Challenge

Week 3 - Solving second order ODEs

AIM : To solve second order ODE programme in which showing motion of pendulum

clear all

close all

clc

% Inputs

b = 0.05

g = 9.81

l = 1

m = 1

OBJECTIVE:

To simulate the motion between 0-20 sec,at time t = 0, angular displacement = 0, angular velocity = 3 rad/sec.

% function

function [dtheta_dt] = ode_fun(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; dtheta_2dt];

end

% main programme

theta_0 = [0;3];

t_span = linspace(0,20,50);

[t,result] = ode45(@(t,theta) ode_fun(t,theta,b,g,l,m),t_span,theta_0)

ct = 1

for 1 = 1:length(result);

x0 = 0;

y0 = 0;

x1 = l*sin(result(i,1));

y1 = l*cos(result(i,1));

figure(1)

plot([-0.5, 0.5],[0,0])

hold on

plot ([x0,x],[y0,y])

hold on

plot(x,y,'marker','.','markersize',50)

axis([-2 2, -2 2])

ct = ct+1,

hold off

end

Ship work like this
in your own course.