: Consider a mass$-$spring$-$damper system with displacement and velocity initial

conditions. Derive an expression for its transient response $($or IC response$)$ starting from

the governing equation. Consider the overdamped case. Show all details.

a$)$ Consider M$=5$ kg$,$ K $25$ N$/$m$,$ and damping ratios of z $=1\mathrm{.}1,2,5,10.$ Plot the IC

response of this MSD system to an initial displacement of $25$ mm using

MATLAB all on the same chart.. Comment on your results.

b$)$ Consider M$=5$ kg$,$ K $25$ N$/$m$,$ and damping ratios of z $=1\mathrm{.}1,2,5,10.$ Plot the IC

response of this MSD system to an initial velocity of $0\mathrm{.}5$ m$/$s using MATLAB all

on the same chart. Comment on your results.