{
 "metadata": {
  "name": "",
  "signature": "sha256:23e62ea1be7f1a01eefd28e5f518f88236c2dd90be9c7efc1440259ffae4ad47"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pylab import *\n",
      "%matplotlib inline\n",
      "from matplotlib import animation\n",
      "from IPython.html import widgets\n",
      "from IPython.display import display\n",
      "import cmath\n",
      "\n",
      "# nastavitve za izris grafov (http://matplotlib.org/1.3.1/users/customizing.html)\n",
      "rc('text', usetex=True)\n",
      "rc('font', size=12, family='serif', serif=['Computer Modern'])\n",
      "rc('xtick', labelsize='small')\n",
      "rc('ytick', labelsize='small')\n",
      "rc('legend', fontsize='medium')\n",
      "rc('figure', figsize=(5, 3))\n",
      "rc('lines', linewidth=2.0)\n",
      "rc('axes', color_cycle=['k'])\n",
      "rc('contour', negative_linestyle='solid')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Animacije"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Pripravimo animacijo utripanja dveh vzmetnih nihal z masama $m$ in koeficientoma vzmeti $k$, sklopljenih s \u0161ibkej\u0161o vzmetjo s koeficientom $k^\\prime$. Na za\u010detku je raztezek vzmeti prvega nihala A, vzmet drugega pa je neraztegnjena. Obe ute\u017ei na za\u010deku mirujeta. Re\u0161iti moramo sklopljen sistem diferencialnih ena\u010db\n",
      "\n",
      "$$m\\ddot{x_1}=-kx_1+k^\\prime(x_2-x_1),$$\n",
      "\n",
      "$$m\\ddot{x_2}=-kx_2-k^\\prime(x_2-x_1),$$\n",
      "\n",
      "z za\u010detnimi pogoji $x_1(0)=A$, $x_2(0)=0$, $\\dot{x_1}(0)=0$ in $\\dot{x_2}(0)=0$. Re\u0161itev je\n",
      "\n",
      "$$x_1(t)=\\frac{A}{2}\\left(\\cos(\\omega_1 t)+\\cos(\\omega_2 t)\\right),$$\n",
      "\n",
      "$$x_2(t)=\\frac{A}{2}\\left(\\cos(\\omega_1 t)-\\cos(\\omega_2 t)\\right),$$\n",
      "\n",
      "z $\\omega_1=\\sqrt{\\frac{k}{m}}$ in $\\omega_2=\\sqrt{\\frac{k+2k^\\prime}{m}}$. V animaciji <a href=\"http://burana.ijs.si/rovf14/10/utripanje.gif\">utripanje.gif</a> je prikazana ena perioda utripanja za $A=3\\,$cm, $\\omega_1=10\\pi\\,$s$^{-1}$ in $\\omega_2=12\\pi\\,$s$^{-1}$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ((axa), (axb)) = subplots(2, 1, figsize=(6, 3))\n",
      "axa.set_xlim([0, 30])\n",
      "axa.set_ylim([-1, 1])\n",
      "vzmet1,=axa.plot([], [], lw=3)\n",
      "vzmet2,=axa.plot([], [], lw=1)\n",
      "vzmet3,=axa.plot([], [], lw=3)\n",
      "utez1,=axa.plot([], [], 'or', markersize=40)\n",
      "utez2,=axa.plot([], [], 'ob', markersize=40)\n",
      "axa.set_xlabel(r'Polo\\v zaj (cm)')\n",
      "axa.set_yticks([])\n",
      "axa.grid()\n",
      "axb.set_xlim([0, 1])\n",
      "axb.set_ylim([-3, 3])\n",
      "axb.set_xlabel(r'\\v Cas (s)')\n",
      "axb.set_ylabel(r'Odmik (cm)')\n",
      "axb.grid()\n",
      "crta,=axb.plot([], [])\n",
      "\n",
      "A=3.0\n",
      "w1=5.0 * 2 * pi\n",
      "w2=6.0 * 2 * pi\n",
      "x1t=lambda t: 0.5 * A * (cos(w1 * t) + cos(w2 * t))\n",
      "x2t=lambda t: 0.5 * A * (cos(w1 * t) - cos(w2 * t))\n",
      "\n",
      "t=linspace(0, 1, 200)\n",
      "axb.plot(t, x1t(t), 'r', t, x2t(t), 'b')\n",
      "\n",
      "def init():\n",
      "    vzmet1.set_data([], [])\n",
      "    vzmet2.set_data([], [])\n",
      "    vzmet3.set_data([], [])\n",
      "    utez1.set_data([], [])\n",
