Problem $2[50$ pts$]$

Consider a mass$-$spring$-$damper system where a mass $m$ is attached to a spring with spring

constant $k$ and a damper with a damping coefficient $c.$ The system experiences an external force

$F(t),$ and the mass displacement from its equilibrium position is denoted by $x(t).$

The governing equation for this system is a second$-$order differential equation:

$m\frac{d^{2}x(t)}{d{t}^2}+c\frac{dx(t)}{dt}+kx(t)=F(t)$

Initial Conditions: