Three people, each with a mass of 72.9 kg, are in a car with a mass of 1190 kg.

Question

Three people, each with a mass of 72.9 kg, are in a car with a mass of 1190 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 1.40 Hz, the car exhibits a maximum amplitude of vibration. The earthquake ends and the three 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

The natural frequency of the loaded car must be f =1.4 Hz. That gives us (2*pi*f)^2 = k/(M+m), where m is the sum of the masses of the 3 men. 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] gives, delta_x = 0.107 m so, distance that the car's undamaged suspension lift the car's body as the people get out = 0.107 m

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