      "    utez2.set_data([], [])\n",
      "    crta.set_data([], [])\n",
      "\n",
      "nf=200;    \n",
      "def animate(f):    \n",
      "    t=f / float(nf)\n",
      "    x1=x1t(t)\n",
      "    x2=x2t(t)\n",
      "    vzmet1.set_data(linspace(0, 10 + x1, 41), 0.25*10/(10+x1)*sin(arange(41)*pi/2))\n",
      "    vzmet2.set_data(linspace(10 + x1, 20 + x2, 41), 0.25*10/(10+x2-x1)*sin(arange(41)*pi/2))\n",
      "    vzmet3.set_data(linspace(20 + x2, 30, 41), 0.25*10/(10-x2)*sin(arange(41)*pi/2))\n",
      "    utez1.set_data([10 + x1], [0])\n",
      "    utez2.set_data([20 + x2], [0])\n",
      "    crta.set_data([t, t], [-A, A])\n",
      "    fig.tight_layout(pad=0.3)\n",
      "\n",
      "anim=animation.FuncAnimation(fig, animate, init_func=init, frames=nf, interval=25, blit=True)\n",
      "anim.save('utripanje.gif', writer='imagemagick');\n",
      "close()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<img src=\"http://burana.ijs.si/rovf14/10/utripanje.gif\">"
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Interaktivni grafi"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Graf prikazuje odmik du\u0161enega nihala v odvisnosti od \u010dasa. Lastno frekvenco nedu\u0161enega nihala $\\omega_0$ in du\u0161enje $\\beta$ spreminjamo z drsnikoma nad grafom (glej ROVF10.ipynb). "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def narisi_nihanje(omega0, beta):\n",
      "    omega = cmath.sqrt(omega0 ** 2 - beta ** 2)\n",
      "    t = linspace(0, 20, 200)\n",
      "    y = [(exp(-beta * t1) * cmath.cos(omega * t1)).real for t1 in t]\n",
      "    y0 = exp(-beta * t)\n",
      "    \n",
      "    fig, ax = subplots(1, 1, figsize = (7.5, 4.5))\n",
      "    ax.set_xlim([0, 20])\n",
      "    ax.set_ylim([-1.1, 1.1])\n",
      "    ax.set_xlabel(r'\\v Cas (s)')\n",
      "    ax.set_ylabel(r'Odmik (cm)')\n",
      "    ax.grid()\n",
      "    ax.plot(t, y)\n",
      "    if beta <= omega0:\n",
      "        ax.fill_between(t, -y0, y0, alpha = 0.2)    \n",
      "    \n",
      "omega0_slider = widgets.FloatSliderWidget(min = 0, max = 2, step = 0.1, value = 1)\n",
      "beta_slider = widgets.FloatSliderWidget(min = 0, max = 2, step = 0.1, value = 0.1)\n",
      "display(widgets.interactive(narisi_nihanje, omega0 = omega0_slider, beta = beta_slider))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ICfEiMNAbb29v1Gp1BbwjQRDcjSteB3wSWw2Ygp8p/3p8GHAFWAJcBVrd6CDvvfcc1arV\nBsBo9KVBg3BateoEXBv+LMn9Bg3CUavVnDlzhNTUK/j6Btj1enHf8ff/+ut7Pv74f1gsZp5++k3a\nt3+QPXs2l+j1NWrcwUsvTeKLL0Zx6tQhXn65OyNGfIxWqy96/o4d64mNPU3jxk1RKBI4eXIv/v4G\nHnzwfry8vNi82bY6WqdOtucXDgWK++K+uF+570dFRfHjjz8CULt2bezlDD3gu4BuwKdAP8CKrdbr\ni21ouvjM5zexJex/14Id1gMGGDbsPvbs2cyXX66gY8deDjtuZRYbG1WU8OyRkZHK00+3IiHhJA8/\n/BzvvvtDqRbiuHLlEkOH3svZs8fo2rUfH3/8x02Pk5ubTVZWOpKUgUKRRWCgnpAQb7y9vTAYDG65\nEEhUVFTRLxjBOYk2cn6uOAt6b8HProAf15LrhoKfS7ANSffFNgu6XCdiAUUTsUQdWF6SJPH++8+T\nkHCSBg3u4u23vyt18gsIqMIXX/yFweDFxo2LmT//05s+V6fzJCAghMDAevj7NyczsxoHDljZujWB\niIg49u8/zqVLl8jOzi7tWxMEQXCKHrAjOLQHvHnzCl5//RFatLiX2bPF7khyWbv2N9555wmMRh9+\n/nkPoaFhZT5mVNRfvPHGY3h4ePD999E0bXqPXa+3WCxkZ2eQl5eBJGWg0eRTpYoXQUFeGI1GPD3F\nGuKCUFnZ2wMWCfgGUlOT6dYtCK1Wx6ZN6ahUYlJORUtLS6F//4akpFxm/Pg5PPbYEIcde/r0t1iw\n4FNq1WrAwoV70elKv9mD2WwuSsiQgVZrJjjYKBKyIFRCrjgE7XR8fQOpVasBeXm5HD26T+5w3IK9\n1wFPm/YGKSmXadHiPh59dLBDYxk+/APq1GnIP/8cZebMCWU