A standard mass$-$spring$-$damper system is subjected to the harmonic $($sinusoidal$)$ excitation force $\backslash ($ f$($t$)\backslash )$ with amplitude $100$ N $.$ The system mass $\backslash ($ M$=5\backslash$mathrm$\{$~kg$\}\backslash ).$ When the excitation frequency is $2\mathrm{.}5$ Hz $,$ the $($steady$-$state$)$ vibration displacement amplitude is $82\mathrm{.}3$ mm ; when the excitation frequency increases to $5$ Hz $,$ the displacement amplitude is $28\mathrm{.}7$ mm $.$ Determine the stiffness $\backslash ($ k $\backslash )$ and damping coefficient $\backslash ($ c $\backslash )$ of the system.

$[$Solve it algebraically and show all work. Pay attention to the units.$]$