Damped Simple Harmonic Motion problem

AI Thread Summary
To solve the damped simple harmonic motion problem, the spring constant k can be determined using Hooke's law, where the force exerted by the spring at the new equilibrium position equals the gravitational force acting on the chassis. The compression of the spring when the chassis is placed on it provides the necessary information to calculate k. For the damping constant b, it can be derived from the equation Xe^(-bt/2m)=0.65X, where the time t corresponds to one complete oscillation period, which can be calculated once k and m are known. The discussion emphasizes the importance of understanding the relationship between the spring's compression and the forces involved to find the required constants. Overall, the approach involves applying fundamental physics principles to derive the necessary values.
davegillmour
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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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a) I know that k=mw^2 but don't 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 can't get a t.

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

Any help is appriciated
 
davegillmour said:
a) I know that k=mw^2 but don't 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 can't 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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