6lkqlwtvbj6CgmgQFNcbTszGXL/uz\nZ08uW7acISJiH/HxJ7h06RJZWVlIkuO+KDpS4cQSwXmJNnI/IgHfRGEdWKwLXfEOHtzFihXz0Gi0\nvPPObIdPetJqdUyc+BNKpZKFC78gPn6nw45dPCEHBjbCYGhCcnIge/fms2XLWSIi4ti37xgXLlwk\nIyNDLAoiCJWYSMA3IRbkcKySzoCWJImvv34bgCeeeI1ateqXSzyNG9/NoEGvI0kSU6eOKLdEqFKp\n8PLyJSioBkFBDfHyakpaWhUOHLASHX2BDRv2Ext7hLNnE0hNTZVthycxu9b5iTZyP6IGfBOnTx+m\nf/9GBAVVY9WqBLe89MQZRUevZuTInnh7+7Fs2Um8vf3K7VxZWRn07duA5OSLTJjwPY8++kK5netm\nJEkiJyeLnJxMrNZMFIosjEYlwcFG/PyMGI1GdDpdhcclCIL9RA3YQWrVaoC3tx9JSRdITDwrdzgu\nryQ1YKvVyjffjAHghRfeKdfkC2AweDFypO1ypG++GUNGRuptXuF4CoUCT08jAQEhBAXdQWBgcxSK\nOzh71khsbCabNp0kImIf+/cf5+LFi6Snp2OxWBweh6gvOj/RRu5HJOCb8PDwKFYHFsPQFSEycinH\nj++nSpUa9O//coWcs0ePQYSHd+Dq1STmz59aIee8Ha1Wh69vIEFBtQkMbIzB0ISrV4PZv9/Ktm2J\nbNx4gO3bD3Hy5D9cuXJF7PYkCC5KJOBbaNKkDQAHDzpukk5ldbsasCRJzJv3IQDPPvs2Wm3FDLsq\nFIqiXvAvv0wjOflihZzXHiqVCqPRh8DA6gQG1sffvzkWS21On/YkNjajqJccF3ec8+cvkJaWhslk\nsuscor7o/EQbuR9nWAvaaV1LwDtkjsT97dixniNH9uDvH8wjj1RsLbZp03vo3Lk3kZFLmTt3EmPG\nfFeh57eXQqFAp/NEp/MEggDbAiGpqVkkJmYBSUAWnp4eBAYa8Pc34OnpicFgKNEGFoIgVAzxabyF\nRo3uBuDIkT2YTPkyR+PablcD/uEHW+930KBRZVoYo7ReemkyHh4eLF06h3PnTlT4+ctKqVRiNHoT\nGFiVwEBbLVmlqs/Fi77s22ciOvoC69fHsW3bQY4dO0NSUhJZWVlFs79FfdH5iTZyPyIB34K3tx81\na9YnPz+P48f3yx2O24qP38mePZswGn3o1+8lWWIIC2vEQw89g8Vi5ocfpsgSg6NpNFp8fPwJDAwl\nKKgBgYF3YbWGce6ckT17ctiy5SwbNsSxc+dhzp9PLErKzrpYiCC4GzEEfRtNmrTh7NljHDy4k0aN\nbrgTolACt6oB//77VwD06fMiRqNPBUX0X4MHj2fVqgWsWrWAIUPepXr1OrLFUl50Ov11IwySJJGX\nl0NISBC7d2cByXh45OLtrSUgwBMfH088PW03MXwtL1EDdj/iE3UbhXXg+HhRBy4PycmJrF//Bx4e\nHrL1fguFhtblgQcGYbFY+PHHj2WNpaIU1pNts65rERTUEH//cCyW2pw9a2TPnly2bk1g/fo4YmIO\ncuTIaRITE0lPT5dt0RBBcBciAd+GSMCOcbMa8LJlczCbTXTs+DDVqtWu0Jhu5IUXxqFQKFixYh6J\niefkDqfCFG+f65NyTYKC7iQw8C4kKYwLF3yIizMTE5PIxo0H2bx5PwcOnCAh4TxXr14Vl0SVI1ED\ndj9iCPo26tVrhkaj5Z9/jpKRkYqXl6/cIbkNs9nEkiUzARg48BWZo7GpXftOuncfyLp1v7Fw4eeM\nHj1N7pCcxrXha/+ivzOZ8klJyeHChWzgKpJ0HpXKhK+vHl9fPT4+nuj1evR6PUqlUrbYBcEZucv6\nig5firK4559vy4ED2/nmm3Xcc0/3cjtPZbNhw2LGjOlPnToN+eOPg06z3OfRo/t48sm78PQ0smpV\ngqx1aVdktVrJy8shNzcbiyUHsN08PZX4+urx89Pj6WlLyjqdzmnaXRDKyt6lKEUPuASaNGnDgQPb\niY/fIRKwA/3111wA+vYd7lS/hBs0COfuu7uwa1cEy5bN5amnRssdkkvx8PBArzeg1xuu+/vC3vLF\nizlIUhqQiEKRh7e3tqC3rCvqLWu1WnmCF4QKJGrAJdC4sViQo6z+XQNOTDzL9u3rUKs19OjxpDxB\n3cKTT74OwK+/Tq8Uk43s3a+5NNRqDUajDwEBIQQG1iEwsFHBhK86XLjgw4EDEjt2XCEq6jjr1+9l\n587DRZO+UlNTycvLK/cYnZmoAbsf0QMugSZNWgO2JSklSXKq3pqrWrHiRyRJolOn3vj6Bsgdzn+0\na/cgtWo14J9/jhIRsYT77x8od0huyTbhS/+fxVesViv5+bmcP5/DP//kIknJKBS5eHiY8PHR4e2t\nK+ox63Q6tFqt+FwKLsdd/seWaw1YkiS6dw8mNTWZ5ctPO8VsXVdmtVp57LG6XLhwxqnr6kuWzOKj\nj4bTqNHd/PTTDvEL3gkUJua8vFxMphwkKReFIheFIh+FIp/z509y7txJUlNTsVqtGI1GwsLCaNiw\nIa1atUKlEn0OofyIGnA5UCgUNG7cmujoVcTH7xAJuIx27YrgwoUzVK1ai9atu8odzk099NDTfPfd\nOxw6tIu4uBjCw9vLHVKl5+HhUWwdbNtM+g0bFrF69UK2b1+HxXLzcoGXlzedO3di8ODB3H///aLX\nLMhOJOASatKkTVECFsOR9ouNjSpaDWvlyvkA9Or1nFOvrqTTedKv30t8//1kFi78wq0TcPH2cQUW\ni4WVK+fz/feTOX/+FGBLzo0ataJ+/XCqVKmBWq0lOzuDhISTHD4cy7lzJ1i+fDnLly+nZs0wnnnm\nJXr06IGPjx5vby2enrahbJ1Oh1qtlvkd/ldUVJRYDcvN2JuA6wBhgC+QCuwC0h0dlDNq3PhaHVgo\nvZycLCIj/wSgZ8+nZI7m9vr3f5n586cSFbWUhISThIbWlTukSu/MmSN88MFg9u+37dNds2Z9nnhi\nJF279sPfP/imr0tIOMWaNQtZsmQmZ8+eYvLkN1m+fCmvvfYZ1auHYbVmoVCkALkolRaMRi0+Pjq8\nvLTodNqiWrMzJmfBNZV0/KUvcDdwBTiFLfn6FvwdwG/APodHV3LlWgMGSEtLoWvXALRaHZs2paNS\niQ9haaxZ8yvjxw+iadN7mDdvm9zhlMj77z/PihU/8vjjr/LGG9PlDqdSW7ZsLlOnjiA/P4/AwKq8\n+upUHnjgCbsW+TCbTSxbNpeZM98lNTUZjUbL//73IYMGvVY0ImOrNeeRn5+LyZSH1ZoL5KFQ5BUl\nZy8v202v16LV2m4ajUYMa1di9taAS/LEvsAe4PQtnlNYyNtY0hM7WLknYIA+fepz9uxxfv55N3fe\n2aLcz+eORo58iOjoVbz11jcMGPCy3OGUyLFjcQwaFI7B4M3q1efx9DTKHVKlYzab+Pzz11i0yLZX\n88MPP8eoUV/g7e1X6mNmZqYxffqbLF06B7DNfJ8y5ZfbrnZXmJxNpjzy8/OQpDzAdlMoTBgM6qIE\nbTBcS8xarVasBubmyiMBl5QPkObA49mjQhLwhAlPs3r1z4wZ853sGwe4mtjYKMLCGvHgg9UAWLPm\nIn5+QTJHVXKDB3cgLi6aceNm0afPMLnDcThnrgHn5ubw9tv9iI5ehVqtYdy4WTz88HMOO/6WLX8z\nceJzpKVdoWbNenzxxXJq176zVMeSJAmTKb8oQVsseUA+hQlaraZYctag119LzhqN5pZzIkQN2PlV\n9Czo2sCZgj/LlXwrTOPGrVm9+mcOHtwpEnAprF//BxaLhQ4dHnKp5AvQr99LxMVFs3jxDHr3HiqG\nGStIdnYmo0c/yq5dEfj6BjJt2t9FG6Q4SseOvViwIJbRox/l+PH9DB7cnunTV5XqPAqFAo1Gi0Zz\n45W8LBYLJlMeiYl5mEz5SFIOtl+dtkSt0ykxGDQYjVqMRg1a7bXkbLVay/Q+Bedj72+Ru4CB2Oq/\nAC25VgeWU4X0gOPjd/Lcc22oU6chixYdKvfzuZvCXuTkyQvp0WOQ3OHYJT8/j549Q0lNTeaHH2Jo\n1qyt3CG5vby8XEaO7ElsbCQBASHMmLGRsLBG5Xa+nJwsxo4dyNatK9HrDXz66dIKv0bdbDYV60Hn\nY+s9F/ag89FoPDAYNEU3T09bci68ieuc5VXeQ9AfA78Xe+1A4G07j1EeKiQB5+fncd993pjNJiIj\nr4pF+u1w6VICDz1UA61Wx7p1lzEYvOQOyW5ffz2Gn376hJ49n+aDD+bLHY5bs1gsjB07kIiIJQQE\nhDBnzmZq1qxX7uc1m01MmjSElSvno9Fo+fLLv2nTplu5n7ekzGYzZnM+JpPtZrXaErQk2erPHh4W\nPD3VeHpeS9JarQa1Wl2UpEUduvyUdwLuyvUTreSs+xZXIQkY4Lnn7iE+fgfffrveqT6Yzu6TT0aw\naNG3dO7ch08/XSJ3OKVy/vxpHnusLiqVmtWrz+PrGyh3SA7jbDXgTz99ld9//xqj0Yc5czZTr16z\nCju31Wpl6tQRLF48A61Wx7RpK7n77i4Vdv6bKUkbFdagC29mc2EP2kRhb1qtBp1OXawXbUvOhUla\nrVaLnnQplXcNOAUYiu1yJAXQDahUxdDGjVsTH7+Dgwd3igRsh927IwHo3n2AzJGUXvXqdWjX7kGi\no1exfPk8nnnmTblDcktLl87h99+/Rq3W8MUXyys0+YJtQY+33voGi8XM0qVzGD36UWbP3sydd95V\noXGUxu1q0GAbXTCbTaSm5pOcbMJszkeSslAoCpO0CaXSil6vRq/XFPSo1eh0tuRcPFGLuRBlY++/\n3kzgZLHXdgPud2hEpVNhPeDVqxcyYcJT3HvvI3zxxV8Vck5Xl5h4ll69aqHV6tmwIek/29S5ki1b\n/mbUqIepXj2MpUuPO/VKXq5o375ohg/vjNlsYuLEH+nV61nZYrFarbz77tOsWfMLAQEh/PjjdqpW\nrSVbPBXJarViNpuKatJmswmrNb8gSV+7aTQeBYnadvP0VBcNeRe/VZZEXd494EVcPwQ9y87Xu7zC\nmZEHD+4QOyOV0IYNiwHbbFNXTr5gu1a0atVanD9/iu3b19GuXQ+5Q3IbKSmXGTOmP2aziSeeeE3W\n5Au2nvC77/5AUtIFdu+O4tVXH+T776PLdO2xq/Dw8LhtTxoKa9ImUlNNJCebsFhMSFIukpROYZJW\nKMxoNB4jZQ8YAAAgAElEQVRotap/Jerrk7RKpap0Q9+lebe1sQ1FK4D+wFxHBuTsQkPr4uPjz5Ur\nl0hMPFtpvhGXRUSErebbrVt/mSMpO6VSSZ8+L/Ltt+NYtOg7t0nActeArVYrEyc+S3LyRVq0uJeR\nIz+VLZbiNBotn322lMGDO3Dq1EHeeKM333yz9raJqTzI3UY3ci1p6m/5vMJh74wME1ev2nrWkmQC\nsrElajO2ZG1Br1cXJWudTo1er0KjuZak3SlZ2/sOZmFbirJQGJUsARfujBQTs4aDB3eKBHwbycmJ\nHDiwDZVKTbt2D8odjkM8+uhgZs16j+jolSQmniMkpIbcIbm8n3/+nJiYNfj4BDB58i9O9cvVy8uX\nr75axfPPt2XPnk28//7zTJ68UIx+2UGpVKJUKtFqdbd8niRJWCxmTCYTOTmmoh627TKsLIona7Cg\n06mKkrVWqyqYUGZLztnZ2Zw9e5aUlBTS0tJQKBR4eHjg5+dHUFAQdevWxc9P3tEMe/+XDwc2FLtf\nKddjbNy4DTExa4iP3+EWvbrytHnzciRJom3bB9xmCUd//2A6d+7D+vW/89dfc3nxxfflDqnM5OxZ\nHT26j+++eweA99//ieDg6rLFcjMhITWZNm0lQ4d2ZO3aX6lXrxnPPTemQmNwtt5veVAoFKhU6hKt\ntV+YrM1mM6mpJs6ePcaOHeuJi9vKkSN7SU6+eNtjBAYGER7enLZt29KlSxdatmxZoT1se89wBdtE\nrOHYLkGqmJlPTqawDhwfv0PmSJxfVNQyAO677zGZI3Gsvn2Hs3797yxbNpfBgyc4VY/NleTn5/He\ne89gNpvo3/9lOnR4SO6QbqpBg3AmT/6F119/hG+/HUeDBnfRtu0DcodVaSkUCjIz0/n77x9ZvXoh\nR4/uve5xrVZHzZr1CQgIwdvbHw8PJRaLibS0K1y5cpnz50+SnJzEhg0b2LBhA5MmTSIwMIQOHbrR\nvXsv6tath0ajRKtVFfW0NRoVer0KlUpZlKSL3+xVmt8anxT8TAP8S/F6l1e4NeHhw7sxm01iZ6Sb\nyMxMZ9eujXh4eODj417/VVq2vI9atRrwzz9H2br1bzp1cu0vGHLVF2fPnsiJEweoUeMOXn31k9u/\nQGb33vswQ4e+x5w57/POO08wf34soaFhFXJuZ6wByyUh4STz5n3EmjULycvLBcBg8KJ9+4do3bor\n4eEdqVHjjlsuOmK1Wrlw4Qz798ewd+9mtm5dSVLSBZYt+5lly36mYcOWPPnkaO699xGysiTS081Y\nLBYsFjOSZMY2LG4GbPfV6jy