Four people, each with a mass of 73.9 kg, are in a car with a mass of 1110 kg. A

Question

Four people, each with a mass of 73.9 kg, are in a car with a mass of 1110 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 1.50 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?

Explanation / Answer

When the driving frequency was f=1.5 Hz, there was resonance, which means w^2= k/m (2*pi*f)^2 = k/(M+m), where m is the sum of the masses of the four men. m=295.6kg M=1110kg Suppose x1 is the compression when the load is M+m, and x2 when load is M. Then, (M+m)g – mg = k(x2-x1) => Mg = k*delta_x => delta_x = Mg/[(M+m)(2*pi*f)^2]. delta_x=0.092m

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