$2\mathrm{.}40.$ A machine, modeled as a linear spring$-$mass$-$damper system, is driven at resonance $({}_n==2ra\frac{d}{s}).$ Design a damper $($that is$,$ choose a value of $c)$ such that the maximum deflection at steady state is $0\mathrm{.}05$ m $.$ The machine is modeled as having a stiffness of $2000k\frac{g}{m},$ and the excitation force has a magnitude of $100$ N $.$