM+h/eJ7grg08aYIRHpBv4DuB24hHcYlKZh3/0q3qfBpwNzgc/jfcL5VuAccIcxZiAk/0GlLKB3KkoFyXcx/3vgu3gH5RspoSwA3o93wMClwBDwQd/HqXiHulkCbMebmEYyB++wGXcB/wO8YoxZhDcR3Wbd/0gp60XSKMVKOcGteIfmuBbv3BLD3YR34M293ql8mAQ0+z7rB57x/bwPuHmUbTxnjBkQkYN4J536g+/9g3jHmlLKsTSpKBUkEVmKNxGsAXaIyK+NMY3DFwN+Zoy5f4RVDJg365uHGP386wMwxnhEJPA7nit8RylH0OovpYLgm0H0h3irvc4C3wH+bYRFXwbe65snAxHJ0h5iKpZoUlEqOJ8Azhpj/FVe/wnMF5HACdYwxhwBvoR3Vr8qvFVk08MaqVI20t5fSimlLKN3KkoppSyjSUUppZRlNKkopZSyjCYVpZRSltGkopRSyjKaVJRSSllGk4pSSinL/H+VMJnVqosy+wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# on importe des bibliothèques, des fonctions\n",
    "from math import sin,cos, pi\n",
    "# pour pouvoir tracer des courbes, on a besoin de 'pyplot' objet du module 'matplotlib'\n",
    "from matplotlib import pyplot\n",
    "\n",
    "# longueur maximale d'affichage\n",
    "# écrire 2.0 avec le point définit un nombre flottant (float)\n",
    "# écrire 2 définit un entier (int)\n",
    "\n",
    "Xmax=2.0\n",
    "\n",
    "# on définit les axes (x,y), auxquels on rajoutera les courbes\n",
    "ax = pyplot.axes(xlim=(0, Xmax), ylim=(-2, 2))\n",
    "\n",
    "# nombre d'échantillons\n",
    "NbEchantillons=100\n",
    "\n",
    "# on définit les positions de calcul de la courbe\n",
    "PositionX=[i*Xmax/NbEchantillons for i in range(NbEchantillons)]\n",
    "TEST: print (PositionX)\n",
    "\n",
    "# date d'observation\n",
    "t=0.0\n",
    "\n",
    "# Amplitude du signal\n",
    "A=1\n",
    "\n",
    "# longueur d'onde\n",
    "Lambda=0.5\n",
    "\n",
    "# déphasage\n",
    "Phi = pi/2\n",
    "\n",
    "# courbe\n",
    "macourbe=[A*cos(2*pi*(x/Lambda) + Phi) for x in PositionX]\n",
    "TEST: print (macourbe)\n",
    "\n",
    "# on rajoute la courbe sur le graphique\n",
    "ax.plot(PositionX,macourbe)\n",
    "\n",
    "# des noms pour les axes\n",
    "ax.set_xlabel('X en m')\n",
    "ax.set_ylabel('Y en m')\n",
    "ax.set_title('Une onde?')\n",
    "\n",
    "# on demande l'affichage\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Expliquer le rôle des lignes 13, 19, 35, 39, 44 ?\n",
    "Ajouter un # au début des lignes 20 et 36 pour que les tableaux ne soient pas affichés.\n",
    "\n",
    "Faire varier un à un les paramètres :\n",
    "NbEchantillons (5,10,100,1000); lambda (0.1,0.5,1.0); A(0.5,1.0,2.0); Phi (-pi,-pi/2,-pi/4,0,pi/4,pi/2,pi)\n",
    "2. Que modifie chacun de ces paramètres ?"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Modifier le programme suivant pour qu'il affiche l'image d'une onde de longueur d'onde 1.0 m, d'amplitude 1.5 m , de période 4.0 s et de déphasage 0 à t = 0 s, à instant donné t choisi.\n",
    "Aide : \n",
    "Comment est modifiée la courbe quand t = 1s , 2s ou 4s ?\n",
    "Quel relation existe-t-il entre le déphasage, le temps et la période ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# on importe des bibliothèques, des fonctions\n",
    "from math import sin,cos, pi\n",
    "# pour pouvoir tracer des courbes, on a besoin de 'pyplot' objet du module 'matplotlib'\n",
