A motorcycle travels over a road whose contour is approximately sinusoidal, \(y(z)=0.2 \sin (0.4 z) \mathrm{m}\) where \(z\) is measured in meters. Using a SDOF model, design a suspension system with a damping ratio of 0.1 such that the acceleration felt by the rider is less than \(15 \mathrm{~m} / \mathrm{s}^{2}\) at all horizontal speeds between 30 and \(80 \mathrm{~m} / \mathrm{s}\). The mass of the motorcycle and the rider is \(225 \mathrm{~kg}\).