{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "(motion_in_2d)=\n", "# Motion in 2D" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": false, "tags": [ "remove-output" ] }, "outputs": [], "source": [ "import numpy as np\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "from matplotlib import animation, rc\n", "from IPython.display import HTML" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Newton's laws in two dimensions\n", "\n", "Both force and position are vectors, so Newton's second law becomes:\n", "\n", "\\\\[F=m\\frac{d^2\\vec{r}}{dt^2}\\\\]\n", "\n", "where \\\\(\\vec{r}\\\\) is the position vector \\\\(r=x(t)\\vec{i}+y(t)\\vec{j}\\\\), with unit vectors \\\\(\\vec{i}\\\\) and \\\\(\\vec{j}\\\\) in \\\\(x\\\\) and \\\\(y\\\\) directions respectively.\n", "\n", "Thus, this equation represents two individual equations, one for each Cartesian direction:\n", "\n", "\\\\[F_x=m\\frac{d^2x}{dt^2}\\\\]\n", "\n", "\\\\[F_y=m\\frac{d^2x}{dt^2}\\\\]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tutorial Problem 2.1\n", "\n", "A cricket ball is hit at an angle \\\\(\\alpha=53.1˚\\\\) to the horizontal, at a speed of \\\\(37m/s\\\\). Find:\n", "\n", "1. The maximum height that the ball will reach\n", "2. The total time that the ball travels before it hits the ground\n", "3. How far the ball will travel horizontally before it hits the ground" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": false }, "outputs": [], "source": [ "def total_time(a, v0, g=9.81): # obtain total time of flight\n", " a = a * 2 * np.pi / 360 # convert degrees to radians\n", " \n", " # vertical component: -v0sin(a) = v0sin(a) - gt\n", " # rearrange for t\n", " return 2 * v0 * np.sin(a) / g\n", "\n", "def get_xy(a, v0, start, end, interval):\n", " a = a * 2 * np.pi / 360\n", " t = np.arange(start, end, interval)\n", " \n", " # horizontal component: x(t) = vcos(angle)*t\n", " x = v0 * np.cos(a) * t\n", " \n", " # vertical component: y(t) = vsin(angle)*t - 1/2 gt**2\n", " y = v0 * np.sin(a) * t - 0.5 * 9.81 * t**2 \n", " return x, y" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total time the ball travels before hitting the ground = 6.03s\n", "Maximum height that the ball will reach is 44.62m\n", "The ball travels horizontally 133.96m before hitting the ground\n" ] } ], "source": [ "end_1 = total_time(53.1, 37)\n", "\n", "print(\"Total time the ball travels before hitting the ground = %.2fs\" % (end_1))\n", "\n", "X1, Y1 = get_xy(53.1, 37, 0, end_1, 0.01)\n", "\n", "print(\"Maximum height that the ball will reach is %.2fm\" % (max(Y1)))\n", "\n", "print(\"The ball travels horizontally %.2fm before hitting the ground\" % (X1[-1]))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": false, "tags": [ "remove-output" ] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# making the animation\n", "nframes = len(X1)\n", "\n", "# plot background axes\n", "fig, ax = plt.subplots(figsize=(13,5))\n", "\n", "# customise axes\n", "ax.set_xlim((0, 135))\n", "ax.set_ylim((0, 45))\n", "ax.set_xlabel('x (m)')\n", "ax.set_ylabel('y (m)')\n", "ax.set_title('Projectile motion for tutorial problem 2.1 in real time')\n", "\n", "# plot line\n", "line, = ax.plot([], [], 'ro', lw=2)\n", "\n", "# plot background for each frame\n", "def init():\n", " line.set_data([], [])\n", " return (line,)\n", "\n", "# plot data for each frame\n", "def animate(i):\n", " x = X1[i]\n", " y = Y1[i]\n", " line.set_data(x, y)\n", " return (line,)\n", "\n", "# call the animator\n", "anim = animation.FuncAnimation(fig, animate, init_func=init,\n", " frames=nframes, interval=10, \n", " blit=True)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "scrolled": false, "tags": [ "remove-output" ] }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HTML(anim.to_html5_video())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tutorial Problem 2.2\n", "\n", "A rock is ejected from a volcano at an angle \\\\(\\alpha=89˚\\\\) with the horizontal with initial speed \\\\(200m/s\\\\). Find:\n", "\n", "1. The