Week 3 - Solving second order ODEs

main code :

clear all 
close all 
clc 
m = 1;
b = 0.05;
g = 9.81;
l = 1;
 %Initial Conditions 
 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)
 y = results(:,1);
 plot(t,y)
 hold on 
 plot(t,results(:,2))
 xlabel('time')
 ylabel('plot')
 ct = 1;
 for i = 1:length(y)
     x0 = 0;
     y0 = 0;
     y1 = -l*cos(y(i));
     x1 = l*sin(y(i));
     plot([x0 x1],[y0 y1],'linewidth',4);
     hold on
     plot(x1,y1,'o','markersize',20,'color','r')
     hold on
     plot([-2 2],[0,0],'linewidth',5,'color','y')
     axis([-2,2,-2,2])
     pause(0.01)
     M(ct)= getframe(gcf)
     hold off
     ct = ct+1
 end 
 movie(M)
 videofile = VideoWriter('Pendulum Animation.avi');
 open(videofile)
 writeVideo(videofile,M)
 close(videofile)
 

function code :

function [dtheta_dt] = ode_func(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 

youtube video link for the pendulum animation :

https://youtu.be/lQaizR-oeKM

report : (inserted below)