Week 3 - Solving second order ODEs

b = 0.05;
g = 9.81;
l = 1;
m = 1;
% initial contition
theta_0 = [0;3];
% time position
t_span = linspace(0,20,200);
%solveing ode
[t, result] = ode45(@(t,theta) ode_func(t,theta,b,g,l,m),t_span,theta_0);
figure(1)
plot(t,result(:,1))
hold on
plot(t,result(:,2))
legend('displacement','velosity')
xlabel('plot')
ylabel('time')

ct = 1
for i = 1:length(result(:,1));
x0 = 0;
y0 = 0;
x1 = l*sin(result(i,1))
y1 = -l*cos(result(i,1))
figure(2)
plot([-0.5 0.5],[0 0],'linewidth',2,'color','r')
line([x0 x1],[y0 y1],'linewidth',1,'color','k')
hold on
plot(x1,y1,'marker','o','markersize',20, 'markerfacecolor','y')
xlabel('x axis')
ylabel('y axis')
axis([-1.5 1.5 -1.5 1.5])
pause = 0.01
M(ct)=getframe(gcf);
hold off
ct =ct+1
end
movie(M)
videofile = VideoWriter('pandulum_animation.avi')
open(videofile)
writeVideo(videofile,M)
close(videofile)

function used in the above code

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