734e9CdgfKP4149bbhrgpX98AatS4g3PnTnDixAGxM9JNbNu2BpMp\nn7vu6oiXl3vNHFUoFPTuPYxp00bz55+zXD4By+HIkT3Mnz8VDw8PJk78yWVmyA8d+i5Hjuxmy5a/\nefPN3vzwQ4zLxO7qLl8+z4wZE1i1aj4WiwWAtm0foE+fF2nX7sHb1piL8/DwIDQ0jNDQMHr2fAqr\n1cqhQ7GsWrWAtWt/4fDh3YwfP4gaNe7g6affpFevZ285+S45+bDd78feixjrYluOsm/Bz4r56ueE\nmjS5BxDD0LdSfPjZHb+5F34gt21by/nzt9qt0/lVdPtYLBY+/PBFrFYrAwe+SvPm7Sr0/GXh4eHB\npEk/U7NmfY4f38/kyUORpPKvxrnjZ6ik8vPzmDt3Mn361GfFinmAbUvKJUuO8vXXa+jcubddyfdG\nPDw8aNKkNW+99TWrVp1n7NiZVK8exrlzJ/jwwxd55JE6/PXXDw7dFMPeBDwbiMW2AcMuwDmuFZCB\nqAPfmsmUz9atKwHo1OlRmaMpH76+AXTt2h9Jkli2bI7c4biURYu+49ChWKpUCeWllybJHY7djEYf\nPvtsKZ6eRtau/ZXffvtK7pDc1r590QwaFM7MmRPIzc2mc+c+LF58hPfem0etWvXL5ZxarY6+fV9k\nyZKjfPjhb9SvH05y8kUmTRrM00+3Ys+ezQ45T2mW8VkMjAFcc0FfBxEJ+NZiYyPJykrnjjuaEhpa\nl9jYKLlDKhd9+74IwPLlPxRcLuGaKrJ9bMOItlnPb775tcvOjg8La8R77/0IwLRpb7B//7ZyPZ+7\nfoZuxmw28+234xg6tCNnzhyhVq0GzJwZwaefLqFGjTsqJAaVSsX99w9k4cI9TJ78C1Wq1ODo0b0M\nG3Yfb73Vj8TEs2U6fkkScNcSHqukz3ML9es3R6PRcubMETIyUuUOx+kUDj+7e220efP2hIU15sqV\nS0RFiaVJS+Lzz18jKyuD++571OX/f3Tt2pdBg0ZhsZgZO3YAV68myR2SW0hMPMuwYfcxb95HKBQK\nnn9+HL/8so9WrTrLEo9CoaBHjydYsuQIw4d/gE7nSUTEEgYMaMwff3xb6mHpkiTg08CbwI22A/HB\nVg8eyvVLVLo9tVpDgwa2xdkPHtwpczTOxWq1smmTLRkV/oJ11/qVQqGgTx9bL/jPP2fKHE3pVVT7\nbN26io0bF6PXG3jzza8r5Jzl7dVXP6FZs3ZcupTA+PFPFk0OcjR3/Qz926ZNyxk0KJz9+2MIDq7O\nzJmRvPzylDLXeB1Bp/NkyJAJ/PnnMbp06Ut2diZTp45g6NB7OXfu1O0P8C8lScCnsNV6PbBdAzwT\n+KPg59iCxytlAUxMxLqxQ4d2kZx8kZCQmkVfUtzZQw89jVarZ+fOjZw7d0LucJxWbm42U6e+DMCL\nL37gNiuIqVRqPv74D/z8gtixYz1z534gd0guyWq18vXXYxg9+lHS06/SocND/PLLPlq0uFfu0P4j\nOLg6U6cuZupU237VcXHR/O9/ve0+jj014A3YFuAYDgwo+DmG6y9LqlREHfjGIiOXArbeb+Fyfe5c\nv/Ly8uX++x8H4M8/Z8scTelURPssWPAZFy6coX79cB5//NVyP19FCg6uzpQpv6JQKJg7dxIxMWsc\nfg53/gzl5GTx9tv9+OmnT1Aqlbz22md88cVyp99zu0uXPixadIhHHx2MyWT/HBCxl1oZFE/AFXEZ\ngqv49/BzZVA4GWvFinnk59t/Qb67S06+yPz5UwF4443pbrlyWOvWXXnxxQ+QJIkJE54s8wSdyiIp\n6QLDht1HZORSjEYfvvpqDU89Ndpltvr09vZjwoS5fPTR93a/1jXeoZOqVq02fn5BpKYmc/68/eP/\n7igh4SRnzhzBaPQhPLxD0d+7e/2qcePW1K/fnNTUZCIi/pQ7HLuVd/vMnPkuOTlZdOr0mFMOKTrK\nCy+Mo337nqSlpfD22/0d+mXMHT9DR4/u49lnW3P48G6qVw9j3rxttGnTTe6wSuWuu9ra/RpnScBD\nsc2iHlrKx2WhUCjEMPS/FF7727btA5VqiU7bZKzhAPz5Z6XbJvuWTpw4wPLlP6BUqnjlFedfbrIs\nPDw8+OCDBVStWouDB3fy5Zej5Q7Jae3du4Vhw+7j8uXzhId34KefdlCnTkO5w6pQzpCAW2Bb0nIj\ntn2G+9r5uKzERKzrFSbg9u2vX1TfnetXhXr0GIReb2DPnk2cOXNE7nDsUp7tM336m1itVvr1e6nc\nFk5wJj4+/nz88SLUag2LFn3LmjW/OuS47vQZio5ezYgR95OVlU63bv357rsNTl/vLQ/2JuB/X4r0\nhgNi6Mq1PYZPAd3tfFxWogd8TXZ2Jrt3R6FQKGjf3j32/rWH0ehNjx6DAFiyRPSCAbZtW8u2bWsx\nGn0YOvRducOpMI0b383o0dMAmDJlKKdOHZI5Iuexbt3vvP76I+Tl5fLYY0OYMuXXW66x7M7sTcBT\ni/35zX/dL626QOFKFjfaYel2j8uqceO7USgUHD26t9JPvtm5cyMmUz6NG7fGzy/ousfcsX51I4XX\nBK9c+RO5uTkyR1Ny5dE+FouF6dPfBOCFF96pdD2cvn2H06PHoKIZvtnZmWU6njt8hpYuncM77zyB\nxWLm6aff4J13Zt9yxyJ3Z28CHoNtCHgdtqToXlvclILR6EPt2ndiMuVz7Ng+ucORVXS0bfjZmfd0\nLW8NG7akUaNWpKdfZePGxXKHI6sVK37kxIkDVK1ai4EDX5E7nAqnUCgYN24WYWGNOH36MFOmDKvU\nV0vMn/9p0b/B//43hVdfnVp0mWJlZe+1ABuwrX4FtrWg+wBlnfJ5kmvbGvpiq/Pa8zgA7733HNWq\n1QbAaPSlQYPwom+MhbWT8rofElKT06cPEx+/gyZN2pT7+ZzzvkR09CoA/P2rXLd3aWxsFEeP7uPJ\nJ19zonjL736LFp04dCiWJUtm8tBDT8seT0nuO7p98vJymDFjPAA9ez7DgQPbner9VtR9T08jzzzz\nFh9+OJy1a38tWrq0NMcr/Dtnen8lux/JsmXfs2bNQgAef/xVmjVr9581Apwn3pLfj42NYsWKHwHw\n9bV/S8qSfP04wbUh4EKFSbAVZR8Svgvohm21rX6AFVtS9y04780eL06KjZXvm+WSJbP46CPbcNPk\nyQtli0NOtl/gdxEYWJXVq8//55ttZdpMPDs7kwcfrE5WVjq//XaAO+5oIndIt+Xo9pk1ayJz5rxP\n48at+fHH7ZW