    "from matplotlib import pyplot\n",
    "\n",
    "# temps maximal d'affichage\n",
    "# écrire 2.0 avec le point définit un nombre flottant (float)\n",
    "# écrire 2 définit un entier (int)\n",
    "# pour voir la différence essayer de calculer 1/2 et 1/2.0 ou 1/2. avec le point\n",
    "Xmax=2.0\n",
    "\n",
    "# on définit les axes (x,y), auxquels on rajoutera les courbes\n",
    "ax = pyplot.axes(xlim=(0, Xmax), ylim=(-2, 2))\n",
    "\n",
    "# nombre d'échantillons\n",
    "NbEchantillons=100\n",
    "\n",
    "# on définit les instants de calcul de la courbe\n",
    "PositionX=[i*Xmax/NbEchantillons for i in range(NbEchantillons)]\n",
    "#TEST: print temps\n",
    "\n",
    "# date d'observation\n",
    "t=1.0\n",
    "\n",
    "# période de l'onde\n",
    "T=4.0\n",
    "# Amplitude du signal\n",
    "A=1.0\n",
    "\n",
    "# longueur d'onde\n",
    "Lambda=0.5\n",
    "\n",
    "# déphasage\n",
    "Phi = 0\n",
    "\n",
    "# courbe\n",
    "macourbe=[A*cos(2*pi*(x/Lambda) + Phi) for x in PositionX]\n",
    "#TEST: print macourbe\n",
    "\n",
    "# on rajoute la courbe sur le graphique\n",
    "ax.plot(PositionX,macourbe)\n",
    "\n",
    "# des noms pour les axes\n",
    "ax.set_xlabel('X en m')\n",
    "ax.set_ylabel('Y en m')\n",
    "ax.set_title('Une onde?')\n",
    "\n",
    "# on demande l'affichage\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Création d'une animation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# -*- coding: utf-8 -*-\n",
    "# 201707\n",
    "\n",
    "# on importe des bibliothèques, des fonctions\n",
    "from math import sin, cos, pi\n",
    "# pour pouvoir tracer des courbes, on a besoin de 'pyplot' objet du module 'matplotlib'\n",
    "# pour pouvoir créer une animation, on a besoin de matplotlib.animation\n",
    "from matplotlib import pyplot, animation\n",
    "from IPython.display import HTML\n",
    "\n",
    "# échelle max selon l'axe de propagation\n",
    "Xmax=10.0\n",
    "\n",
    "# échelle max selon le temps\n",
    "Tmax=10.0\n",
    "\n",
    "# on définit un nom pour la figure et les axes (x,y), auxquels on rajoutera les courbes\n",
    "fig = pyplot.figure()\n",
    "ax = pyplot.axes(xlim=(0, Xmax), ylim=(-2, 2))\n",
    "\n",
    "# nombre d'échantillons\n",
    "NbEchantillons=100\n",
    "\n",
    "# on définit les positions de calcul de la courbe\n",
    "positionsx=[i*Xmax/NbEchantillons for i in range(NbEchantillons)]\n",
    "\n",
    "temps=[i*Tmax/NbEchantillons for i in range(NbEchantillons)]\n",
    "# on définit les instants de calcul de la courbe\n",
    "#TEST: print temps\n",
    "\n",
    "# période\n",
    "T=2.0\n",
    "\n",
    "# vitesse\n",
    "c=1.0\n",
    "\n",
    "# courbes: une liste qui contient des listes de valeurs\n",
    "mescourbes=[[cos(2*pi*((x/c)-t)/T) for x in positionsx] for t in temps]\n",
    "\n",
    "# la virgule sert à unpacker courbe \n",
    "courbe, =ax.plot(positionsx,mescourbes[0])\n",
    "\n",
    "def incrementemps(i):\n",
    "\tcourbe.set_ydata(mescourbes[i])\n",
