Week 3 - Solving second order ODEs

To write code in MATLAB that can animate a simple pendulum motion

Steps:

• Derive the equation of motion
• The position it. The angular displacement at 3, or the ‘x’ as it in the code
• Make a function in another file which called ‘ode_func’
• Plot the angular displacement with respect to Time
• Make an animation of the pendulum motion

During the first (file) Programming

The Objective here is to calculate the parameters that is involved and also plotting it.

• Inserting the inputs: Mass of the ball, Damping coefficient, length of the pendulum, gravity
• Inserting the initial condition
• Inserting the time span points
• Solve ODE45 function
• Plotting the code and animate it

THE YOUTUBE LINK OF THE VIDEO:

https://www.youtube.com/watch?v=7YqsixqmO7Y&feature=youtu.be

Problems or Errors that has been faced during the program:

• Faced minor errors, such as the position of marker of the pendulum

  clear all 
  close all 
  clc
  %Inputs
  b = 0.05;
  m =1;
  l=1 ; 
  g = 9.81;
  %Initial Condition
  x0 = [0 2]
  % Time points
  t = linspace(0,20,500)
  
  %Solve ODE45
  [t x] =  ode45('ode_func',t,x0);
  
  %plotting 
  plot(t,x(:,1));
  hold on;
  plot(t,x(:,2));
  xlabel('TIME')
  ylabel('Angular Displacement')
  
  % Animate the motion of the PENDULUM
  X0 = 0;
  Y0 = 0;
  ct =1; 
  for i=1:length(t)
      X1= l*sin(x(i,1));
      Y1= -l*cos(x(i,1));
  
      figure(2)
      plot([-1 1],[0 0],'linewidth',6,'Color','b');
      axis ([-1.5 1.5 -1.5 1.5]);
      line([X0 X1],[Y0 Y1]);
      hold on;
      plot (X0, Y0,'O','markersize',2,'MarkerFaceColor','r');
      plot(X1,Y1,'O','markersize',10,'MarkerFaceColor','g');
      title('Simple Pendulum');
      grid on;
      hold off;
     F(ct) = getframe(gcf);
      ct= ct+1;
  
  end
  
  movie(F);
  video = VideoWriter('Simple_Pendulum.avi','Uncompressend.AVI');
  open(video)
  writeVideo(videofile,F)
  close(video)​