Problem $2.$ A simple spring$-$mass$-$damper consists of a block with a mass of $150$ kg and negligible size, stiffness of $3000$N$//$m$,$ and damping coefficient of $300$N$.$s$//$m is moved such that the spring is stretched $0\mathrm{.}1$ m beyond its free length and then released from rest. Answer the following questions:

a$.$ Write down the equation of motion for the system. Is the system underdamped,

overdamped or critically damped?

b$.$ Find the critical damping value for the system and the damping ratio of the system.

c$.$ Find the response of the system x$($t$)$

d$.$ Plot x$($t$)$