Damped Simple Harmonic Motion problem

  • #1
I'm having trouble with this problem.


The suspension system of a 2100 kg automobile "sags" 7.2 cm when the chassis is placed on it. Also, the oscillation amplitude decreases by 35% each cycle. Estimate the values of (a) the spring constant k and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming each wheel supports 525 kg.
 
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Answers and Replies

  • #2
a) I know that k=mw^2 but dont know where I can get w from.

b)Xe^(-bt/2m)= .65X which breaks down to b=(-2m*ln(.65))/t but I don't know how/if I cant get a t.

Is there something I'm not seeing or am I totally off in my approach?

Any help is appriciated
 
  • #3
nrqed
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davegillmour said:
a) I know that k=mw^2 but dont know where I can get w from.
You can't get omega. The way to do it is to use Hooke's law. You know the distance by which the springs get compressed when the chassis is laid down. The force exerted by the spring at the new equilibrium position must cancel the force exerted by gravity. That will give you k.
b)Xe^(-bt/2m)= .65X which breaks down to b=(-2m*ln(.65))/t but I don't know how/if I cant get a t.

Is there something I'm not seeing or am I totally off in my approach?

Any help is appriciated

The time wil correspond to one period (since it`s after one cycle). Knowing k and m you can find the period.
 

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