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Extrapolating the Quality factor for decay in amplitudes

  1. Sep 17, 2014 #1
    1. The problem statement, all variables and given/known data
    By what factor does the amplitude decay in the time interval (which I had to find).

    E: stored energy
    γ:damping rate
    a: amplitude
    t: time
    Q: quality factor
    T:Period
    ω: frequency

    2. Relevant equations

    Q = 2∏E/(ΔE)

    3. The attempt at a solution
    I found the interval to be t=QT
    but "one cycle" indicates T=2∏?

    So I'm not exactly sure if I got the right answer for the quality factor by which the quality factor decays? I feel like there is supposed to be a numerical answer. Any insights? Did I mess up anywhere or took the wrong approach? Anything will help!

    Thanks!
     

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    Last edited: Sep 17, 2014
  2. jcsd
  3. Sep 17, 2014 #2

    BvU

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    Suppose the amplitude decays by a factor of 2 in a certain interval. What does that mean for the stored energy ?

    Vice versa yields your answer without much effort !

    [edit] In fact your answer can be made to look more attractive if you realize that ##\omega T = 2\pi## :smile:
     
    Last edited: Sep 17, 2014
  4. Sep 17, 2014 #3


    It would lose half of it's stored energy?
     
    Last edited: Sep 17, 2014
  5. Sep 17, 2014 #4

    BvU

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    Nope.
     
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