Week 3 - Solving second order ODEs

https://www.youtube.com/watch?v=9KXgYVlIv88

clear all
close all
clc


b=0.05;
g=9.81;
l=1;
m=0.1;

% initial condition
theta_0 = [0;5];

% time points
t_span = linspace(0,10,500);

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

plot(t,results(:,1))
hold on
plot(t,results(:,2))
ylabel('Plot')
xlabel('time')

grid on
% Simulation of Pendulum
ct = 1;
for i = 1:length(results(:,1))
    x0 = 0;
    y0 = 0;
    x1 = l*sin(results(i,1));
    y1 = -l*cos(results(i,1));

    plot([-0.5,0.5],[0,0],'linewidth',3,'color','r');
    line([x0 x1],[y0 y1],'linewidth',2,'color','b');
    hold on;

    plot(x1,y1,'o','MarkerSize',20,'markerfacecolor','g');
    grid on;
    axis([-1.5 1.5 -1.5 0.5]);
    pause(0.01);
    hold off;
    M(ct) = getframe(gcf);
   
    ct = ct +1;
end

% Creating movie
movie(M)
videofile = VideoWriter('ode_using_matlab.avi','Uncompressed AVI')
open(videofile)
writeVideo(videofile,M)
close(videofile)


FUNCTION CALLING

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