An automobile, of mass \(1500 \mathrm{~kg}\) when empty and \(2500 \mathrm{~kg}\) fully loaded, vibrates in a vertical direction while traveling at \(100 \mathrm{~km} / \mathrm{h}\) on a rough road having a sinusoidal waveform with an amplitude \(Y \mathrm{~m}\) and a period \(4 \mathrm{~m}\). Assuming that the automobile can be modeled as a singledegree-of-freedom system with stiffness \(5.4 \mathrm{MN} / \mathrm{m}\) and damping ratio \(\zeta=0.2\), determine the amplitude of vibration of the automobile when it is (a) empty and (b) fully loaded.