Week 3 - Solving second order ODEs

Theory:The main purpose of second order odes is used to help solve various problems in real life like calculating the velocity of a simple pendulum,spring mass and damper system. Moreover, real life applications based on spring, mass and damper systems can be further applied to modelling component systems in automotives.
Equations for second order odes:
1.θ=θ1
2.dθ/dt=dθ1/dt=θ2

3.d2θ/dt2=d2θ1/dt2=d/dt(dθ1/dt)=d/dt(θ2)

4.d2θ/dt2+(b/m)(dθ/dt)+(g/l)sinθ=0

5.d2θ1/dt2+(b/m)θ2+g/lsinθ1

6.dθ2/dt+(b/m)θ2+(g/l)sinθ1
7. b=damping;m=mass;g=gravity;l=length
Diagram:

Simple pendulum:

Code
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')

Code for 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

Output graph