Example A mechanical system consists of a mass $($m$)$ of $3$ kg$,$ a spring with stiffness $($k$)$ of $600$N $/$ m $,$ and a damper with damping coefficient $($c$)$ of $15$Ns $/$ m $.$ When the system is subjected to an initial displacement of $0.$ Im$,$ determine the displacement of the mass at time t $=0\mathrm{.}25$ s $.$