Consider an automobile traveling over a rough road at a speed of \(v \mathrm{~km} / \mathrm{hr}\). The suspension system has a spring constant of \(40 \mathrm{kN} / \mathrm{m}\) and a damping ratio of \(\zeta=0.1\). The road surface varies sinusoidally with an amplitude of \(Y=0.05 \mathrm{~m}\) and a wavelength of \(6 \mathrm{~m}\). Write a MATLAB program to find the displacement amplitude of the automobile for the following conditions:

(a) mass of the automobile \(=600 \mathrm{~kg}\) (empty), \(1000 \mathrm{~kg}\) (loaded),

(b) velocity of the automobile \((v)=10 \mathrm{~km} / \mathrm{h}, 50 \mathrm{~km} / \mathrm{h}, 100 \mathrm{~km} / \mathrm{h}\).