Week 3 - Solving second order ODEs

b = 0.05;                       % Damping Coefficient
g = 9.81;                       % Gravity in m/s2
l = 1;                          % Length of Pendulum in m
m = 1;                          % Mass of the ball

               % Initial Condition
theta_0 = [0;3];

                 % Time Points
t_span = linspace(0,20,500);

                  % Solve ODE
[t,results] = ode45(@(t,theta) ode_func(t,theta,b,g,l,m),t_span,theta_0);


                  % Plotting

figure(1)
plot(t,results(:,1))
hold on
plot(t,results(:,2))
title(\'Motion of a Simple Damped Pendulum\')
ylabel(\'Plot\')
xlabel(\'Time\')
legend(\'Displacement(rad)\',\'Velocity(rad/s)\')
hold off


              % Pendulum Animation

figure(2)
O = [0 0];
axis(gca,\'equal\');             % Aspect Ration of The Plot
axis([-1 1.2 -1.5 0.2]);       % Limits of the Plot
grid on

ct=1;                          % Loop for Animation
for i=1:length(t_span)
    
    %Mass point 
    P = l*[sin(results(i,1)) -cos(results(i,1))];
    
    %Circle of origin
    O_circ = viscircles(O,0.01);
    
    %Pendulum
    pend = line([O(1) P(1)],[O(2) P(2)]);
    
    %Ball
    ball = viscircles(P,0.05);
    
    %Time intervals at which the plots should be updated
    pause(0.001);
    M(ct) = getframe(gcf);
    ct = ct+1;
    
    %Deletes previous object if they are not in the final loop
    if i<length(t_span)
        delete(pend);
        delete(ball);
        delete(O_circ);
    end
end

% Video of the animation
movie(M) 
videofile = VideoWriter(\'Pendulum.AVI\',\'Uncompressed AVI\');
open(videofile)
writeVideo(videofile,M)
close(videofile)