+p7N27W+8884TqFRq5s7dSpMmre0+hit+hiRJ4osvRvHrr9NRKpW8996P9Oz5lNxh\nlYvk5MP06NEISpZXgZINQQ/HlmiL3+4vuDliA4bClbS6YhvSLkyuG27zuNMQE7GKz37uecNftq72\ni6MsPD2NRb9kXOWSJEe2T1LSBRYssO1UOmrU55U++QI88MDjDBgwArPZxJgx/UlNvWL3MVztM2S1\nWvnoo5f49dfpqFRqPvlksdsm39IqSQLeUOzP3sVuPkBLB8XxKbbLjIqvKd3qNo87jbp1m6DTeZKQ\ncLLS7oYi6r/XuzYZaz45OVkyR1OxZsy4tm9r8cVYKrtRoz6nSZM2JCae5d13n3Loxu7OxmKxMGnS\nYP78cxZarY7PP/+rUq2MV1IlScCFq8v3A/Zg2w94MbAI26SsSk+lUtGwoe27SGXcGSk1NZkDB7aj\nUqlp3frGq9i40zWMJVGvXjOaNWtLVlY669b9Lnc4t+Wo9jl2LI4VK+YVLLrxsUOO6S7Uag0ff/wH\nPj4BxMSs4Ycfptj1elf5DJnNJiZMeIoVK35Ep/Nk2rSVlfKyxJIoSQIu3Pl4N9cPP9+PbVMGgco9\nDB0TswZJkmjR4j4MBi+5w3Ea17YpdI1h6LKSJIlp095AkiQGDHiZmjXryR2S0wkJqcnkyQtRKBTM\nmvUe27evlzskh8rPz2Ps2IGsW/cbBoMX33yzlrvvvtFOtgLYdxnSaW4+GavSq8wrYhXWf281/Oxq\n9StH6NZtAF5evhw8uJMjR5x70zBHtE9MzBp27tyAl5cvgwdPKHtQbqpt2wcYMuRdJEninXeeKPEW\nls7+GcrNzeHNN/sQGbkULy9fvv12gyhB3Ia91wHfBXzMtX2BFzk8IhdVvAfszrWdfzObzWzbZtt6\nTdR/r6fT6enV61kA/vjjG5mjKV9ms5np020L4w0ePB5f3wCZI3JuQ4ZMoF27B0lLu8Irr/Rw+bkj\nOTlZjBrVi+joVfj4BDBjRkSpZnpXNvYm4IHA78AsYDYQ4fCIXFSVKqEEBVUjMzONs2ePyR1OhTlw\nYBsZGanUrFnvlkOOrlK/crQBA0agUChYs2YhKSmX5Q7npsraPsuX/8CpU4eoXr0OAwaMcExQbkyp\nVPLRR7/ToMFdJCSc5LXXepGbm33L1zjrZygzM51XXunBrl0RBARUYfbsTdx5511yh+US7E3A67Fd\nFrQX24SsDx0ekQurjHXga8PPvWSOxDnVqHEHHTs+TH5+HosXz5A7nHKRlZXBrFm2dZ5HjPi40q7r\nay+DwYvp01cW7Zw0btwTWCwWucOyy5Url3jxxU7s27eVKlVCmT17M3XrNpY7LJdhbwJOwbYlYB9s\nS1KKaY7FNG5cmRPwrYefnb1+VZ4GDRoFwOLF35GXlytzNDdWlvaZP38qV65comnTe+jWrb/jgqoE\nAgOr8tVXq/H29mPz5uV89tmrN12u0tk+Q+fOneCFF9px9OheatS4g9mzN1eK3a4cyd4E/CK2Farq\nFrsJBZo2rVwTsRITz3LyZDwGgxd33dVR7nCcVsuW91G/fjgpKZdZu9YxW9M5i0uXEvj5588BeO01\nsehGadSp05DPP/8LjUbLokXf8d13451+zejDh3fzwgvtOH/+FA0btuT776OpXr2O3GG5HHsT8CJs\ni2J8im0nJPF1t5iGDVuiVCo5fjyuzDufuILC3m/r1t1RqzW3fK6z1q8qgkKhKOoF//LLl075y7W0\n7TNjxnjy8nLo2rUfzZu3c2xQlchdd3VkypRfUSqVzJv3IXPmfPCf5zjLZ2jbtrW8+GInrl5N4p57\n7mfWrCj8/YPlDssl2ZuAAWpzbSUskYCL8fQ0Ur9+OBaLpVIsyFHS4WcB7r9/IAEBIZw4cYDY2Ei5\nw3GII0f2snLlfFQqtVh0wwE6d+7NBx/8jIeHB7NnT3S6nrAkSSxY8BkjR/YsWO/8Sb78cgWenka5\nQ3NZ9ibgwtnPYiWsm2jevD0A+/ZtlTmS8pWbm8OuXbZJ8O3b97zt852tflXRNBot/fv/D7D1gp2N\nve0jSRLTpxcuujGC0FBRjXKEBx54nPffn49SqeSHH6YwdeorRZc1yvkZys3NZsKEp5g+/U2sVitD\nhkzg/ffn33bkqzKQJAmz2VSqL0v2bkc4nOvXhm5h9xndXHh4B3777Svi4qLlDqVcxcZGkpeXQ8OG\nLQkMDJE7HJfQt+9wfvhhClu2/M0//xxz6QkrmzYtZ9euCLy9/Rg8eLzc4biVBx98Er3ewNixA1m0\n6FuuXEnkgw/mo9N5yhJPYuJZRo9+jKNH96LXG3j//fl06dJHlljKmyRJWCxmzGYzFsv1NzAjSbaf\nCoUFKPyzFa1WRWCgvem0dPsBF3fS7jO6ucIe8IED27BYLCiVSpkjKh/2br7gilupOZqfXxA9ez7N\nsmVz+eWXLxk71nkuS7KnffLz85g2bTQAw4a9j49PWXckFf6tU6fH+Oqr1bzxRm8iIpZw8eIZnnnm\nbbp3r9iqX2TkUiZPHkJaWgrVq4fx+ed/ucT2moWsVmtRAjWbTUWJtTCR2m4m/p1MtVoVnp4qdDrb\nn3U6FSqVFpXKgEqlQqVSoVQqi36WVkkS8F3cfM/fYdgW5xAKBAVVo3r1Opw/f5oTJw7QoEG43CE5\nnCRJxbYfFPVfewwaNIply+ayYsU8hg59l8DAqnKHZLc//viGhIST1K59J/36DZc7HLd1991dmDdv\nG6NG9eLw4d1MnjwEvd5Ahw63L/mUVUZGKtOmvcFff30PQLt2DzJp0s9O8WXLbLYl08KkarGYsVqv\nJdHChCpJJlQqChKoGm/va8lUo1GhVuuKkmnxpFqRSpKAP8G26AZAGHCq4M++2PbnFf6lWbP2nD9/\nmn37trplAj516hAXL/6Dv38wjRq1uv0LEDXgQmFhjejcuTeRkUtZuPBLRo6cKndIQMnb5+rVpKIZ\nuqNGfYFKpS7HqISwsEb89NNOxo9/ku3b1/Haaw/Rv//LjBjxUblsfCJJEhs3LuGzz14lOfkiGo2W\nV1+dysCBr5TrJWaFSbV4YpWkwqRqongvVaNRoterMRjU6HQq9Ho1Wq2th6pWq4uSqVqtxsOjNPOM\nK05JEvBwriXdrtj25S0k1hu7gfDwDqxe/TNxcdEMHOh+y/IV9n7btXvQ6f+DO6Pnnx9HZORSliyZ\nwXPPjXGKXkVJzZgxgaysdNq1e1BsMVdBfH0D+eqr1cyfP5UZM8azaNG3bN78F6NGfUHXrv0clhjj\