A $2\mathrm{.}5$ kg mass oscillates on a spring with a period of $0\mathrm{.}813$s spring constant $0$f $250\mathrm{.}0$ N$/$m$.$ a$)$ Determine the damping constant for the system. $(1)$ b$)$ Determine if the system is undamped, underdamped, critically damped or overdamped. Please explain your reasoning. $(2)$ c$)$ How long will take the system to lose $90\%$ of its initial amplitude? $(1)$ d$)$ How long will take the system to lose $90\%$ of its initial energy? $(1)$