Week 3 - Solving second order ODEs

BODY OF THE PROGRAM CONTENT :

% Solving the Second Order ODE’s

clear all

close all

clc

%inputs

b=0.05;

g = 9.81;

l = 1;

m = 1;

%initial conditions

theta_0 = [0;3];

%time _span

t_span = linspace(0,20,150);

% solve ode

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

ODE FUNCTION LOOP

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

figure(1)

plot(t,results(:,1))

hold on

plot(t,results(:,2))

ylabel('velocity')

xlabel('displacement')

hold off

theta = results(:,1);

ct = 1;

for i = 1:length(theta);

THETA = theta(i) ;

% coordinate

x = 0;

y = 0;

x1 = l*sin(THETA);

y1 = -l*cos(THETA);

%plotting

figure(2)

plot([x x1],[y y1],'linewidth',3)

hold on

plot(x1,y1,'o','MarkerSize',15,'MarkerFaceColor','r','MarkerEdgeColor','r')

axis([-1 1 -1.5 1.5])

pause(0.2)

M(ct)=getframe(gcf)

hold off

ct = ct+1

end

movie(M)

videofile = VideoWriter('pendulum','uncompressed AVI')

open(videofile)

writeVideo(videofile,M)

close(videofile)

animation video link

https://drive.google.com/file/d/1iSn2202gY4tL6ExDviPjPoEAbvgzQUuZ/view?usp=sharing