Week 3 - Solving second order ODEs

Aim :- To find second order eqation in simple harmonic motion of simple pendulum

Introduction:-

in second order ode

((d^2theta/dt^2)+(b/m)*(dtheta/dt)+(g/l)*sin_theta)=0

code:-

clear all

close all

clc

b = 0.05;

g = 9.81;

l = 1;

m = 1;

% initial condition

theta_0 = [0;3];

% time points

t_span = linspace(0,10,20);

% solve ODE

[t,results] = ode45(@(t,theta) sode(t,theta, b,g,l,m),t_span,theta_0);

plot(t,results(:,1))

hold on

plot(t,results(:,2))

% To defined pivot point of pendulum and plot it.

x0 = 0;

y0 = 0;

plot(x0,y0,'marker','o')

% to extract the first column of result and assigned it to y

y = results(:,1); % Theta/Angular displacement

% to create image for each time value and stored it in array 'M'

ct = 1;

for i=1:length(t_span) % i=1,2,3,,,,,,500

x1 = 1*sin(y(i));

y1 = -1*cos(y(i));

plot([x0,x1],[y0,y1],'linewidth',3,'marker','o')

hold on

plot(x1,y1,'marker','o','color','g','markersize',30,'markerfacecolor','g')

hold off

title({'Simple harmonic motion';'of a pendulum'}, 'color','r')

axis([-1 1 -2 0])

pause(0.03)

M(ct)= getframe(gcf);

ct=ct+1;

end

% To create animation of S.H.M of simple pendulum

movie(M)

videofile = VideoWriter('pendulum.avi','Uncompressed AVI');

open(videofile)

writeVideo(videofile,M)

close(videofile)

Outputs:-

Animation of simple pendulum:-

https://drive.google.com/file/d/1kLyfVue0RBV9ABikmV8pzoW6eFYCwv9G/view?usp=sharing