(Solved): Consider the spring-mass-dashpot system shown in Figure. Assume that the displacement u of point P ...

Consider the spring-mass-dashpot system shown in Figure. Assume that the displacement $u$ of point $P$ is the input to the system. Assume also that the input $u(t)$ is a small bump, as shown in Figure. Obtain the response $y(t)$ of the mass $m$. The displacement $y$ is measured from the equilibrium position in the absence of the input $u(t)$. To obtain the response curve, assume that $m=100\mathrm{kg},b=400\mathrm{N}?\mathrm{s}/\mathrm{m}$, and $k=800\mathrm{N}/\mathrm{m}$.