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 \(0.2 \mathrm{~m}\) and the distance along the road between the peaks is \(35 \mathrm{~m}\). If the natural frequency of the automobile is \(2 \mathrm{~Hz}\) and the damping ratio of the shock absorbers is 0.15, determine the amplitude of vibration of the automobile at a speed of \(60 \mathrm{~km} / \mathrm{hour}\). If the speed of the automobile is varied, find the most unfavorable speed for the passengers.