Oscillatory motion and Hooke's law

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SUMMARY

The discussion centers on calculating the vertical oscillation of a car's suspension system during an earthquake, specifically using Hooke's Law. The total mass of the system is 1415.2 kg, and the spring constant (k) is calculated to be 109505 N/m based on a frequency of 1.40 Hz. The user attempts to find the displacement (x) of the car's body as the four passengers exit, resulting in a calculated lift of 0.127 m. The user questions the accuracy of their calculations, particularly regarding the weight consideration of the car and passengers.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Knowledge of oscillatory motion and frequency calculations
  • Familiarity with Newton's second law (F=ma)
  • Basic algebra for solving equations
NEXT STEPS
  • Review the derivation and application of Hooke's Law in oscillatory systems
  • Study the effects of mass changes on spring displacement in dynamic systems
  • Learn about the relationship between frequency and amplitude in oscillatory motion
  • Explore advanced concepts in mechanical vibrations and damping effects
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Physics students, mechanical engineers, and anyone studying dynamics and oscillatory motion in mechanical systems.

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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.
 
Physics news on Phys.org
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?
 

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