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Homework Help: Q factor (Quality Factor)

  1. Apr 12, 2008 #1
    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


    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
  2. jcsd
  3. Apr 12, 2008 #2
    Actually I just figured out another part of the problem. I now think that the units [tex]F_0[/tex] / 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?
  4. Apr 13, 2008 #3
    anybody have any ideas at all?
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