The suspension system of a car traveling on a bumpy road has a stiffness of and the effective mass of the car on the suspension is m=750kg. The road bumps can be considered to be periodic half- sine waves as indicated in Figure. Determine the displacement response of the car. Assume the damping of the system to be negligible.

: The Fourier series representation of the bumpy road, y(t), is given by

y(t)=\frac{1}{\pi}+\frac{1}{2}sin~2\pi t-\frac{2}{\pi}\{\frac{cos~4\pi t}{1(3)}+\frac{cos~8\pi t}{3(5)}+\frac{cos~12\pi t}{5(7)}+\cdot\cdot\cdot\}

x(t)

t(time)

7777

J_{f}

m

(20 marks)

8^{k}

y(t)

hann