Question

Using a mathematical software (MATLAB, MAPLE, and etc) plot the free and forced vibration response of a viscously damped system (x(t), dx(t)/dt, d2x(t)/dt2) with m=4kg, k=2500 N/m, x0=100 mm, v0=-10 m/s, Δt=[0,0.01], [0,1], and [0,10] for the following values. Also determine the nature of the system (un-damped, under damped, critically damped, and over damped). (5 marks) a. c=0, F=100 sinωt (ω=20,25,30)

Answer 1

`Hey,

Note: Brother if you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

clear all

clc

close all

m=4;

k=2500;

w=[20,25,30];

for i=1:length(w)

figure;

f=@(t,y) [y(2);(100*sin(w(i)*t)-k*y(1))/m];

[T,Y]=ode45(f,[0,0.01],[100,-10]);

plot(T,Y(:,1),T,Y(:,2));

legend('x(t)','dx/dt');

s=sprintf('For w=%d',w(i));

title(s);

figure;

f=@(t,y) [y(2);(100*sin(w(i)*t)-k*y(1))/m];

[T,Y]=ode45(f,[0,1],[100,-10]);

plot(T,Y(:,1),T,Y(:,2));

legend('x(t)','dx/dt');

s=sprintf('For w=%d',w(i));

title(s);

figure;

f=@(t,y) [y(2);(100*sin(w(i)*t)-k*y(1))/m];

[T,Y]=ode45(f,[0,10],[100,-10]);

plot(T,Y(:,1),T,Y(:,2));

legend('x(t)','dx/dt');

s=sprintf('For w=%d',w(i));

title(s);

end

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Kindly revert for any queries

Thanks.