Week 3 - Solving second order ODEs

https://drive.google.com/drive/folders/16ERKcFqdGH9AuUsWjOaaaLZK8cVCykOi?usp=sharing

% inputs for pendulum %

b=0.05;
g=9.81;
l=1;
m=1;
theta_0=[0;3];
t_span=linspace(0,20,200);
[t, results] = ode45 (@(t,theta) ode_function(t,theta,b,g,l,m) , t_span, theta_0);

% plot %
plot(t, results (:,1))
hold on
plot(t, results (:,2))
xlabel('time')
ylabel('plots')
legend ('displacement', 'velocity') ;
hold off
ct=1;
B=(results (: ,1)) ;

% Animation %
for i=1: length(B)
    B1=results(i,1);
    X0=0;
    Y0=0;
    Y1=-1*cos(B1);
    X1=1*sin(B1) ;
    plot ( [X0 X1], [Y0 Y1], 'linewidth',8)
    hold on
    plot (X1, Y1,ct ,20, 'r');
    plot ([-0.2 0.2], [0 0], 'linewidth',7)
    axis ([-0.6 1.2 -1.5 0.11]);
    title('OSCILATION OF SIMPLE PENDULUM' )
    legend (' connecting tread(rod) ', 'mass', 'fixed position' ) ; 
    xlabel (' X-axis')
    ylabel('Y-axis')
    hold off
    % Making video %  
    M(ct)= getframe(gcf);
    ct=ct+1;
end

movie (M)
videofile=VideoWriter('simple pendulum.avi', 'Uncompressed AVI');
open (videofile);
writeVideo (videofile,M) ;
close(videofile);

function [dtheta_dt]= ode_function(t,theta,b,g,l,m);
theta1=theta(1);
theta2=theta(2);
dtheta1_dt=theta2;
dtheta2_dt=-(b/m)*theta2-(g/l)*sin(theta1);
dtheta_dt=[dtheta1_dt;dtheta2_dt];
end