Week 3 - Solving second order ODEs

b=0.05;

l=1;

m=1;

g=9.81;

%intialcondition

theta_0=[0;5];

%timepoints

t_span=linspace(0,10,400);

%solveode

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

figure(1)

plot(t,results(:,1))

hold on

plot(t,results(:,2))

ylabel('plot')

xlabel('time')

%animation

x0=0;

y0=0;

ct=1;

for i=1:length(t)

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

y1=-l*cos(results(i,1));

figure(2)

plot([-1 1],[0 0],'linewidth',6,'Color','r');

axis([-2 2 -2 2])

line([x0 x1],[y0 y1],'linewidth',4,'color','r');

hold on

plot(x0,y0);

plot(x1,y1);

title('damping of a simple pendulum')

grid on

hold off

M(ct)=getframe(gcf);

ct=ct+1;

end

movie(M);

videofile = VideoWriter('simple_pendulum.AVI','Uncompressed AVI')

open(videofile)

writeVideo(videofile,M)

close(videofile)

function[dtheta_dt]=ode_function(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

I faced a problem in the animation of the simple pendulim but i rectified the mistake which was i typed hold on instead of hold off.

the ode_2.m file contains the main code

the ode_function.m contains the function code

the ode_3.fig contains the frequency curve

the simple_pendulum.AVI.zip contains the animation of the damping of the pendulum