Create a MATLAB program to simulate motion of a pendulum in 2-D. The pendulum is
ID: 1842176 • Letter: C
Question
Create a MATLAB program to simulate motion of a pendulum in 2-D. The pendulum is a uniform slender rod with its upper end inertially fixed with a frictionless pin joint. Use Euler integration to solve the equation of motion. The pendulum should have a length of 1 meter and a mass of 5 kg. First, plot and animate the motion of the pendulum for 5 seconds using an initial angle of 40 degrees and initial angular velocity of 0 deg/sec. You will need to determine dt such that the pendulum motion is as expected. Then, vary the time step until the pendulum becomes unstable. Plot and animate the motion. How does this compare to the motion simulated in #1 above? Why does this happen?
Explanation / Answer
solution:
here matlab code is given as follows
displacment or equation of motion is given by
m1=.5*alpha*t^2
alpha=w/t
m1=.5*w*t
it is radian so we get angle in degree by considering initial condition as
m=mo-m1
m=mo-(180/pi)*(w/2)*t
for first half
mo=320
next half
mo=230
matlab code:
clc;
clear all;
close all;
L=input('length of bar');
L1=L/2;
g=9.81;
w=sqrt(g/L1);
T=2*pi*sqrt(L1/g);
for t=0:.001:T/2
mo=320;
m=mo-(180/pi)*(w/2)*t;
end
for t=T/2:.001:T
mo=230;
m=mo+(180/pi)*(w/2)*(t-(T/2));
end
for t=T:.001:3*T/2
mo=320;
m=mo-(180/pi)*(w/2)*(t-T);
end
for t=3*T/2:.001:2*T
mo=230;
m=mo+(180/pi)*(w/2)*(t-(3*T/2));
end
for t=2*T:.001:5*T/2
mo=320;
m=mo-(180/pi)*(w/2)*(t-2*T);
end
for t=5*T/2:.001:3*T
mo=230;
m=mo+(180/pi)*(w/2)*(t-(5*T/2));
end
for t=3*T:.001:7*T/2
mo=320;
m=mo-(180/pi)*(w/2)*(t-3*T);
end
for t=7*T/2:.001:3.524841*T
mo=230;
m=mo+(180/pi)*(w/2)*(t-(7*T/2));
end
plot(t,m)
title('graph')
xlabel('value of time');
ylabel('pendulum position');