Week 4.1 - Solving second order ODEs

MAIN CODE

%clear all is clear all variables in the current workspace
%close all is for closing figures which are open
%clc is for clearing text in command window
clear all
close all
clc

%Damping coefficient
b = 0.05;
%Gravity
g = 9.81;
%Length of the pendullum
l = 1;
%Mass
m = 0.1;

%Initial conditions
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
plot(t,results(:,1))
hold on
plot(t,results(:,2))
xlabel('Plot')
ylabel('time')

ERROR

ode45 is an inbuilt function in matlab

define ode function by a seperate matlab function

FUNCTION TO SOLVE ERROR

ode_func is the name of ode function definition

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/1)*sin(theta1);
     dtheta_dt = [dtheta1_dt; dtheta2_dt];
end

PLOT