Question $4$:

An automobile is modeled as a single$-$degree$-$of$-$freedom system vibrating in the vertical direction. It is driven along a road whose elevation varies sinusoidally$.$ The distance from peak to trough is $0\mathrm{.}2$ m and the distance along the road between the peaks is $60$ m $.$ If the natural frequency of the automobile is $2$ Hz and the damping ratio of the shock absorbers is $0\mathrm{.}15$ determines the amplitude of vibration of the automobile at a speed of $60k\frac{m}{h}$our. If the speed of the automobile is varied, find the most unfavorable speed for the passengers.