Mass$-$Spring$-$Damper System:

a$)$ For a mass$-$spring$-$damper system where the mass $m,$ spring constant

$k,$ and damping coefficient $c$ are given, derive the system of linear first

order ordinary differential equation for the displacement $x(t).$

b$)$ If $m=2kg,k=10\frac{N}{m},$ and $c=1N\frac{s}{m}.$ By means of matrix

and Laplace transform methods, determine the system's displacement and velocity.