Pendulum

Run The code and wait untill the animation stops and the graph will appear(if you close the animation window in the middle it will cause disturbance to the program).

I have tried to create the movie out of the animation but some error is popping up saying permission is denied. So I have recorded the video using the phone camera and uploaded it to the youtube.

https://youtu.be/KlLRGTeGpG4

clear all 
close all
clc

%given data
g = 9.8;% gravity in m/sec^2
l= 1; %length of the pendulam
m=1; %mass of the ball in kg
b=0.05; %damping co-efficient

%simplifying
k=b/m;
r=g/l;

% simple pendulum ode

f= @(t,x) [x(2);-k*x(2)-r*sin(x(1))];

%initial conditions
y=[0; 3];

%solving the ode. The time interval starts from 0 to 20 seconds
[t,x]=ode45(f,[0 20],y);

% creating the animation of the pendulam

o=[0 0];
axis(gca,\'equal\');
axis([-1.5 1.5 -1.5 0.2]);
grid on;

%loop for animation

for j=1:length(t);
     %mass point
     p=[sin(x(j,1)), -cos(x(j,1))];
     
     %circle origin
     
     origin_circle= viscircles(o,0.01);
     
     %pendulum
     Pendulum= line([o(1) p(1)], [o(2) p(2)]);
     
     %Ball
     ball=viscircles(p,0.05);
     
     %Time interval to update the plot
     pause(0.0001);
     
     %delete the previous object if it is not the final loop
     if j<length(t);
         delete(Pendulum);
         delete(ball);
         delete(origin_circle);
     end
end

%plotting the graph
plot(t,x(:,1));
hold on;
plot(t,x(:,2));
xlabel(\'time(sec)\');
ylabel(\'amplitude\');
legend(\'angle\',\'angular speed\');

This is the graph that laid between the two plots and the time is (0-20) seconds. position is 0 and initial velocity is 3 rad/sec^2 which is 3m/s2 since lenght of pendulum is 1 meter.

plot(1) :- it is the graph between the time and the angular displacement or angle of the pendulum.

Plot(2) :- This graph is between the time and angular speed.