$3\mathrm{.}47.$ Consider the base$-$excitation problem of Section $2\mathrm{.}4$ as applied to an automobile

model of Example $2\mathrm{.}4\mathrm{.}2$ and illustrated in Figure $2\mathrm{.}17.$ Recall that the model is a

spring$-$mass$-$damper system with values m$=1007$kg$,$c$=2000$k$($g$)/($s$),$k$=40,000($N$)/($m$).$

In this problem let the road have a random stationary cross section producing a PSD of

S$\_(0).$ Calculate the PSD of the response and the mean$-$square value of the response.

Figure $2\mathrm{.}21$ A simple model of a vehicle traveling with constant velocity on a

wavy surface that is approximated as a sinusoid$.$