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## Q factor (Quality Factor)

1. The problem statement, all variables and given/known data
The amplitude of a driven harmonic oscillator reaches a value of 20.0 F_0 /m at a resonant frequency of 390 Hz.
What is the Q value of this system?

Since our Professor accidentally gave us the problem set from a different book instead of the one we have, and the one we have makes no mention of Q, the only introduction I have to Q value is a few sentences near the end of class, and it is just confusing me to no end.

2. Relevant equations
Okay, so as far as I know, Q value is equal to the resonant frequency (w_0) over the width of the resonance. I have several equations relating q to nu (v) and the resonant frequency:

Q = (resonant frequency)/(width of resonance)

Q = (w_0/ v) where v is nu

and

width of resonance at K = Kmax/sqrt(2) = W

3. The attempt at a solution
The main trouble I am having with this problem is trying to figure out how to use the two units given to convert and insert them into the equations I was given. I have assumed that the resonant frequency of 390 Hz was equal to w_0. After this, I have tried several methods to get the final answer:

At first I attempted to insert 390 into w_0 and 20 F_0/m into v and find Q that way.
This resulted in Q = (w_0/v) = 19.5, which was incorrect, and the units are probably off (since Q is unitless)

After this, I tried to use the equation where width = Kmax/sqrt(2). I substituted 20 F_0/m into Kmax and got a width of 14.142 F_0/m. I then substituted this value into the Q equation where: Q = (390 Hz / 14.142 F_0/m) = 27.577, which is incorrect, and again I am pretty sure that my units are off.

After this, I had only two more chances to answer the question so I have just been searching for how to convert the Amplitude given into a width of resonance with no success. Can anybody help me go through the process of converting the two values given into values that I can use in the Q equation?

Thank you to anyone who replies

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Actually I just figured out another part of the problem.  I now think that the units $$F_0$$ / m are actually values themselves represented by variables.   F0  	 = maximum driving force  and m is the mass of the object.  This just means that now I think I have to find a way to take this amplitude and plug it into something that gives me the range of resonance frequency values to divide the resonant frequency by.  Anyone have any idea how I would go about doing that?

anybody have any ideas at all?

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