maximum height that the ball will reach\n", "2. The total time that the ball travels before it hits the ground\n", "3. How far the ball will travel horizontally before it hits the ground" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total time the rock travels before hitting the ground = 40.77s\n", "Maximum height that the rock will reach is 2038m\n", "The rock travels horizontally 142m before hitting the ground\n" ] } ], "source": [ "# reuse functions above\n", "\n", "end_2 = total_time(89, 200)\n", "\n", "print(\"Total time the rock travels before hitting the ground = %.2fs\" % (end_2))\n", "\n", "X2, Y2 = get_xy(89, 200, 0, end_2, 0.1)\n", "\n", "print(\"Maximum height that the rock will reach is %.fm\" % (max(Y2)))\n", "\n", "print(\"The rock travels horizontally %.fm before hitting the ground\" % (X2[-1]))" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": false, "tags": [ "remove-output" ] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# animation again\n", "nframes = len(X2)\n", "\n", "# plot background axes\n", "fig, ax = plt.subplots(figsize=(5,7))\n", "\n", "# customise axes\n", "ax.set_xlim((0, 150))\n", "ax.set_ylim((0, 2050))\n", "ax.set_xlabel('x (m)')\n", "ax.set_ylabel('y (m)')\n", "ax.set_title('Projectile motion for tutorial problem 2.2 fast forward x10')\n", "\n", "# plot line\n", "line, = ax.plot([], [], 'bo', lw=2)\n", "\n", "# plot background for each frame\n", "def init():\n", " line.set_data([], [])\n", " return (line,)\n", "\n", "# plot data for each frame\n", "def animate(i):\n", " x = X2[i]\n", " y = Y2[i]\n", " line.set_data(x, y)\n", " return (line,)\n", "\n", "# call the animator\n", "anim = animation.FuncAnimation(fig, animate, init_func=init,\n", " frames=nframes, interval=10, \n", " blit=True)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "scrolled": false, "tags": [ "remove-output" ] }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HTML(anim.to_html5_video())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tutorial Problem 2.4\n", "\n", "Consider a rock block of mass \\\\(m\\\\) sitting on a flat floor of a quarry, with a friction coefficient of \\\\(\\mu\\\\) between the rock and the floor. \n", "\n", "A quarryman wraps a rope around the rock, and pulls with a force of magnitude \\\\(F\\\\). His goal is to slide the block along the floor at some constant speed. He does not necessarily have to pull horizontally; he can pull at any angle \\\\(\\alpha\\\\) to the horizontal. \n", "\n", "Find an expression for \\\\(F\\\\) as a function of \\\\(\\alpha\\\\), \\\\(\\mu\\\\), \\\\(g\\\\), and \\\\(m\\\\). \n", "\n", "What would be the optimum choice of \\\\(\\alpha\\\\), so that the block can be pulled with the smallest value of \\\\(F\\\\)?" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plug in random numbers\n", "u = 0.7\n", "m = 10 #kg\n", "g = 9.81 #m/s2\n", "\n", "alpha = np.linspace(0, 0.5*np.pi, 100) # range of angles between 0 and 90 degrees in radians\n", "\n", "# horizontal: Fcos(a) = uN\n", "# vertical: Fsin(a) + N = mg\n", "# N = mg - Fsin(a)\n", "# sub to horizontal\n", "# Fcos(a) = u(mg-Fsin(a))\n", "# rearrange for F\n", "\n", "F = (u*m*g)/(np.cos(alpha)+u*np.sin(alpha))\n", " \n", "alpha = alpha*360/(2*np.pi) # convert angles from radians to degrees\n", "\n", "minimum = np.where(F == min(F))[0][0] # find index of minimum F\n", "\n", "# plot force needed to pull the mass at different angles\n", "\n", "fig = plt.figure(figsize=(8,6)) \n", "plt.plot(alpha, F, 'g')\n", "plt.plot(alpha[minimum], F[minimum], 'ro', label='angle = %.f degrees, min. force = %.f N' % (alpha[minimum], F[minimum]))\n", "plt.xlabel('Angle (degrees)')\n", "plt.ylabel('Force (N)')\n", "plt.title('The force needed to pull a %.fkg mass at different angles' % (m), fontsize=14)\n", "plt.grid(True)\n", "plt.legend(loc='upper left', fontsize=12)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Circular Motion\n", "\n", "### Position, velocity and acceleration in Cartesian coordinates\n", "\n", "For a body moving in a circle counterclockwise, its motion is represented by:\n", "\n", "\\\\[x(t)=Rcos(\\omega t)\\\\]\n", "\n", "\\\\[y(t)=Rsin(\\omega t)\\\\]\n", "\n", "where \\\\(\\omega\\\\) is the angular frequency, and \\\\(R\\\\) is the radius of the circle.