A springmassdamper system has k 65 Nm m 75 kg and c 3 Nsm

A spring-mass-damper system has k = 65 N/m, m = 7.5 kg and c = 3 N-s/m. If a harmonic force with an amplitude of 1 Newton is applied to the mass, plot in Matlab the amplitudes of

a)the steady-state displacement,

b)velocity, and

c)acceleration as a function of the driving frequency for 0 < < 10 rad/s. Include a Matlab code and plots. Use proper labels for your plots.

Solution

% Single DOF spring mass damper system
k = 65;
m = 7.5;
c = 3;
F0 = 1;
Fr = 0:0.01:10;
NatFr = sqrt(k/m);
omega = Fr/NatFr;
zeta = c/sqrt(2*k*m);

X0 = (F0/k)./(sqrt((1-omega.^2).^2+(2*zeta.*omega).^2));
%phi = atan((2*zeta.*omega)./(1-omega.^2));
V0 = -Fr.*X0;
a0 = -(Fr.^2).*X0;
figure(1)
plot(Fr,X0,\'linewidth\',2);
title(\'Displacement Amplitude\')
xlabel(\'\\omega/\\omega0\')
ylabel(\'Displacement (m)\')
grid on
figure(2)
plot(Fr,V0,\'linewidth\',2);
title(\'Velocity Amplitude\')
xlabel(\'\\omega/\\omega0\')
ylabel(\'Velocity (m/s)\')
grid on
figure(3)
plot(Fr,a0,\'linewidth\',2);
title(\'Acceleration Amplitude\')
xlabel(\'\\omega/\\omega0\')
ylabel(\'Acceleration (m/s^2)\')
grid on