!apt update -y !apt install ffmpeg -y import numpy as np import sympy import math import matplotlib.pyplot as plt from numpy.linalg import solve from matplotlib.animation import FFMpegWriter from matplotlib.patches import Circle from matplotlib.patches import Rectangle k= 10 #N/m m1= 1 #kg m2= 2 #kg L= 1 #m#Setting Up Animation fig, ax = plt.subplots() Lo= 1 #m g= 9.8 #m/s^2 dt= 0.001 #seconds t_vec= np.arange(0, 10, dt) #For 10 seconds x_vec= np.zeros(len(t_vec)) dx_vec= np.zeros(len(t_vec)) theta_vec= np.zeros(len(t_vec)) dtheta_vec= np.zeros(len(t_vec)) x_vec[0]= 0 #initial x-position dx_vec[0]= 0 #initial x-velocity theta_vec[0]= 1 #initial theta (radians) dtheta_vec[0]= 0 #initial theta velocity (radians) for i in range(1, len(t_vec)): #spliiting apart the equations since they are VERY long A= (x_vec[i-1]**2 - 2 * x_vec[i-1] * L * sympy.sin(theta_vec[i-1]) + L**2 * sympy.sin(theta_vec[i-1]) * sympy.sin(theta_vec[i-1]) + 1.5**2 - 3 * L * sympy.cos(theta_vec[i-1]) + L**2 * sympy.cos(theta_vec[i-1])*sympy.cos(theta_vec[i-1])) ddx= ( (-0.5)*k * ( (A**(0.5)) - Lo) * (A**(-0.5)) * (2 * x_vec[i-1] - 2 * L * sympy.sin(theta_vec[i-1])) ) / (m2) ddtheta=( ((-0.5)*k * ( (A**(0.5)) - Lo) * (A**(-0.5)) * ((-2) * x_vec[i-1] * L * sympy.cos(theta_vec[i-1]) + 3 * L * sympy.sin(theta_vec[i-1]) )) - m1 * g * L * sympy.sin(theta_vec[i-1]) ) / (m1 * L**2) x_vec[i]= x_vec[i-1]+ dx_vec[i-1]*dt theta_vec[i]= theta_vec[i-1]+ dtheta_vec[i-1]*dt dx_vec[i]= dx_vec[i-1] + ddx*dt dtheta_vec[i]= dtheta_vec[i-1] + ddtheta*dt plt.plot(t_vec,x_vec) plt.show() plt.plot(t_vec,theta_vec) plt.show() p, = ax.plot([], [], color='black') ground,= ax.plot([-5, 5], [-0.1, -0.1], color= 'brown') spring, = ax.plot([], [], color= 'grey') ax.set_xlim([-2, 2]) ax.set_ylim([-2, 2]) ax.set_xlabel("X-Value") ax.set_ylabel("Y-Value") ax.set_title("Pendulum and Spring") video_title= "Simulation2" mass1= Circle((0,0), radius= 0.1, color= 'blue') mass2= Circle((0,0), radius= 0.1, color= 'green') ax.add_patch(mass1) ax.add_patch(mass2) FPS= 20 sample_rate= int(1/FPS/dt) dpi = 300 writerObj = FFMpegWriter(fps= FPS) simulation_size= len(t_vec) x_m1= np.zeros(simulation_size) y_m1= np.zeros(simulation_size) x_m2= np.zeros(simulation_size) y_m2= np.zeros(simulation_size) x_pendulum_arm = np.zeros(simulation_size) y_pendulum_arm = np.zeros(simulation_size) origin = (0, 1.5) with writerObj.saving(fig, video_title+".mp4", dpi): for i in range(0, simulation_size, sample_rate): x_m1[i]= L*sympy.sin(theta_vec[i]) y_m1[i]= 1.5- L*sympy.cos(theta_vec[i]) x_m2[i]= x_vec[i] x_data_points = [origin[0], x_m1[i]] y_data_points = [origin[1], y_m1[i]] p.set_data(x_data_points, y_data_points) x_spring= [x_m1[i], x_m2[i]] y_spring= [y_m1[i], y_m2[i]] spring.set_data(x_spring, y_spring) patch_center= x_m1[i], y_m1[i] mass1.center= patch_center patch_center= x_m2[i], y_m2[i] mass2.center= patch_center fig.canvas.draw() writerObj.grab_frame() from IPython.display import Video Video("/work/Simulation2.mp4", embed=True, width=640, height=480)