Week 3 - Solving second order ODEs

Solving Second Order ODEs

Explanation

It ha 2odes

1. Initial Displacement

2. Initial Velocity

The ode45 is an inbuilt solver in matlab

Then ode_function represent the function that create on an new window with matlab function represent the time,theta, b,length,,mass,gravity .

The function takes place on the ode_func tab with including all formulas

Then finally the graph takes place .

close all
clear all
clc

b=0.05;
g=9.81;
l=1;
m=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);

%Plotting
plot(t,results(:,1))
hold on
plot(t,results(:,2))
xlabel('Time')
ylabel('Plot')
grid on

ODE_FUNC Tab
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