Week 3 - Solving second order ODEs

https://drive.google.com/drive/folders/1cgFnguKAojQSi_nITflq-E1BRFg4iTj8

clear all
close all
clc

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

% initial condition
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);

plot(t,results(:,1))
hold on
plot(t,results(:,2))
title('simple pendulum consisting damping')
ylabel('plot')
xlabel('time')

ct = 1;

for i = 1:length(results(:,1))
    
    %initial points
    x0 = 0;
    y0 = 0;
    
    %final locations
    x1 = 1*sind(results(i,1));
    y1 = -1*cosd(results(i,1));
    
    
    %Plotting
    figure(2)
    plot([-1 1],[0 0],'linewidth',8,'color','b');
    line([x0 x1],[y0 y1],'linewidth',5,'color','g')
    grid on
    hold on
    plot(x1,y1,'o','markersize',15,'markerfacecolor','r','color','r')
    axis([-2 2 -2 2]);
    title('Pendulum Movement')
    pause(0.3)
    hold off;
    M(ct) = getframe(gcf);
    ct = ct+1;
    
end

%Making Movie

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

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