\n", "\n", "In vector form, this becomes:\n", "\n", "\\\\[r(t)=Rcos(\\omega t)\\vec{i}+Rsin(\\omega t)\\vec{j}\\\\]\n", "\n", "Velocity vector is obtained by differentiating the position vector:\n", "\n", "\\\\[v(t)=-\\omega Rsin(\\omega t)\\vec{i}+\\omega Rcos(\\omega t)\\vec{j}\\\\]\n", "\n", "with magnitude \\\\(|v|=\\omega R\\\\).\n", "\n", "Acceleration vector is found by differentiating the velocity vector:\n", "\n", "\\\\[a(t)=(-\\omega^2Rcos(\\omega t))\\vec{i}+(-\\omega^2Rsin(\\omega t))\\vec{j}\\\\]\n", "\n", "with magnitude \\\\(|a|=\\omega^2R\\\\). It is called centripetal acceleration, and acts in the direction towards to the centre of the circle.\n", "\n", "![](images/circular-motion.png)\n", "\n", "### Position, velocity and acceleration in polar coordinates\n", "\n", "In polar coordinates, position is described by:\n", "\n", "\\\\[r(t)=r(t)\\vec{e_R}\\\\]\n", "\n", "where \\\\(r\\\\) is the distance from the origin (centre of rotation) to the body, and \\\\(\\vec{e_R}\\\\) is a unit vector pointing radially away from the origin.\n", "\n", "Velocity in polar coordinates becomes:\n", "\n", "\\\\[v(t)=r'\\vec{e_R}+r\\omega\\vec{e_{\\theta}}\\\\]\n", "\n", "where \\\\(\\vec{e_{\\theta}}\\\\) is the unit vector rotated anticlockwise from \\\\(\\vec{e_R}\\\\) by \\\\(90˚\\\\).\n", "\n", "Differentiating velocity, the centripetal acceleration in polar coordinates is found to be:\n", "\n", "\\\\[a(t)=(r\"-\\omega^2r)\\vec{e_R}+(2\\omega r'+\\omega'r)\\vec{e_\\theta}\\\\]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tutorial Problem 2.6\n", "\n", "Imagine a bicycle wheel rotating at constant angular velocity \\\\(\\omega\\\\), with an ant crawling outward along one of the spokes, at a constant speed \\\\(v\\\\) (relative to the spoke). Express the ant’s velocity and acceleration in terms of polar coordinates. Discuss each of the terms." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Period = 2 s\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "angles = np.linspace(0, 2*np.pi, 201) # make an array of angles between 0 and 360 degrees in radians\n", "\n", "drdt = np.ones(len(angles)) \n", "drdt = 0.5 * drdt # speed at which the ant is crawling outward, plug in arbitrary number 0.5 m/s\n", "\n", "t = np.linspace(0, 2, len(angles)) # make a list of time between 0 and 2 seconds\n", "\n", "r = drdt * t # distance from centre of wheel over time\n", "\n", "w = np.pi # angular velocity plug in arbitrary number pi\n", "\n", "print(\"Period = %.f s\" % (2*np.pi/w)) # show period = 2 seconds\n", "\n", "# angular velocity\n", "v_r = drdt # radial component\n", "v_a = r * w # angle component\n", "\n", "# acceleration\n", "a_r = -w**2 * r # radial component\n", "a_a = 2 * w * drdt # angle component\n", "\n", "# plot figures showing trajectory of ant, angular velocity, and acceleration\n", "\n", "fig = plt.figure(figsize=(18, 6))\n", "\n", "ax1 = fig.add_subplot(131, projection='polar')\n", "ax1.plot(angles, r, 'k')\n", "ax1.set_title('Trajectory of ant over 1 period')\n", "\n", "angles = angles * 360 / (2 * np.pi)\n", "\n", "ax2 = fig.add_subplot(132)\n", "ax2.plot(r, v_a, 'r', label='angular')\n", "ax2.plot(r, v_r, 'b', label='radial')\n", "ax2.set_xlabel('distance from centre (m)')\n", "ax2.set_ylabel('velocity (m/s)')\n", "ax2.set_title('Angular and radial velocity over 1 period', fontsize=14)\n", "ax2.legend(loc='best', fontsize=12)\n", "ax2.grid(True)\n", "\n", "ax3 = fig.add_subplot(133)\n", "ax3.plot(r, a_a, 'r', label='angular')\n", "ax3.plot(r, a_r, 'b', label='radial')\n", "ax3.set_xlabel('distance from centre (m)')\n", "ax3.set_ylabel('acceleration (m/s2)')\n", "ax3.set_title('Angular and radial acceleration over 1 period', fontsize=14)\n", "ax3.legend(loc='best', fontsize=12)\n", "ax3.grid(True)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tutorial Problem 2.7\n", "\n", "Consider a small body of mass m, suspended at the end of a “rigid” rod of length \\\\(l\\\\), which is suspended from the ceiling in a manner that allows it to freely swing from left to right.