A machine with a mass of (30 mathrm{~kg}) is mounted on springs with an equivalent stiffness of

Question:

A machine with a mass of $30 \mathrm{~kg}$ is mounted on springs with an equivalent stiffness of $4.8 \times 10^{4} \mathrm{~N} / \mathrm{m}$. During operation, it is subject to a force of $200 \sin \omega t$. Determine and plot the response of the system if the machine is at rest in equilibrium when the forcing starts and at

(a) $\omega=20 \mathrm{rad} / \mathrm{s}$,

(b) $\omega=40 \mathrm{rad} / \mathrm{s}$, and

(c) $\omega=41 \mathrm{rad} / \mathrm{s}$.