Week 4.1 - Solving second order ODEs

aim:to solve on ordinary different equation (O

close all
clc
b=0.05;
g=9.81;
l=1;
m=0.1;
%intial condition
theta_0=[0;5];
% time points
t_span=linspace(0,10,600);
%solve ODE
[t,results]=ode45(@(t,theta)ode_function(t,theta,b,g,l,m),t_span,theta_0);
%plotting
figure(1)
hold on
plot(t,results(:,1))
plot(t,results(:,2))
title('Damped Harmonic motion of a Pendulum')
legend('Angular displacement', 'Angular velocity')
ylabel('Plot')
xlabel('Time(seconds)')



% For loop 
% Before starting the for loop, a counter value was defined

ct =1;
 for i = 1:length(results(:,1))
 x_start = 0     
 y_start = 0
 x_end = l*sin(results(i,1))
 y_end = -l*cos(results(i,1))
 
 % plotting the animation
 figure(2)
 plot([-1 1], [0 0], 'linewidth', 5)
 hold on
 plot([x_start x_end],[y_start y_end],'linewidth',3)
 hold on
 
 plot(x_end,y_end,'o','markersize',20,'markerFacecolor','y')
 title('Animation of transient behaviour of a Pendulum')
 axis([-1.5 1.5 -1.5 1])
 pause(0.03)
 hold off 
 
 M(ct) = getframe(gcf)
 ct = ct+1
 
 end
 
 
% Animation of the pendulum

 movie(M)
videofile=VideoWriter('Pendulum Animation.avi', 'uncompressed avi')
open(videofile)
writeVideo(videofile,M)
close(videofile)

DE)and use the calculated information to animate the motion of the pendulum