\n", "\n", "The pendulum starts its motion from rest, at an angle \\\\(\\theta_o\\\\). It is shown that the motion was given by \\\\(\\theta(t) = \\theta_ocos(\\omega_{n}t)\\\\), where \\\\(\\omega_n=\\sqrt{\\frac{g}{l}}\\\\) is the natural angular frequency of the mass.\n", "\n", "What can you say about the implications of the other governing equation, obtained from Newton’s law in the “r-direction”: \\\\(−T+mg=−m\\omega^2l\\\\)? Since we have already found \\\\(\\theta(t)\\\\), is this other equation irrelevant? If it is not irrelevant, what exactly does it tell us? Carry out your analysis as far as possible. Assuming that the rod will break if the tension it carries becomes too large, at what angle \\\\(\\theta\\\\) might this occur?" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "scrolled": false }, "outputs": [], "source": [ "g = 9.81 # m/s2\n", "\n", "# plug in arbitrary numbers\n", "l = 1 # m\n", "m = 1 # kg\n", "\n", "wn = np.sqrt(g/l) \n", "\n", "t = np.linspace(0, 2*np.pi/wn, 100)\n", "\n", "# sub into function describing motion\n", "angle = np.pi/12 * np.cos(wn*t)\n", "\n", "# convert to x and y coordinates\n", "X = np.sin(angle) \n", "Y = 1 - np.cos(angle)\n", "\n", "# angular velocity over time\n", "w = -wn * np.sin(wn*t)\n", "\n", "# tension over time\n", "T = m * g + m * w**2 * l" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "scrolled": false, "tags": [ "remove-output" ] }, "outputs": [ { "data": { "image/png": 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90/Tvc/2OAb6e5BCaq04vaMdfRXPWcMfVvB+afeIPJwZ6DrB+QdOMbGGS9dYmiaI5YXIAzW/L96tqsv33apof44kYNqHZF9Zkf9+u5/XEvg7NuvjHqvrHNZjXhGsGzLfXmnzfazLtmlpl/dHEuYK7ErBjgHenuVdtY+Bb7firgO9U1TOmmPfqtsE1tfmAev0CmtYIt9I0H5zse58qlquB7ZKs01OvL6Rpzr6cZn1sR3PFeaJs3qmqSvIL4IVVdXZ/eZJBJ157338R8NI2EdkH+GKS/ntTrgYWDPidXJP9+R6rqttomjEfnOTBwMk0ndF8hsm3pbXd3q+haVYNNPclMskJoPY7uJZmn504Yd2/fo6hOUbaAjirqiYSkatorsL85RSxTPc+O9Wx1C00zQfXZn1eTdM0r3/ev6BZn1sm2agniVpIc2VuJHkFanxtStO867dpbgD/f4Mmqqo7gE8CH02yII1tc1cnCUcAByR5apobk7dNMtFN7HU0TdgmnAD8QZobxtdL8uc093WcuJpY/4umWc1vq+qMSeK8HFgK/FN7A+UuNJeG16QHoa2SHNjGtg9NYvi1tiL6DvAvSe7TLudDe2+MnExV/Yzm8vXfJ9mgfU9vEvkTYNMkz0pzQ+i7adoND7Im02p6PB+4g+Y+kF3av0fStEXfb4j3fxX4wyTPbxPeN7DqgfC5wJPT3EC9GU2zuclsSvPj85sk2wBvm2LagarqhzQHh58ETq6qieew/AC4Kc0N9xunuWn8Ub036PY4HvizJE9vt8O30CRO32vncw1wSJobsjdKzw3LffrrB2hOpjyG5l6ET0+xKJ8FXpVklzSdRPwTcGZVXTH1GljFG9r6aguaq23HteM/AbwuyePa+m6TNDd7bzrEPI8HXplkpyT3otlHe50LvDDJvdJ04f6aKea1JtOuqWOANyXZIcm9adbfcT1J74k0B2vvbcdPJBgnAA9L8oo0nXysn+Sx6elEZHXabWsjmiR5nXYbWV099p62/nwSzYm+z7UxfQL4SJL7t/PeZpIrHIOcSZOk/k27HLvR3Cd8bPu790WaevteaW7G77/qPJ98jGaf3g5WXg0fqmvpJPsluV+7Tm+kOUDuPxF5Kc3v5Pva3+/H0KzvWe0BME1HTTu1ycxNNEn0HW3xoPrqnlhCczX3Oe1vw5uZutODiZMa92u393exaq94x9DsGwfQ1I8TjgZe0tbX67b1+9OTDH1Cpj0m2oimaeu67T471ZW57dJ0/rBemk4xFtK04ric5sT9B5Js2h5L7ZjkiUOGsgR4dJIXt/Per53312hOfPwE+Lu2rngqzT2pI8sEany9haaCupnmatRxq5n2SpqDoxuBr9O0WaaqvkfTLvXf2rJvcdcZ2I8C+6a5VPvhqlpO0wX022ma27wJeG5Vra5nl0/T3MT7X6uZ7qVtXNfS3D/xzqr61tRvWcX3aNoS30DTDv5FVTVx9uLlNDcT/5jmjMbnGP6M8D40N1XfQFPprVyOdv5/SVPJ/aKd5toB81ijaTVt9qe5D+jnVXXtxB/NlZ+XZTXdrLbNWl5Cc5/Mr2gSsaU0CQdVdQrNvnc+zT0sJ0wxu/fQJBc30iRmX1zLZTqG5n66lT+y7cHN82gSxMtpzu5/kqYzgv5luphmf/j3drrn0XR7fHvPfB5Kc7/VMpr9cpC/B45u64e923nfStN+f4eplq+qvkFzH8wXaBK2h3BXk7NhfZamLrus/XtfO++lNHXaoTT7+qU09x+tVlWdRFPvfbN93zf7JvkIzRX962j246kOENdk2jV1JE09dBrN9/17mroFWHkm/ovcfTu5GXgmzbq+mqb+meikYVivoLly9J809yHdSpMITeZamu/happ18Lqqmrgq9Haa9XxGmmatp9Lcz7VaVXU7ze/Rs2m24/8A9uuZ94E0za2upe00YbjFm5M+QLNuv5mmJ9/v0dRFw3gucHH7vn8G9u6/Ot1ejdibpn68lqZOfFtVfXea4h/WNsCXaY6LLqA5kXB8W/YRYL80vXZ+4J5+UFVdQ3PF6N9otr9taTrJum2StxxMc/xxIc3Jlf+l+V4m5ncFTQc+j6U5PpkYfxlNy533tJ9zJc0JqjU5fp/ooOqvaRK0W5n6BN5pwKO565jnBVV1Y1u2L02nGz9py49jcFPxu2lbQe3ZzvNXNPvoc6vqN+029FKajrpuoOmUY1a