Week 3 - Solving second order ODEs

function[dtheta_dt] = ode_function(t,theta_0,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];

dtheta_dt = dtheta2_dt+(b/m)*theta2+(g/l)*sin(theta1)

end

% PROGRAM TO SOLVE 2ND ODE

clear all
close all
clc

b=0.05;
l = 1;
m = 1;
g = 9.81;
t = 3;

%initial condition

(theta_0) = [0;3];

% time points
(t_span) = linspace(0,20,100);

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

plot(t,result(:,1)
hold on
plot(t,reults(:,2)
ylabel('plot')
xlabel('time')

% EXPLANATION OF COMMAND

1.ode45 is in build command in matlab.

2.ode is function of (time,theta).

3. In the initial stage of program we create a function of dtheta_dt.