Week 3 - Solving second order ODEs

https://docs.google.com/document/d/15xWj-EOLbhuU3MI0QTIemlnZmyaeZ8LUDG39-1ojUV4/edit?usp=sharing

clear all; close all; clc;

%inputs
b=0.5;
g=9.81;
l=1;
m=1;
ct=1;

%initial conditions
t_theta=[0;3];

%time points 
t_span=linspace(0,20,1000);

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

%plotting 
figure(1)
hold on
subplot(2,1,1)
plot(t,results(:,1));
plot(t,results(:,2));
hold on
xlabel('Time')
ylabel('Plot')

for i=1:length (results(:,1))
    x0=0;
    y0=0;
    x1=1*sin(results(i,1));
    y1=-1*cos(results(i,1));
    subplot(2,1,2)
    plot([-1 1],[0 0],[x0 x1],[y0 y1],LineWidth=2);
    grid on 
    pause (0.0002)
    hold off
    M(ct)=getframe(gcf);
    ct=ct+1;
end    

%creating movie 
movie(M)
videofile=VideoWriter('2nd Order ODE','Uncompressed AVI');
open(videofile)
writeVideo(videofile,M)
close(videofile)

function [dtheta_dt]=ode_func(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