Consider the simplified model for a mechanical system given in the figure on the right. Consider this two$-$degree$-$of$-$freedom system with k$1=1,000$ N$/$m$,$ k$2=10,000$ N$/$m$,$ m$1=2,000$ kg$,$ m$2=50$ kg$,$ Suppose an impact on the system modeled as the initial conditions zero initial conditions except for an initial velocity of $0\mathrm{.}1$ m$/$s in mass $($m$2).$ Determine the response of the system using mode shape and modal analysis approach. $(50$ points$)$