(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The logarithmic decrement δ of a lightly damped oscillator is defined to be the natural logarithm of the ratio of successive maximum displacements (in the same direction) of a free damped oscillator. That is, δ = ln(An/An+1) where An is the maximum displacement of the n-th cycle. Derive the simple relationship between δ and Q.

Find the spring constant k and damping constant b of a damped oscillator with mass m, frequency of oscillation f and logarithmic decrement δ.

[Data: m = 4.0 kg; f = 0.9 Hz; δ = 0.029.]

First, the spring constant k...

Also, the damping constant b...

2. Relevant equations

[itex]\beta[/itex]=b/(2m)

Q=[itex]\omega_{o}/(2\beta)

3. The attempt at a solution

Given the diff eq:

d^{2}x/dt^{2}+2[itex]\beta[/itex](dx/dt)+[itex]\omega[/itex]_{o}^{2}x=0

I can solve this to find x(t), however I feel this is irrelevant because no initial condition or boundary conditions are given, so I am kinda lost here as to where go or to start at for that matter. Any suggestions are greatly appreciated, Thanks

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Logarithmic decrement of a lightly damped oscillator

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