Hi I need help with the following question and I do not know where to start. Fou

Question

Hi I need help with the following question and I do not know where to start.

Four people, each with a mass of 72.3 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 1.60 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

mass of the system m =4*72.3kg+1110 kg =1399.2 kg
frequency f =1.6 Hz
frequency f =(1/2p)sq.root (k/m) force constant k =4p^2f^2 m=1.41 *10^5 N/m total force F =-kx ..... (1) and force F =mg ..... (2) compare (1) and (2),we get mg =-kx x =mg/-k =-[(1399.2 kg)(9.8 m/s^2)]/(1.41 *10^5 N/m)=9.72*10^-5 m

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