7XV9TE705aQ5J0/XtbcA2NQIPhEvTPOd6mhs7L5+hzziA5ubN3WZi/hKsbKaxDHjZGib380aSg4GHVdWUD628h59xBU0HDaeublp1p70q9N9V1d8kSJpT2pNx19KcjPp+1/GsrSSvA15cVT4yZTW8AjU3PYrmnp/ruw6k9QaabnVnJHmSZlLb5PK+bVOzd9L0XDWwKep81zanew1weNexSNJMSvLsJJu1zePeTXPcdbf7zDQ3dZpAJdkjzYP8Lk1y0CTT7J3mQV4XJvnsoGl0lyQvpWnW8jdreRP4dMezjOb5RW/tOhZpLf0JzY2/E83dnt/X25RoHoxLc5PxSVV12uqml8ZBmgdLfyvNw9kvTPLGdvwWaR5IfEn7f7Qf+qmZ8GSaJrTX03SO8IK2aanmgc6a8LU3sP2U5sFqy2ieJ7RvVf24Z5odadqvPq2qfp3k/lU1KldVJEnSHJZkK2Crqjqn7YjkbJrOaV4J3FBVh7QngDevqrd3GKqkWdTlFahdgUur6rI2Yz+W5sFivV4LHDbREYDJkyRJmi1VdU1VndO+vhm4iKazgr1oOgeh/f/8biKU1IUuE6htWPWBW8u4ex/6D6PpcvV/k5yRZKS7NJQkSXNTku1peic7k+ahxdfAyh7Z7j/5OyXNNV0+SDcDxvW3J1yPplvr3Wi6iPxukkf1PPukmVGyGFgMsMkmm/zxIx7xiOmPVtJaO/vss39ZVQu6jmNNbbnllrX99tt3HYakHl3UJ+3ztr4A/HVV3ZQMOoQZ+D6PT6QRtrb1SZcJ1DJWfeL7ttz1JPneac6oqv8DLk9yMU1CdVbvRFV1OG2vT4sWLaqlS5fOWNCS1lySK7uOYW1sv/32WJ9Io2W265P2QcFfAD5TVRPPN7suyVZVdU17n9TAWww8PpFG29rWJ1024TsL2LF9kvoGNA/2W9I3zf/QPFSLJFvSNOm7bFajlCRJ81KaS01HABdV1Yd7ipbQPKib9v+XZzs2Sd3p7ApUVa1IciBwMrAucGRVXZjkvcDSqlrSlj0zyY+BO2iebP2rrmKWJEnzyhOAVwA/SnJuO+6dwCHA8UleA/wceElH8UnqQJdN+KiqE4ET+8Yd3PO6gDe3f5IkSbOmqk5n8D3b0Dz7R9I81OmDdCVpNiXZKMkPkpzXPhTzPV3HJEmSxkunV6AkaZbdRvNg7lvaG8NPT3JSVZ3RdWCSJGk8mEBJmjfaZsG3tIPrt3/9j0+QJEmalE34JM0rSdZtbwa/Hjilqs7sK1+cZGmSpcuXL+8mSEmSNLJMoCTNK1V1R1XtQvPsuV2TPKqv/PCqWlRVixYsGLtn/0qSpBlmAiVpXqqq3wDfBvboOBRJkjRGTKAkzRtJFiS5b/t6Y2B34CfdRiVJksaJnUhImk+2Ao5Osi7NCaTjq+qEjmOSJEljxARK0rxRVecDj+46DkmSNL5swidJkiRJQzKBkiRJkqQhmUBJkiRJ0pBMoCRJkiRpSCZQkiRJkjQkEyhJkiRJGpIJlCRJkiQNyQRKkiRJkoZkAiVJkiRJQzKBkiRJkqQhmUBJkiRJ0pBMoCRJkiRpSCZQkiRJkjQkEyhJkiRJGpIJlCRJkiQNyQRKkiRJkoZkAiVJkiRJQzKBkiRJkqQhmUBJkiRJ0pBMoCRJkiRpSCZQkiRJkjSkThOoJHskuTjJpUkOGlD+yiTLk5zb/h3QRZySJEmSBLBeVx+cZF3gMOAZwDLgrCRLqurHfZMeV1UHznqAkiRJktSnyytQuwKXVtVlVXU7cCywV4fxSJIkSdKUukygtgGu6hle1o7r96Ik5yf5fJLtZic0SZIkSbq7LhOoDBhXfcNfAbavqp2BU4GjB84oWZxkaZKly5cvn+YwJUmSJKnRZQK1DOi9orQtcHXvBFX1q6q6rR38BPDHg2ZUVYdX1aKqWrRgwYIZCVaSJEmSukygzgJ2TLJDkg2AfYAlvRMk2apncE/golmMT5IkSZJW0VkvfFW1IsmBwMnAusCRVXVhkvcCS6tqCfBXSfYEVgA3AK/sKl5JkiRJ6iyBAqiqE4ET+8Yd3PP6HcA7ZjsuSZIkSRqk0wfpSpIkSdI4MYGSJEmSpCGZQEmSJA2Q5Mgk1ye5oGfcLknOSHJu+wiVXbuMUdLsM4GSNG8k2S7Jt5JclOTCJG/sOiZJI+0oYI++cR8A3lNVuwAHt8OS5hETKEnzyQrgLVX1SODxwBuS7NRxTJJGVFWdRtML8Cqjgfu0rzej7xmWkua+Tnvhk6TZVFXXANe0r29OchGwDfDjTgOTNE7+Gjg5yb/QnIj+08kmTLIYWAywcOHC2YlO0ozzCpSkeSnJ9sCjgTO7jUTSmPkL4E1VtR3wJuCIySasqsOralFVLVqwYMGsBShpZplASZp3ktwb+ALw11V1U1/Z4vbG8KXLly/vJkBJo2x/4Ivt688BdiIhzTMmUJLmlSTr0yRPn6mqL/aXe8ZY0mpcDTylff004JIOY5HUAe+BkjRvJAlNc5uLqurDXccjabQlOQbYDdgyyTLg3cBrgX9Nsh7we9p7nCTNHyZQkuaTJwCvAH6U5Nx23Dur6sQOY5I0oqpq30mK/nhWA5E0UkygJM0bVXU6kK7jkCRJ48t7oCRJkiRpSCZQkiRJkjQkEyhJkiRJGpIJlCRJkiQNyQRKkiRJkoZkAiVJkiRJQzKBkiRJkqQhmUBJkiRJ0pBMoCRJkiRpSCZQkiRJkjQkEyhJkiRJGpIJlCRJkiQNyQRKkiRJkoZkAiVJkiRJQzKBkiRJkqQhmUBJkiRJ0pBMoCRJkiRpSCZQkiRJkjSkThOoJHskuTjJpUkOmmK6FyepJItmMz5JkiRJ6tVZApVkXeAw4NnATsC+SXYaMN2mwF8BZ85uhJIkSZK0qi6vQO0KXFpVl1XV7cCxwF4DpvsH4APA72czOEmSJEnq12UCtQ1wVc/wsnbcSkkeDWxXVSfMZmCSJEmSNEiXCVQGjKuVhck6wEeAt6x2RsniJEuTLF2+fPk0hihJkiRJd+kygVoGbNczvC1wdc/wpsCjgG8nuQJ4PLBkUEcSVXV4VS2qqkULFiyYwZAlSZIkzWddJlBnATsm2SHJBsA+wJKJwqq6saq2rKrtq2p74Axgz6pa2k24kiRJkua7zhKoqloBHAicDFwEHF9VFyZ5b5I9u4pLkiRJkiazXpcfXlUnAif2jTt4kml3m42YJEmSJGkynSZQktQrybY0zXmfBGwN3ApcAHwVOKmq7uwwPEmSJBMoSaMhyadoHmVwAvB+4HpgI+BhwB7Au5IcVFWndRelJEma70ygJI2KD1XVBQPGXwB8se1sZuEsxyRJkrSKLnvhk6SVBiVPSTZPsnNbfntVXTr7kUmSJN3FBErSSEny7ST3SbIFcB7wqSQf7jouSZIkMIGSNHo2q6qbgBcCn6qqPwZ27zgmSZIkwARK0uhZL8lWwN40HUpIkiSNDBMoSaPmvTQP2L60qs5K8mDgkumYcZIjk1yfZFBnFZIkSatlAiVpJCTZN8n9qupzVbVzVb0eoKouq6oXTdPHHEXTJbokSdJasRtzSaPiQcDnkqwPfAM4CfhBVdV0fUBVnZZk++manyRJmn+8AiVpJFTVIVX1NOA5NL3vvRo4J8lnk+yX5AGzEUeSxUmWJlm6fPny2fhISZI0RkygJI2Uqrq5qr5UVf+vqh4NvA9YAHx6lj7/8KpaVFWLFixYMBsfKUmSxogJlKSRk2TnJHsmeSHwCODyqnpW13FJml8m63gmyV8muTjJhUk+0FV8krrhPVCSRkqSI4GdgQuBO9vRBXyxs6AkzVdHAYfScwU8yVOBvYCdq+q2JPfvKDZJHTGBkjRqHl9VO83EjJMcA+wGbJlkGfDuqjpiJj5L0vibpOOZvwAOqarb2mmun+24JHXLJksztfsAAB1uSURBVHySRs33k8xIAlVV+1bVVlW1flVta/IkaS08DHhSkjOTfCfJY7sOSNLs8gqUpFFzNE0SdS1wGxCgqmrnbsOSJKA5dtoceDzwWOD4JA