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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

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

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