Oscillatory motion and Hooke's law

[tarzanna]

Homework Statement

Four people, each with mass of 71.3 kg, are in a car with a mass of 1130 kg. An earthquake strikes. The vertical oscillations of the ground surface make the car bounce up and down on its suspension springs, but the driver manages to pull off the road and stop. When the frequency of the shaking is 1.40 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?

Homework Equations

k=m(2pi*f)^2
x=F/-k
F=ma

The Attempt at a Solution

m=4*71.3 kg + 1130kg = 1415.2kg

1415.2kg (2pi*1.4)^2 = 109505 = k

x=(1415.2kg*9.8m/s^2) / 109505 = 0.127 m

This was not the correct answer. Where am I going wrong? Thank you.

 

[vector3]

Spring constant K look good... however, only 4 people get out of the car and we're removing the weight of the car and the people?

 

[ogb p]

Your approach and equations seem to be correct. However, there may be a few factors that could affect the accuracy of your answer.

Firstly, the maximum amplitude of vibration may not necessarily occur at the same frequency as the frequency of the earthquake (1.40 Hz). It could be slightly higher or lower, which would affect the value of k and ultimately the displacement x.

Secondly, the mass of the car and the people may not be distributed evenly throughout the car. This could affect the calculation of the total mass and consequently the value of k.

Lastly, there may be other external factors such as friction and damping that could affect the oscillatory motion of the car, leading to a different displacement value.

To improve the accuracy of your answer, you could try taking into account these factors and also try using a more precise value for the mass of the car and the people.