A spring$-$mass$-$damper system returns to its equilibrium position just before it oscillates. The mass is $500kg$ and the spring stiffness is $10K\frac{N}{m}.$

a$.$ Find the damping coefficient $(c)$ of the damper.

b$.$ The system starts motion after $0\mathrm{.}4m$ at a velocity of $-0\mathrm{.}2\frac{m}{s}.$ Find the system displacement after $0\mathrm{.}5sec.$