Distance Lifted by Car Suspensions in Earthquake

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    Car Earthquake
AI Thread Summary
The discussion revolves around calculating the distance a car's undamaged suspensions lift the body when four passengers exit during an earthquake. The car, with a total mass of 1419.6 kg, experiences vertical oscillations at a frequency of 1.8 Hz, resulting in maximum amplitude of vibration. The user attempts to apply concepts of forced and simple harmonic oscillation to derive the displacement of the car body. They express confusion over the equations and calculations, particularly regarding the relationship between acceleration, displacement, and the effects of the passengers exiting quickly. The user seeks clarification and hints to simplify the problem-solving process.
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Homework Statement


4people with uniform mass= 72.4kg
car mass= 1130kg
earthquake strikes,car is stationary.
vertical oscillations make car bonuce on suspensions.
when frequency= 1.8 Hz car exhibits maximum Amplitude of vibration.
Earthquake over,4 people leave the car quickly,what distance does the cars undamaged suspensions lift the car body as the people get out?



Homework Equations


sorry I am new to this i don't understand what this section wants


The Attempt at a Solution



i took this as a forced oscillation and as a simple harmonic oscillation.
total mass = 1419.6 kg
Velcoity = 3.6*pi*Amax (Amax=max amplitude)
this comes from Vel=omega*Amax
omega=2*pi*Frequency

Acceleration = 2Amax/period
i don't know i thought this one up...
as max displacement= Amax + A max
and time taken => period = 1/frequency...

Acc= 3.6 Amax

x=displacement of car body by suspension...

x=Asin(omega*t)
x'=A*omega*sin(omega*t)
x''= - omega^2 *(x)

...
3,6Amax = -(2*pi*1.8)^2 *x

=> x= - 0.028*Amax

my head is exploding someone please give me some hint...i have an awful feeling that this could be a lot easier...

fiendishly difficult differential equations are suspected but I'm not sure how to relate everything...its kinda late here in Ireland!please have some pity...
 
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I just thought that since they left the car quickly then t must be tending towards zero...?
right track?
 

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