Vibrations $-$ Introductory Problem Set

For the mass$-$dashpot$-$spring systems listed below, determine whether the system is overdamped, critically$-$damped, or underdamped. Then draw a qualitative picture of how the system returns back to its equilibrium position from an initial displacement. $($the effect of gravity is negligible$)$

a$.,m=1kg,k=1\frac{(N)}{(m)},c=0\mathrm{.}1\frac{Ns}{m}$

b$.m=1kg,k=1\frac{(N)}{(m)},c=10\frac{Ns}{m}$

c$.,m=1kg,k=1\frac{(N)}{(m)},c=2\frac{Ns}{m}$