Animating the driven damped pendulum.ipynb

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    "# Animating the Driven Damped Pendulum\n",
    "\n",
    "# Set up the differential equation with various parameters.\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import solve_ivp\n",
    "\n",
    "# Define the equation\n",
    "def eqn(t, phi, phi_dot):\n",
    "    return phi_dot, -2 * beta * phi_dot - omega0**2 * np.sin(phi) + gamma * omega0**2 * np.cos(omega * t)\n",
    "\n",
    "# Set parameters\n",
    "beta = omega0 / 4\n",
    "omega0 = 1.5 * omega\n",
    "omega = 2 * np.pi\n",
    "gamma = 0.2\n",
    "\n",
    "# Set max time for solution\n",
    "tMax = 10\n",
    "\n",
    "# Set initial conditions\n",
    "phi0 = 0\n",
    "phi_dot0 = 0\n",
    "\n",
    "# Solve the equation\n",
    "sol = solve_ivp(eqn, [0, tMax], [phi0, phi_dot0], dense_output=True)\n",
    "\n",
    "# Plot the solution\n",
    "t = np.linspace(0, tMax, 100)\n",
    "phi_values = sol.sol(t)[0]\n",
    "plt.plot(t, phi_values, label='phi')\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('Phi')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
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   "source": [
    "# import numpy as np\n",
    "# import matplotlib.pyplot as plt\n",
    "from matplotlib.animation import FuncAnimation\n",
    "\n",
    "# Set the pendulum length\n",
    "length = 1.0\n",
    "\n",
    "# Calculate the position of the pendulum bob\n",
    "x_bob = length * np.sin(sol.sol(t)[0])\n",
    "y_bob = -length * np.cos(sol.sol(t)[0])\n",
    "\n",
    "# Create the figure and axes\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Set the axis limits\n",
    "ax.set_xlim(-length, length)\n",
    "ax.set_ylim(-length, length)\n",
    "\n",
    "# Create the line and disk objects\n",
    "line, = ax.plot([], [], 'k-', lw=2)\n",
    "disk, = ax.plot([], [], 'ko')\n",
    "\n",
    "# Animation update function\n",
    "def animate(time):\n",
    "    x = [0, x_bob[int(time*10)]]\n",
    "    y = [0, y_bob[int(time*10)]]\n",
    "    line.set_data(x, y)\n",
    "    disk.set_data(x_bob[int(time*10)], y_bob[int(time*10)])\n",
    "    return line, disk\n",
    "\n",
    "# Create the animation\n",
    "animation = FuncAnimation(fig, animate, frames=np.arange(0, tMax, 0.1), interval=50, blit=True)\n",
    "\n",
    "# Show the animation\n",
    "plt.show()\n"
   ]
  }
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