A boy riding a bicycle can be modeled as a spring-mass-damper system with an equivalent weight, stiffness, and damping constant of \(800 \mathrm{~N}, 50,000 \mathrm{~N} / \mathrm{m}\), and \(1000 \mathrm{~N}-\mathrm{s} / \mathrm{m}\), respectively. The differential setting of the concrete blocks on the road caused the level surface to decrease suddenly, as indicated in Fig. 2.116. If the speed of the bicycle is \(5 \mathrm{~m} / \mathrm{s}(18 \mathrm{~km} / \mathrm{hr})\), determine the displacement of the boy in the vertical direction. Assume that the bicycle is free of vertical vibration before encountering the step change in the vertical displacement.

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Kea v Coq t=0 A 10 m 5 cm FIGURE 2.116 Bicycle on uneven concrete blocks. 15 m t=3s B C. 1'= 0 10 m