n43cyffob7N27BYBmzdoxfvwcwsIalep4hZOTTKb8ouRqtRZPqNcSa2HP1GhUo9Op0etVaLVq1GrP\nomRamFzdSUnezalbPOY6vzkqUGEdOC7OPWdC21v/BVEDLq5Ro1bcc8/9bN++jt9//5phw96TO6QS\ntc/x4/tZtmwOSqWSUaM+r5jABAA8PDxo0uQe5s+PZcqUoRw6FMuYMQNo2LAlQ4a8S4cOD5Vq+FSS\nJHbtimD+/Kls374OsCX84cMn0afPsBt+wS5MrMWTq20I2HaTpHzAhEolFfVU9frCxKpGpTIUJdTC\npFpZF3Cx9+tEXWwzn08BdwNXuL5HLGAbNvLy8uXSpQQSE88SElJT7pAcJj39KnFx0SiVKu655365\nw3FZzz8/ju3b1/HLL1/y+OOv4u3t3NUcSZL48svXsVqtDBz4CnXqNJQ7pEqpQYNw5s3bztKls5k7\ndxKHD+9m9OhHqVq1Fr16PUvHjg9z550tbjkyZTabOXJkN9HRq1i16mfOn7f1sfR6A/36/Y8nn3wd\nnU5PenoKZrMJsCVUScpHoTDh4WFFr1fj6WlLqIXJVaPRX5dY3XUCqiOV5mtHt4LbLmCJY8MpNSk2\n1nkuWAd47bVebN26ksmTF9KjxyC5w3GYdet+Z9y4x2nZshOzZrnHghJyGT68C7GxkQwePJ6XXpok\ndzi3VNju3t5+LF16wqWGzd1Vbm42S5bMYtGib0lIuHZBire3H/XqNadWrQb4+Pij1erJyckiJeUy\nZ84c4dSpeLKyMoqeHxhYhQcf7Mcjj/QjIMCvoNeqKfpZmFA1Go1bDgM7UkFPvsR51Z5/yTrYer8S\ntr2Az9gTWGXTvHl7tm5dSVxctFsl4C1b/gagY0ex+1FZDR8+iSFDOvDrr9N44omR+PoGyh3SDWVk\npPL55yMBeOWVT0TydRI6nSdPPjmKJ54YyY4d69m4cQnR0atISjrP7t1R7N4dddPX1qxZi3vv7Ujv\n3r3p0qULer3eJSYtuZuSJuCPgX7Yhp79sc2GngWMLae4XF54eAfAvVbEslgsxMSsAuzfflDUgP8r\nPLw97dr1ICZmDT/9NFXWGdG3ap9vvhnLlSuXaN68PY8+OrhiAxMA27Dxzp3radLkHkym/II6az6S\nlAfkc+edwbRoMZKJE98kIyOFM2eOc+HCBTIzM8nLy8PHxwc/Pz/q169Pw4YNqVatmtxvSaBkCbgv\ntuHmfy87OQwYAsx1dFDuoGHDVqhUak6cOEBGRipeXr5yh1RmBw5sIy0thRo17nDpVZycyfDhk4iJ\nWcMff3zNwIGvEBJSQ+6QrrN//zaWLJmJUqli3LhZoodUTgonNOXn52E252O15qFQ2JIs5KPVKtFo\nkggJuYrBoEGn06LReKHRaNBqtf+pt3bo0EaW9yHYpyQJOJUbT7SajS05Czeg0+lp1KgV+/dv48CB\n7bRr10PukMrs2vDzw3bPWhS93xtr1KgV3bsPYP36P/j223FMmrRAljhu1D5ms4kpU4YB8Mwzb4mN\n1svAYrFgMuWRn59X0IO19VzB9lOnU2IwaAgM1GI0atDpDGg0fmg0GjQaDR4eHnTq1EzmdyE4WkkS\ncMotHkt1VCDuqHnz9uzfv419+7a6WQIW9V9HGjHiY6KilrF69c888cTIEi9uUt5+/vkLTp6Mp3r1\nMLHecwkU9mBNpjzM5jwgD0my9WTVagmjUYufny3B6vV6NBoftFptUYIVKp+SJOAwYO9NHnP9cdVy\n1Lx5BxYs+MwtNmY4f/40p04dxGDwLqpv20PUgG+uevU6PP74SBYs+JQvv3yd2bM3Vfh1kf9un4SE\nk8yZ8z4AY8fOQKfTV2g8zkiSpKIEm5+fh9VqS7JgS7J6vQovLy1eXlqMRi1arV9RgnXEzOGoqCg6\ndepU5uMIzqMk/yvSgDeAz/71929y60U6Kr3CDcrj43dgNptcetm+wtWv2rZ9QGxBVg5eeGEcK1bM\nY+/eLaxcuYBevZ6RLRaLxcJ77z1LXl4ODzzwRKW63rt4ks3Lyy0YKs5DknJRKs0YDBr8/W1J1tNT\ni1brjVarRavVVtrFJITSK0kC3oCtF5zCteHoMOBFnOc6YKfk5xdErVoN+Oefoxw6FEuzZm3lDqnU\ntm61DT/bO/u5kOj93pqXly+vvfY5Eyc+y7Rpo+nQ4SF8fQMq7PzF22fBgk+Ji4smMLAqb731TYXF\nUJFMpnzy8nILhotzUSjygFwUChNGoy3Jenvr8PTUo9X6FiVZOYner/sp6bjIbOAPoLA4FYuo/5ZI\ny5ad+Oefo+zZs8llE3B2diaxsZEoFAqx/m85euihp1mxYh67d0fx9ddvM2FCxV9gcOTIXmbOfBeA\n996b59LX/FqtVvLzcwsSbS6QiyTZkq2npwofHx3e3lqMRh1arTc6nQ6NRiN6skKFsafyn4qtN7wB\nkXxLrGXLToBtA3tXtXPnBkymfJo2vQc/v6BSHSM2NsqxQbkhhULB2LEzUKnU/PXX90Vr81aE2Ngo\nMjPTGDOmP2azif79/0fbtg9U2PnLwmw2kZWVwdWrSSQnnyM5+TjJyQdIS4tDrf6HatXSaNZMQevW\nftx7b226d29Ox45NCQ+vR1hYTYKDg/Hx8XH6YeSoqCi5QxAcTKwpVs5atrwPsC3I4ap14OKXHwnl\nq3btOxk2bCLfffcOEyc+x2+/HaigoWiJ999/gYSEk9SvH85rrznfZgu2YeOcgtpsLpKUg0KRi07n\ngbe3Dh8fHUajDp3Op6g3KwjOzHm/7tnH6daCLq5fv4acOXOEH36IcblhaKvVyoMPVuPKlUv89tt+\n7rijqdwhuT2LxcKwYfcRFxdNly59+eSTReXeM5s//1O++uotDAZvFi7cQ2ho3XI9360UJtr8/Fws\nFluShVw8PZV4e+vw89Pj6alDp9Oh1+vFov+C0yjPtaCFUmrZshNnzhwhNjbS5RLw4cO7uXLlEiEh\nNalbt4nc4VQKSqWSDz5YwKBBzYmIWMJvv33FE0+MLLfzRUYu5euv3wZg4sQfKyz5ms3mgh5tDlZr\nTlGP1tNTiZ+fDl9fPQaDFzpdEDqdTiRawe2Iq78rQGEd+FaLozurzZuXA7a9f8vSCxM1YPtUr16H\n8QvSpFcAABg1SURBVONtk7CmTRvNjh0byuU8hw7FMn78k0iSxIgRH9G5c2+Hn8NqtZKbm01q6hWS\nkxNISjpGUlIc2dkH8fK6SL16ebRsaaBDh1C6dWtKx45NadasHjVrhhIQEIDBYBDJF