Week 3 - Solving second order ODEs

ODE Program

% ODE
clear all
close all
clc

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

ct = 1
% Initial condition
theta_0 = [0;3];

% Time points
t_span = linspace(0,20,200);

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

plot(t,results(:,1))
hold on
plot(t,results(:,2))
xlabel('time')
ylabel('plot')
pause(0.3)
M(ct) = getframe(gcf);
ct = ct+1

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

ODE function

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

for ODE program we design n function called ode_func.

for programming we assume time span of 0 to 20 of 200 intervas.