Speed Programming in Matlab/Octave for non computer science engineers

Programe :-

clear all
close all
clc

% input variable
% g = gravity m/s^2;
% l = length of the pendulum in m;
% m = mass of the ball kg;
% b=damping coefficient;

g=9.81;
l=1;
m=1;
b=0.05;

%initial condition
theta_0=[0;3];

%time points
t_span=linspace(0,20,200);

%solve ode

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

figure(1)
plot(t,results(:,1))
hold on
grid on
plot(t,results(:,2))
xlabel('time')
ylabel('plot')

%plot for animating motion of simple pendulum 
ct=1
for i=1:length(results(:,1))
    x0=0
    y0=0
    x1=1*sin(results(i,1));
    y1=-1*cos(results(i,1));
    figure(2)
    plot([-0.5,0.5],[0,0],'linewidth',3,'color','r');
    line([x0,x1],[y0,y1],'linewidth',2,'color','b');
    hold on
    plot(x1,y1,'o','markers',20,'markerfacecolor','g');
    grid on
    axis([-1.5 1.5 -1.5 0.5]);
    pause(0.01)

    hold off 
    M(ct)=getframe(gcf);
    ct=ct+1;
end

%creating the movie of motion of simple pendulum

movie(M)
videofile=VideoWriter('order_diff_eq.avi','uncompressed AVI');
open(videofile)
writeVideo(videofile,M)
close(videofile)


FUNCTION PROGRAME:-

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;dtheta2_dt];

end

EXPLANATION:-

To create your Second order differential equation by using input variable like damping coeffficient,mass, gravity,length.

condition:-

theta1=theta(1)
theta2=theta(2)
dtheta1_dt=theta2;
dtheta2_dt=(-b/m)*theta2-(g/l)*sin(theta1);
dtheta_dt=[dtheta1_dt;dtheta2_dt];

After that give the initial condition for Displacement and Velocity theta_0=[0;3] .

For time calculation we have to define t_span=linspace(0,20,200).

To solve the second order equation [t,results]=ode45(@(t,theta)ode_fun(t,theta,b,g,l,m),t_span,theta_0);

Then you have to plot the result.

To run the call function we have to create the Function command =>[dtheta_dt]=ode_fun(t,theta,b,g,l,m).

To create the animating motion of simple pendulum first of all we have to plot the figure 2 by using the for loop command .

In for loop command we have to describe like this because the x-axis & y-axis must be plotted over

plot([-0.5,0.5],[0,0],'linewidth',3,'color','r');
line([x0,x1],[y0,y1],'linewidth',2,'color','b');
hold on

The marker command has been used for to create the sphere plot(x1,y1,'o','markers',20,'markerfacecolor','g');

grid on

axis([-1.5 1.5 -1.5 0.5]);
pause(0.01)

Then you have use counter command to figure one by one

After that you have to create the Moviefile then simple pendulum started to movie half 180 degree

movie(M)
videofile=VideoWriter('order_diff_eq.avi','uncompressed AVI');
open(videofile)
writeVideo(videofile,M)
close(videofile)

ERRORS WHILE RUNING THE PROGRAMME :-

NO ERROR

RESULTS:-

Displacement and velocity figure1 :

0 => Displacement in zero

3 => Initial velocity in3m/s

Simple pendulum Figure 2 :-