Week 3 - Solving second order ODEs

AIM - TO SIMULATE THE TRANSIENT BEHAVIOUR OF A SIMPLE PENDULUM BY USING MATLAB

% Programe for trnsient behavior of a simple pendulum by using second

% oreder ODE equation

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

close all

clear all

clc

% INPUTS

l=1; [ % length of the pendulum m]

m=1; [% mass of the ball kg]

b=0.05; [ % damping coefficent]

g=9.81; [ % accelration due to gravity]

ct=1;

% Initial conditions

theta_x = [0;3];[ % angular displacement]

t_span = linspace(0,20,300); [% time span]

% solution [ Byusing ODE45 FUNCTION]

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

% plot 1

figure(1)

plot(t,results(:,1),'LineWidth',3)

hold on

plot(t,results(:,2),"LineWidth",3)

xlabel('angular displacement (rad) / angular velocity(rad/sec)')

ylabel ('time (sec)')

title (' transient behaviour of a simple pendulum')

legend('angular displacement,angular velocity')

grid on

for i= 1:length(t_span)

j= results(i,1);

x0 = 0;

y0 = 0;

x1 = l*sin(j);

y1 = -l*cos(j);

% plot 2

figure(2)

plot([-1 1],[0 0],'Linewidth',4,'color','g')

hold on

plot([x0 x1],[y0 y1],'LineWidth',3,'Color','b')

plot([0 0],[0 -1],'LineWidth',2,'Color','r')

plot(x1,y1,'Marker','o','MarkerSize',15,'MarkerFaceColor','r')

xlabel('X-axis (m)')

ylabel('Y-axis (m)')

grid on

axis ([-2 2 -1.5 0.5])

pause(0.03)

ct=ct+1;

M(ct)= getframe(gcf);

end

movie(M);

videofile = VideoWriter('Simple Pendulum Motion.avi','Uncompressed AVI');

[ https://drive.google.com/file/d/1KWPzC6w5eQN7zdMAJfto9UgvRu89zj3f/view?usp=sharing]

The line daigram for the SIMPLE PENDULUM are

The Angular VELOCITY and Angular DISPLACEMENT are

In the running the code i am facing several errors , the errors are shown by the command window ,

then the errors are

these error is i am gives the incorrect mismatched variables , untill solve the error is correctly and next i am facing another error are

i am facing the above errors while write the programming and what i am doing my mistake and clearly by find out by using command window ,

THE WORK SPACE IS

CONCULTION

1- IN the make code for running pendulum by the use of ode eqation [ d^2(theta)/dt^2 + b/m*d(theta)/dt +g/lsin(theta) =0

2- these the equation which is used to find the ODE

[t,results]= ODE45(@(t,theta)ode_func(t,theta,b,g,l,m),t_span,theta_0)

the above equations which are used to make the plots .

The ANIMATION OF SIMPLE PENDULUM LINK AS GIVEN BELOW

%[https://drive.google.com/file/d/1KWPzC6w5eQN7zdMAJfto9UgvRu89zj3f/view?usp=sharing]