A $0\mathrm{.}40-kg$ mass is attached to one end of a spring with a force constant of $300\mathrm{.}0\frac{N}{m}$ and the other end of the spring is affixed to a nearby wall. The mass$-$spring system is in oscillatory motion on a horizontal, frictionless surface. A damping force, $F_x=-bv,$ acts on the mass.

$($a$)$ If $b=5\mathrm{.}00k\frac{g}{sec},$ calculate the resultant frequency of oscillation of the system.

$($b$)$ Given the other parameters of the system, compute the required value of $b$ for the system to exhibit Critical Damping.