    "\treturn courbe,\n",
    "#TEST: print(mescourbes[32])\n",
    "\n",
    "# des noms pour les axes\n",
    "ax.set_xlabel('X en m')\n",
    "ax.set_ylabel('Y en m')\n",
    "ax.set_title('Une onde?')\n",
    "\n",
    "# on crée l'animation\n",
    "anim = animation.FuncAnimation(fig, incrementemps, 100, interval=50, blit=False)\n",
    "\n",
    "pyplot.show()\n",
    "anim.save('anim.gif', writer='pillow')"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Pour observer l'animation aller sur la page home et cliqué sur anim.gif\n",
    "\n",
    "1. Que représente cette animation ?\n",
    "\n",
    "2. Montrer que la formule utiliser pour calculer mescourbes dans le programme précédent est équivalente à celle utilisée pour calculer macourbe dans le programme que vous avez modifié.\n",
    "\n",
    "3. Modifier le programme suivant pour qu'il crée une animation d'une onde d'amplitude 0.5 m, de longueur d'onde 5.0 m et de période 1,0 s "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# -*- coding: utf-8 -*-\n",
    "# 201707\n",
    "\n",
    "# on importe des bibliothèques, des fonctions\n",
    "from math import sin, cos, pi\n",
    "# pour pouvoir tracer des courbes, on a besoin de 'pyplot' objet du module 'matplotlib'\n",
    "# pour pouvoir créer une animation, on a besoin de matplotlib.animation\n",
    "from matplotlib import pyplot, animation\n",
    "from IPython.display import HTML\n",
    "\n",
    "# échelle max selon l'axe de propagation\n",
    "Xmax=10.0\n",
    "\n",
    "# échelle max selon le temps\n",
    "Tmax=10.0\n",
    "\n",
    "# on définit un nom pour la figure et les axes (x,y), auxquels on rajoutera les courbes\n",
    "fig = pyplot.figure()\n",
    "ax = pyplot.axes(xlim=(0, Xmax), ylim=(-2, 2))\n",
    "\n",
    "# nombre d'échantillons\n",
    "NbEchantillons=100\n",
    "\n",
    "# on définit les positions de calcul de la courbe\n",
    "positionsx=[i*Xmax/NbEchantillons for i in range(NbEchantillons)]\n",
    "\n",
    "temps=[i*Tmax/NbEchantillons for i in range(NbEchantillons)]\n",
    "# on définit les instants de calcul de la courbe\n",
    "#TEST: print temps\n",
    "\n",
    "# période\n",
    "T=2.0\n",
    "\n",
    "# vitesse\n",
    "c=1.0\n",
    "\n",
    "# courbes: une liste qui contient des listes de valeurs\n",
    "mescourbes=[[cos(2*pi*((x/c)-t)/T) for x in positionsx] for t in temps]\n",
    "\n",
    "# la virgule sert à unpacker courbe \n",
    "courbe, =ax.plot(positionsx,mescourbes[0])\n",
    "\n",
    "def incrementemps(i):\n",
    "\tcourbe.set_ydata(mescourbes[i])\n",
    "\treturn courbe,\n",
    "#TEST: print(mescourbes[32])\n",
    "\n",
    "# des noms pour les axes\n",
    "ax.set_xlabel('X')\n",
    "ax.set_ylabel('Y')\n",
    "ax.set_title('Une onde?')\n",
    "\n",
    "# on crée l'animation\n",
    "anim = animation.FuncAnimation(fig, incrementemps, 100, interval=50, blit=False)\n",
    "\n",
    "pyplot.show()\n",
    "anim.save('anim.gif', writer='pillow')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}