8e9MiFJIuBxQALFy6c1SAlzRwTKEmj5kjgFcCPuOseKEkaFcuAL7YJ0w+S3AlsCdztuQdVdThwOMCiRYum7Zl2krplAiVp1Py8qpZ0HYQkTeJ/gKcB307yMGAD4JfdhiRpNplASRo1P0nyWeArNE34AKgqe+GTNKsGdTxDc5X8yLZr89uB/Qc135M0d5lASRo1G9MkTs/sGWc35pJmXVXtO0nRy2c1EEkjxQRK0kipqld1HYMkSdJk7MZc0khI8rdJtpii/GlJnjubMUmSJPXzCpSkUfEj4CtJfg+cQ9Oj1UbAjsAuwKnAP3UXniRJkgmUpBFRVV8GvpxkR+AJwFbATcB/A4ur6tYu45MkSQITKEkjpqouAS7pOg5JkqRBTKAkSdKcl2QX4EnA1sCtwAXAN6rqxk4DkzR27ERCkiTNWUlenuRs4D3A5sCVNM2Dd6d5GO4RSbbtMkZJ48UrUJJGSpItquqGruOQNGfcD3hyVf12UGGSRcAjgWWzGpWksWUCJWnUnJnkXOBTwElVVV0HJGl8VdW/rqZ86WzFImlu6DSBSrIH8K/AusAnq+qQvvLXAW8A7gBuoemJ68ezHqik2fQwmqY1rwb+PclxwFFV9dNuw5I0jpK8c6ryqvLxCJLWSGf3QCVZFzgMeDawE7Bvkp36JvtsVf1hVe0CfAD48CyHKWmWVeOUqtoXOADYH/hBku8k+ZOOw5M0fu4Y8LcB8P+Av+0wLkljqssrULsCl1bVZQBJjgX2AlZeYaqqm3qm3wSwKY80xyW5H/By4BXAdcBfAktoHqb7OWCH7qKTNG6q6v0Tr5PcGzgQ2A/4PPDBruKSNL66TKC2Aa7qGV4GPK5/oiRvAN5Mc7boaYNmlGQxsBhg4cKF0x6opFn1feC/gOdXVe9N3UuTfKyjmCSNsST3Bf6a5or2Z4DHVtWvuo1K0rjqshvzDBh3tytMVXVYVT0EeDuTXGqvqsOralFVLVqwYME0hylplv1tVf1Db/KU5CWw6plkSRpGkn8Gzgb+D/ijqvpbkydJ90SXCdQyYLue4W2Bq6eY/ljg+TMakaRRcNCAce+Y9SgkzRVvBx4IvBW4IskN7d+vk/jIBElrrMsmfGcBOybZAfgFsA/w570TJNmxqi5pB/8MuARJc1KSZwPPAbZJ8m89RfcBVnQTlaQ5YP2uA5A0t3SWQFXViiQHAifTdGN+ZFVdmOS9wNKqWgIcmGR3msvuv6ZpuyxpbroaWArsSdPcZsLNwJs6iUjSXLBhVf1uqgmS3Gt100jShE6fA1VVJwIn9o07uOf1G2c9KEmdqKrzgPOSfKaqvOIkabqckOQs4MvAOVX1e4AkC4GnAi8FjgKO7yxCSWOl0wRKkiYkOb6q9gZ+mGRQhzI7dxCWpPH3dOB5wBuBJ7Rdmd8JXAp8FXhtVf2iw/gkjRkTKEmjYuKK83M7jULSnFJVRfMsuSVdxyJpbjCBkjQSquqa9uU6wDU9zWw2Bh7QWWCSJEk9uuzGXJIG+RxN85oJd7TjJEmSOmcCJWnUrFdVt08MtK836DAeSZKklUygJI2a5Un2nBhIshfwyw7jkTRHpHH/JFtP/HUdk6Tx4z1QkkbN64DPJDmsHb4KeEWH8UiaA5K8Hngv8CvuaiZcwE6dBSVpLJlASRopVfUz4PFtV8Opqpu7jknSnPBm4JFVtbzrQCSNN5vwSRopSTZL8mHg28C3knwoyWYdhyVp/C0Dbug6CEnjzytQkkbNkcAFwN7t8CuATwEv7CwiSXPBpcA3k5wA3DYxsqr+rbuQJI0jEyhJo+YhVfWinuH3JDl3umaeZA/gX4F1gU9W1SHTNW9JI+2a9u8+XQciabyZQEkaNbcmeWJVnQ6Q5AnArdMx4yTrAocBz6BpznNWkiVV9ePpmL+k0VVVfwcrH85NVU1LvSJp/lntPVBJDkyy+WwEI0nAXwCHJbkiyZXAoTQ9802HXYFLq+qy9vlSxwJ7TdO8JY2wJDslOQu4BLg0yZlJHtl1XJLGzzBXoB5Ic5b2HJp7E06uqprZsCTNV1V1LvBHSe7TDt80jbPfhqZb9AnLgMdN4/wlja7DgXdW1SkASXYHPgE8sdOoJI2d1SZQVfW3Sf4OeCbwKuDQJMcDR7TdDUvSPZbkzZOMB6CqPjwdHzNg3ConhJIsBhYDLFy4cBo+UtKI2HQieQKoqlOTfKjLgCSNp6G6MW+vOF3b/q0ANgc+n+QDMxibpPll09X8TYdlwHY9w9sCV/dOUFWHV9Wiqlq0YMGCafpYSSPgiiTvSLJt+3cQcGXXQUkaP6u9ApXkr4D9gV8CnwTeVlX/l2QdmnbEfzOzIUqaD6rqPbPwMWcBOybZAfgFsA/w57PwuZK692rgH4ATaa5Gn0bTskaS1sgw90BtCbywqlY5S1NVdyZ57syEJWm+SvIw4D+BB1TVo5LsDOxZVe+7p/OuqhVJDgROpunG/MiquvCezlfS6KuqXwGv7zoOSeNvmHugDp6i7KLpDUeS+ATwNuDjAFV1fpLPAvc4gWrndyLNGWhJ80CSD1XVW5J8ib57HgGqyod0S1ojPgdK0qi5V1X9YKLziNaKroKRNPaOa/8f2mkUkuYMEyhJo+aXSR5Ce6Y4yYuBa7oNSdK4qqoftP+/MTEuyWbANj5EW9LaMIGSNGreQPO8lkck+QVwOfCybkOSNO6SfAN4Ac39j+cBNyQ5pare1m1kksbNUN2YS9IsurKqdgcWAI+oqif2d2IjSWthi/bB3C8Ejq6qXYBnTfWGJEcmuT7JBQPK3pqkkmw5Q/FKGlEmUJJGzeVJDgceD9zSdTCS5oz1kiwAXgJ8Zcj3HAXs0T8yyXbAM4CfT1t0ksaGCZSkUfNw4FSapnyXJzk0yRM7jknS+PtH4DvAz9uOah5M00R4UlV1GnDDgKKP0DwH8269+kma+0ygJI2Uqrq1qo5vuxZ+NHAfmoMeSVprVXVsVe1UVYvb4cuqaq81nU+SPYFfVNV50x6kpLFgJxKSRk6SpwAvBZ4NnAXs3W1EksZde6/Sq4Ht6Tn+mUiohpzHvYB3Ac8ccvrFwGKAhQsXrkG0kkaZCZSkkZLkcuBc4HjgbVX1245DkjQ3fBk4AzgduGMt5/EQYAfgvPZZddsC5yTZtaqu7Z+4qg6n6VWURYsW2dxPmiNMoCSNmj9qe8qSpOm0SVW95Z7MoKp+BNx/YjjJFcCiqvrlPYxN0hjxHihJI8XkSdIMOSnJUE3vJiQ5Bvg+8PAky5K8ZmZCkzROOk2gkuyR5OIklyY5aED5m5P8OMn5Sb6R5EFdxClJksbe64CvJbklyQ1Jfp1kUA97K1XVvlW1VVWtX1XbVtURfeXbe/VJmn86S6CSrAscRnOT+E7Avkl26pvshzSXxncGPg98YHajlDSbkqyTxA4jJM2ELYH1gc1oHtS9ZftfktZIl1egdgUubbsRvR04FlilO9Gq+lZV/a4dPIPmZk1Jc1RV3Qkc2HUckuaeqrqD5iG6b29fbwXs0m1UksZRlwnUNsBVPcPL2nGTeQ1w0qCCJIuTLE2ydPny5dMYoqQOnJLkrUm2S7LFxF/XQUkab0kOBZ4KvKId9TvgY91FJGlcddkLXwaMG9jFZ5KXA4uApwwqt5tQaU55dfv/DT3jCnhwB7FImjv+tKoek+SHAFV1Q5INug5K0vjpMoFaBmzXM7wtcHX/REl2p3lo3VOq6rZZik1SR6pqh65jkDQn/V+SdWhP1ia5H3BntyFJGkddJlBnATsm2QH4BbAP8Oe9EyR5NPBxYI+qun72Q5TUhSSPoulcZqOJcVX16e4ikjSukqxXVStoOq76ArAgyXuAvYH3dBqcpLHUWQJVVSuSHAicDKwLHFlVFyZ5L7C0qpYAHwTuDXyufeL3z6tqz65iljTzkrwb2I0mgTqRpqfO0wETKElr4wfAY6rq00nOBnanuY3gJVV1QbehSRpHXV6BoqpOpDlA6h13cM/r3Wc9KEldezHwR8APq+pVSR4AfLLjmCSNr5X3XFfVhcCFHcYiaQ7oNIGSpAFurao7k6xIch/geuxAQtLaW5DkzZMVVtWHZzMYSePPBErSqFma5L7AJ4CzgVtomuBI0tpYl+Z2gEG9/0rSGjOBkjRSqur17cuPJfkacJ+qOr/LmCSNtWuq6r1dByFp7jCBkjQSkjxmqrKqOmc245E0Z3jlSdK0MoGSNCo+NEVZAU+brUAkzSlP7zoASXOLCZSkkVBVT+06BklzT1Xd0HUMkuYWEyhJIyXJfoPG+yBdSZI0CkygJI2ax/a83oim+c05+CBdSZI0AkygJI2UqvrL3uEkmwH/1VE4kiRJq1in6wAkaTV+B+zYdRCSJEngFShJIybJV2h63YPmJM9OwPHdRSRJknQXEyhJo+Zfel6vAK6sqmVdBSNJktTLBErSSKmq73QdgyRJ0mRMoCSNlCQ3c1cTvgk3AkuBt1TVZbMflSRJUsNOJCSNmg8DbwO2AbYF3gp8AjgWOHJtZ5rkJUkuTHJnkkXTEqkkSZp3TKAkjZo9qurjVXVzVd1UVYcDz6mq44DN78F8LwBeCJw2LVFKkqR5yQRK0qi5M8neSdZp//buKetv2je0qrqoqi6ehvgkSdI8ZgIladS8DHgFcD1wXfv65Uk2Bg6c6Q9PsjjJ0iRLly9fPtMfJ0mSxoydSEgaKW0nEc+bpPj0qd6b5FTggQOK3lVVXx7y8w8HDgdYtGjRWl/xkiRJc5MJlKSRkmQB8Fpge3rqqKp69ereW1W7z1xkkiRJJlCSRs+Xge8CpwJ3dByLJEnSKkygJI2ae1XV26d7pkleAPw7sAD4apJzq+pZ0/05kiRpbrMTCUmj5oQkz5numVbVl6pq26rasKoeYPIkSZLWhgmUpFHzRpok6tYkNyW5OclNXQclSZIENuGTNGKqatOuY5AkSZqMCZSkkZNkc2BHYKOJcVV1WncRSZIkNUygJI2UJAfQNOPbFjgXeDzwfeBpXcYlSZIE3gMlafS8EXgscGVVPRV4NLC825AkSZIaJlCSRs3vq+r3AEk2rKqfAA/vOCZJkiSg4wQqyR5JLk5yaZKDBpQ/Ock5SVYkeXEXMUqadcuS3Bf4H+CUJF8Gru44JkmSJKDDe6CSrAscBjwDWAaclWRJVf24Z7KfA68E3jr7EUrqQlW9oH3590m+BWwGfK3DkCRJklbqshOJXYFLq+oygCTHAnsBKxOoqrqiLbuziwAldauqvtN1DJIkSb26bMK3DXBVz/CydpwkSZIkjaQuE6gMGFdrNaNkcZKlSZYuX25nXZIk6Z5LcmSS65Nc0DPug0l+kuT8JF9q79mUNI90mUAtA7brGd6WtbxRvKoOr6pFVbVowYIF0xKcJEma944C9ugbdwrwqKraGfgp8I7ZDkpSt7pMoM4CdkyyQ5INgH2AJR3GI0mStFJVnQbc0Dfu61W1oh08g+YEsKR5pLMEqq18DgROBi4Cjq+qC5O8N8meAEkem2QZ8BLg40ku7CpeSZKkPq8GTuo6CEmzq8te+KiqE4ET+8Yd3PP6LDyzI0mSRkySdwErgM9MMc1iYDHAwoULZykySTOt0wfpSpIkjZsk+wPPBV5WVZN2gOU92tLc1OkVKEmSpHGSZA/g7cBTqup3XccjafZ5BUqSJGmAJMcA3wcenmRZktcAhwKbAqckOTfJxzoNUtKs8wqUJEnSAFW174DRR8x6IJJGilegJEmSJGlIJlCSJEmSNCQTKEmSJEkakgmUJEmSJA3JBEqSJEmShmQCJUmSJElDMoGSJEmSpCGZQEmSJEnSkEygJEmSJGlIJlCSJEmSNCQTKEmSJEkakgmUJEmSJA3JBEqSJEmShmQCJUmSJElDMoGSNC8k+WCSnyQ5P8mXkty365gkSdL4MYGSNF+cAjyqqnYGfgq8o+N4JEnSGDKBkjQvVNXXq2pFO3gGsG2X8UiSpPFkAiVpPno1cFLXQUiSpPGzXtcBSNJ0SXIq8MABRe+qqi+307wLWAF8ZpJ5LAYWAyxcuHCGIpUkSePKBErSnFFVu09VnmR/4LnA06uqJpnH4cDhAIsWLRo4jSRJmr9MoCTNC0n2AN4OPKWqftd1PJIkaTx5D5Sk+eJQYFPglCTnJvlY1wFJkqTx4xUoSfNCVT206xgkSdL48wqUJEmSJA3JBEqSJEmShmQCJUmSJElD6jSBSrJHkouTXJrkoAHlGyY5ri0/M8n2sx+lJEmSJDU6S6CSrAscBjwb2AnYN8lOfZO9Bvh1e/P3R4D3z26UkiRJknSXLq9A7QpcWlWXVdXtwLHAXn3T7AUc3b7+PPD0JJnFGCVJkiRppS4TqG2Aq3qGl7XjBk5TVSuAG4H7zUp0kiRJktSnywRq0JWkWotpSLI4ydIkS5cvXz4twUmSJElSvy4TqGXAdj3D2wJXTzZNkvWAzYAb+mdUVYdX1aKqWrRgwYIZCleSJEnSfNdlAnUWsGOSHZJsAOwDLOmbZgmwf/v6xcA3q+puV6AkSZIkaTas19UHV9WKJAcCJwPrAkdW1YVJ3gssraolwBHAfyW5lObK0z5dxStJkiRJnSVQAFV1InBi37iDe17/HnjJbMclSZIkSYN0+iBdSZIkSRonJlCSJEmSNCQTKEmSJEkakgmUJEmSJA3JBEqSJEmShmQCJUmSNECSI5Ncn+SCnnFbJDklySXt/827jFHS7DOBkiRJGuwoYI++cQcB36iqHYFvtMOS5hETKEmSpAGq6jTghr7RewFHt6+PBp4/q0FJ6pwJlCRJ0vAeUFXXALT/799xPJJmmQmUJEnSDEiyOMnSJEuXL1/edTiSpokJlCRJ0vCuS7IVQPv/+skmrKrDq2pRVS1asGDBrAUoaWaZQEmSJA1vCbB/+3p/4MsdxiKpAyZQkiRJAyQ5Bvg+8PAky5K8BjgEeEaSS4BntMOS5pH1ug5AkiRpFFXVvpMUPX1WA5E0UrwCJUmSJElDMoGSJEmSpCGZQEmSJEnSkEygJEmSJGlIJlCSJEmSNCQTKEmSJEkakgmUJEmSJA3JBEqSJEmShmQCJWleSPIPSc5Pcm6SryfZuuuYJEnS+DGBkjRffLCqdq6qXYATgIO7DkiSJI0fEyhJ80JV3dQzuAlQXcUiSZLG13pdByBJsyXJPwL7ATcCT51kmsXAYoCFCxfOXnCSJGkseAVK0pyR5NQkFwz42wugqt5VVdsBnwEOHDSPqjq8qhZV1aIFCxbMZviSJGkMeAVK0pxRVbsPOelnga8C757BcCRJ0hzkFShJ80KSHXsG9wR+0lUskiRpfHkFStJ8cUiShwN3AlcCr+s4HkmSNIY6SaCSbAEcB2wPXAHsXVW/HjDd14DHA6dX1XNnM0ZJc0tVvajrGCRJ0vjrqgnfQcA3qmpH4Bvt8CAfBF4xa1FJkiRJ0hS6SqD2Ao5uXx8NPH/QRFX1DeDm2QpKkiRJkqbSVQL1gKq6BqD9f/+O4pAkSZKkoc3YPVBJTgUeOKDoXTPwWSsffAncluSC6f6MabIl8MuugxjAuNbcqMY2qnE9vOsA1sbZZ599S5KLu45jFozqdjOdXMa5w/pkdM2XbXA+LOd8WEZYy/pkxhKoqZ7HkuS6JFtV1TVJtgKuv4efdThweDvvpVW16J7Mb6aMamzGteZGNbZRjqvrGNbSxaO4PqfbqG4308llnDusT0bXfNoG5/pyzodlhLWvT7pqwrcE2L99vT/w5Y7ikCRJkqShdZVAHQI8I8klwDPaYZIsSvLJiYmSfBf4HPD0JMuSPKuTaCVJkiSJjp4DVVW/Ap4+YPxS4ICe4SetxewPvwehzbRRjc241tyoxmZc02tc415T82E5Xca5Y1yXc1zjXhPzYRlhfiznfFhGWMvlTFVNdyCSJEmSNCd11YRPkiRJksbO2CdQSV6S5MIkdyaZtLeQJFck+VGSc2erB581iG2PJBcnuTTJQbMQ1xZJTklySft/80mmu6NdX+cmWTKD8Uy5/Ek2THJcW35mku1nKpY1jOuVSZb3rKMDBs1nBuI6Msn1k3XXn8a/tXGfn+QxIxLXbklu7FlfB89