$(15$ points $)$ The mechanical vibration system is shown in following figure $($a$).$ When a step input with $8\mathrm{.}9$ N amplitude is subjected to this system, the movement rule of the mass $m$ is shown in following figure $($b$).$ Evaluate the values of mass $m,$ damping constant $C$ and spring constant $k.$

$($a$)$

$($b$)$