Week 3 - Solving second order ODEs

Description:-

ODE is used to decribe the transient behaviour of a system.A simple example is a Pendulum the way the pendulum moves depends on the Newton second law.

Given :-

l = 1 m (length of the Pendulum in m )

m =1 kg (mass of the ball in kg )

b = 0.05 (damping Coefficient )

g = 9.81 (gravity in m/s2)

Program :- 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

ODE_Main :-

clear all
close all
clc

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

%initial condition
theta_0=[-1;1.5];

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

%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')

Error Faced :-

Error in ode_func (line 3)
theta1 = theta(1)