GXGtiVPfZ6TZqdcB0GtX6ZDqNat00nUa1nlsT86E+mct1CViftOXWJ4NU1Vj/AY+k6cP928CiKaa7Athy1GID1gV+BjwY2AA4D9hphuP6AHBQ+/og4P2TTHfLLKyj1S4/8HrgY+3rfYDjRiSuVwKHzuY21X7uk4HHABdMUv4c4CQgwOOBM0ckrt2AE2Z7fa3hMozkPjsDyzkydcA0L9dI1icdLGMnddM0L+dI1nNruAxzvj6Zq3XJsN+N9cl4/M1EfTL2V6Cq6qKqGskH0w0Z267ApVV1WVXdDhwL7DXDoe0FHN2+Php4/gx/3lSGWf7eeD9P0ytjRiCuTlTVacANU0yyF/DpapwB3DfN89a6jmvkjfA+O91GqQ6YTqNan0ynubD9rdao1nNrYp7UJ3O1LgHrkzljJuqTsU+g1kABX09ydpLFXQfTYxvgqp7hZe24mfSAqroGoP1//0mm2yjJ0iRnJJmpSnGY5V85TVWtAG4E7jdD8axJXAAvai/3fj7JdjMc07C62KaG9SdJzktyUpI/6DqYtTTK63dYo1QHTKdRrU+m0zjXTdNpLuyHMP7LMVfrErA+6WV90qeTbszXVJJTgQcOKHpXVQ37EN4nVNXVSe4PnJLkJ21G2nVsg85U3OOuEaeKaw1ms7BdZw8GvpnkR1X1s3saW59hln9G1tFqDPOZXwGOqarbkryO5izU02Y4rmF0sb6GcQ7woKq6JclzgP8BdpztIEZ1n51uY1QHTKdRrU+m0zjXTdNpJL7H+VCfzNO6BKxPJlifDDAWCVRV7T4N87i6/X99ki/RXLa8xwnUNMS2DOjN5rcFrr6H85wyriTXJdmqqq5pL1FeP8k8JtbZZUm+DTyapq3sdBpm+SemWZZkPWAzZr6p2GrjquZ5ZhM+Abx/hmMa1oxsU/dUVd3U8/rEJP+RZMuq+uUsxzGS++x0G6M6YDqNan0ynca5bppOI7Efzof6ZJ7WJWB9AlifTGZeNOFLskmSTSdeA88EBvbE0YGzgB2T7JBkA5qbEGe6h5olwP7t6/2Bu50lS7J5kg3b11sCTwB+PAOxDLP8vfG+GPhmtXf9zaDVxtXXPnZP4KIZjmlYS4D92l5lHg/cONHEoktJHjjRNjzJrjT1z/9v7+5Vo4jCMAC/H4pE1CaddqaysNQmpRcgeAM2aVLkKkTIFdhZq2BnIVionYhWMaRRS0Es7BWVY7EDipLkRDY7k/g8sOwwy8B35ueDd2f27Oe9t5qkMa7ZeZtSD5inqfaTeTrKvWmeJtnn/sFR7yfHtZck+kkS/WRXB5nFYoqvJDcyS45fk3xK8mRYfyHJ42F5JbOZRbaS7GR2a30StbVfs3+8zezbmEOvLbPnc58meTe8Lw/rryS5OyyvJtke9tl2krVDrOev8Se5leT6sLyU5GGS90leJVlZ0PHbr67N4XzaSvI8yaUF1XU/ycck34bzay3JepL14fNKcmeoezt7zE654Lo2fttfL5OsLqKuA45hktfsIYxzUj1gzmObZD9Z8BhH6U1zHuMk+9wBx3Ds+8lx7iW7HRv9RD9praWGDQEAANjHf/EIHwAAwDwIUAAAAJ0EKAAAgE4CFAAAQCcBCgAAoJMABQAA0EmAAgAA6CRAMTlVdbWq3lTVUlWdqaqdqro8dl0AAOCPdJmkqrqd2T98n07yobW2OXJJAAAgQDFNVXUqyeskX5KsttZ+jFwSAAB4hI/JWk5yNsm5zO5EAQDA6NyBYpKq6lGSB0kuJjnfWtsYuSQAAMjJsQuAP1XVzSTfW2v3qupEkhdVda219mzs2gAA+L+5AwUAANDJb6AAAAA6CVAAAACdBCgAAIBOAhQAAEAnAQoAAKCTAAUAANBJgAIAAOgkQAEAAHT6CfpaLARciNh5AAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "nframes = len(t)\n", "\n", "\n", "# Plot background axes\n", "fig, axes = plt.subplots(1,3, figsize=(14,5))\n", "\n", "# define lines\n", "line1, = axes[0].plot([], [], 'ro', lw=2)\n", "line2, = axes[0].plot([], [], 'k')\n", "line3, = axes[1].plot([], [], 'go', lw=2)\n", "line4, = axes[2].plot([], [], 'bo', lw=2)\n", "\n", "# customise axes \n", "\n", "axes[0].set_xlim((-1.5, 1.5))\n", "axes[0].set_ylim((-0.1, 0.6))\n", "axes[0].set_xlabel('x')\n", "axes[0].set_ylabel('y')\n", "axes[0].set_title('Trajectory of pendulum')\n", "\n", "\n", "axes[1].set_xlim((-1, 1))\n", "axes[1].set_ylim((-3.2, 3.2))\n", "axes[1].set_ylabel('angular velocity (m/s)')\n", "axes[1].set_title('Angular velocity of pendulum over 1 period')\n", "\n", "\n", "axes[2].set_xlim((-1, 1))\n", "axes[2].set_ylim((9, 20))\n", "axes[2].set_ylabel('Tension (N)')\n", "axes[2].set_title('Tension in string over 1 period')\n", "\n", " \n", "lines = [line1, line2, line3, line4]\n", "\n", "# Plot background for each frame\n", "def init():\n", " for line in lines:\n", " line.set_data([], [])\n", " return lines\n", "\n", "# Set what data to plot in each frame\n", "def animate(i):\n", " \n", " x1 = X[i]\n", " y1 = Y[i]\n", " lines[0].set_data(x1, y1)\n", " x_1 = X\n", " y_1 = Y\n", " lines[1].set_data(x_1, y_1)\n", " \n", " x2 = 0\n", " y2 = w[i]\n", " lines[2].set_data(x2, y2)\n", " \n", " x3 = 0\n", " y3 = T[i]\n", " lines[3].set_data(x3, y3)\n", "\n", " \n", " return lines\n", "\n", "# Call the animator\n", "anim = animation.FuncAnimation(fig, animate, init_func=init,\n", " frames=nframes, interval=25, blit=True)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "scrolled": false, "tags": [ "hide-output" ] }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HTML(anim.to_html5_video())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### References\n", "\n", "Course notes from Lecture 2 of the module ESE 95011 Mechanics" ] } ], "metadata": { "celltoolbar": "Tags", "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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 4 }