Four people, each with a mass of 72.1 kg, are in a car with a mass of 1120 kg. A

Question

Four people, each with a mass of 72.1 kg, are in a car with a mass of 1120 kg. An earthquake strikes. The driver manages to pull of the road and stop, as the vertical oscillations of the ground surface make the car bounce up and down on its suspension springs. When the frequency of the shaking is 1.70 Hz, the car exhibits a maximum amplitude of vibration. The earthquake ends and the four people leave the car as fast as they can. By what distance does the car's undamaged suspension lift the car's body as the people get out? cm

Explanation / Answer

total mass
mtotal = 4*72.1+1120 =1408.4kg
and use
f = (1/2)(K/m)
(K/m) =42f2

K =4m2f2 =4*1408.4*2*1.72 =160,688 N/m

Force due to 4 persons

F=mg =4*72.1*9.8=2826.32 N

and force due to compression of spring equals force due to 4 persons so

F=Kx

x=F/K =2826.32/160688 =0.0176m or 17.6mm

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