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A vehicle of mass 1200 kg is travelling on a road the surface of which varies sinusoidally with an amplitude of 0.05m and wave length of 6m.
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The suspension system has a spring const of 400 KN/m and a damping ratio of 0.50. If the vehicle speed is 100 km/hr Find the amp of the vehicle.

M = 1200 kg

Y = 0.05 m

$\lambda$ = 6m

$k = 400 \ \frac{KN}{m} = 400 \ \times 10^3 \ \frac{N}{m}$

$\xi = 0.50$

$V = 100 \ \frac{km}{hr} \ = \ \frac{100 \times 10^3}{3600} \ \frac{m}{sec} \ = \ 27.77 \ \frac{m}{s}$

$w = 2 \pi f$

$= 2 \pi \times \frac{v}{\lambda }$

$= 2 \times \pi \times \frac{27.77}{6} = 29/08$ r/s

$w_n = \sqrt{ \frac{k}{m}}$

$= \sqrt{ \frac{400 \times 10^3}{1200}} = 18.25$ r/s

$r = \frac{w}{W_n} = 1.59$

$\frac{x}{y} = \frac{\sqrt{ 1 + (2 \xi r)^2}}{\sqrt{(1-r^2)^2 + (2 \xi r)^2}}$

X = 0.042m

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