1EDdkeiB1wB\nChNwXFw0JlO+S11HGxm5FIBOnR6TOZLKp3v3ARw7Fse8eR8yduwA5s7dSlhYI4cd/+jRfYwYcT95\neTm0bduDZ599u8zHLBw+zs3NLujR5uDhkY+Pj46gID0+Pnr0+pCi3XcEoTITNeAK0r9/I06fPszc\nuVtKtZKUHP755xh9+zbAy8uXdesuudQXB3dhtVoZPfoxtmxZQUBACLNnb3LIRhjHj+9n+PAupKVd\n4d57H+GTTxbZ1b6SJJGXl0tubjYmUzYKRQ6Qg06nwN/fs6BOq8fT09PpZxcLgqOIGrCTatWqC6dP\nH2bHjg0uk4ALe78dOvQSyVcmHh4efPTR74wa1YtduyIYPrwz33yzrkwbI8TErGHs2AFkZWXQocND\nfPzxH7ds38Ih5NzcbKzWHCAbhSIXb28toaF6fH098fT0Ra/Xi83aBcEOogZcQdq06Q7Ajh3rZY6k\n5KKibAm4S5c+ZT6WqAGXnk6n54svltOixb0kJV3g+efvISrqL7uPY7FYWLDgM1577SGysjLo1q0/\nn3yyGI1GW9Q+FouFrKwMUlIukZR0mqSkg6SmxqHXJ1C3bi4tWxro2LEW3buHc889jWjQoA5VqlTB\ny8tLJN9yJmrA7kd8YipIq1adUCqVHDy4g8zMNIxGH7lDuqXLl88TH78DrVbvMgsyuDO93sBXX63m\n/fdfYP3633njjcfo23c4//vflBKtVnX69GEmTRrC/v0xAAwZMoHBgyeQn59LVlYaaWkXSEqKR602\n4+enp1YtA0ajNwZDVXQ6XXm/PUGolNylMOP0NWCAF15oz/79MXz22TI6dXpU7nBu6Y8/vmXq1BF0\n6vQYn322VO5whAKSJPHTT58wY8Z4LBYLPj4B9O//P3r1eo7Q0LDrnms2m9i/fxu///41ERFLkCQJ\nf/8qvPLKZNq2bYtKZcLPT09goAGj0RNPT0+RbAWhDEQN2Im1adOd/ftj2LFjvdMn4MjIPwHo3Lns\nw8+C4ygUCp57bgwdOz7Mp5++QmxsJHPnTmLu3ElUrVqLOnUaolSqSU9P4dixfeTkZAGgUql49NG+\nTJjwDqGh1TAYDCLZCoLMRA+4Au3bF82QIR2oWbM+f/55VO5wbio19QoPPFAFULB+/WW8vf3KfEyx\nH7DjSZLE7t1RLFs2l8jIpeTl5fznOfXq1ePhhx/m9ddfp3r16jc9lthr1vmJNnJ+ogfsxJo0aY3B\n4MXZs8dITDxLSEhNuUO6oa1b/8ZisdCmTXeHJF/BcSRJIjc3m5ycTCyWLGrXDmTMmLf56KMJZGQk\ncf78ebRaLT4+PtSvX5/Q0FC5QxYE4SZEAq5AKpWali07s3nzcrZtW0vv3kPlDumGIiIKh58dtyqS\n6P2WjtlsIjs7k/z8LCQpEw+PHPz99YSGGvD29sVoDC226cCdpT6P6Fk5P9FG7kck4ArWrt2DbN68\nnOjoVU6ZgLOzM9mxw7YN3n33OXed2h3ZerdZmM2ZQCZ6vURwsIGAAANGYyienp54eIirBwXBHYgE\nXME6dOgJ2K4Hzs/PQ6PRyhzR9WJi1pCXl0uzZm0JCqrmsOOKGvB/Wa1WcnKyyMnJRJIyUSiy8PHR\nEBZmxMfHG6OxGlptxfz/EPVF5yfayP2IBFzBQkJq8v/27j44qvre4/ibhGxIssluQrJ5MpBNeJIE\niIAaLxECAb1Wih1Be+9Mb2mdArX31rlzW2zvQ6tjp2jLtNPO2FGLd0wfplJusXgvpeKFa+rDva12\nKvJQpIICokI2D7t52GySTc794+ySEEhIZB/Obj6vGebsOXsevvqD893f+Z5zfrNmLeDkySP86U8v\nU1u7Jt4hXSJ893N9feRfyj/ZDQwM0NPTRSDQefFycn5+Jm63nZwcF3a7XYMOiEwiSsBxUFd3JydP\nHuG1135jqQTc09PN735nvmFp1ar1Ed33ZOz9BoNB/P5O+vq6MIxO0tL6KCjIwuXKxm6/jqysLMu8\nI1k9K+tTGyUfJeA4qKu7k8bGx3j11d/wla/8IN7hXPTKK3sJBPxUV9982Usd5OqGbpjqxDA6SU8P\n4nLZyc+3k51dTmZmZrxDFBELUQKOg+rqWnJycnn//ZOcOfOXiIxuEwkvvrgTgNtv/9uI7zsZa8Dh\nHm5vbydgJtzCQjv5+dlkZxeQkZER7xDHTfVF61MbJR+rJOBNwLtABbDjCt8/BWwB1gMHAF/sQou8\nqVOncsstf83+/c/yyit7mTnzn+IdEp2dXl57bR9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LJw1r0wnDmjZj/rsJW4w5AtlBzCE/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\neQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1047cb590>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Naloga"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Dvostopenjska raketa na za\u010detku miruje v brezte\u017enem prostoru. Prva stopnja tehta 30 ton, druga pa 10 ton. V vsaki od stopenj odpade 3/4 mase na gorivo. Motorji vsake od stopenj porabijo 100 kg goriva na sekundo. Hitrost izpu\u0161nih plinov glede na raketo je 3 km/s. Napravi animacijo gibanja rakete od trenutka, ko se vklopijo motorji prve stopnje, do trenutka, ko zmanjka goriva v drugi stopnji rakete. Prika\u017ei tudi, kako se s \u010dasom spreminjata hitrost in pospe\u0161ek rakete. Animacijo pripravi v formatu \"animated GIF\". Velikost oddane datoteke naj bo najve\u010d $5\\,$MB, uporabi\u0161 lahko program za stiskanje datotek v format RAR.  "
     ]
    }
   ],
   "metadata": {}
  }
 ]
}