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Energy lost in a lightly damped osciallator

  1. Sep 1, 2008 #1
    Qn2

    The amplitude of a lightly damped osciallator decreases by 3% during each cycle of oscillation. What fraction of the energy is lost in each cycle?

    Okay..i couldnt find anything about energy in the damped oscillation is my textbook..

    but in SHM sections. it showed that

    Energy of the SHM system = (1/2)kAsquare

    where A is the amplitude and k is the coefficient for the spring..

    but for lightly damped osciallator...the Energy of the SHM will change for every cycle..in this case, it will drop by 3%...

    i know that the period for every cycle is the same but only the amplitude will change.

    here is my guess...

    Energy of the SHM system = (1/2)kAsquare -----------> first cycle

    Energy of the SHM system = (1/2)k(A*0.97)square -----------> second cycle

    Energy lost = (1/2)kAsquare - (1/2)k(A*0.97)square ----------> difference

    Fraction of energy lost = difference/(1/2)kAsquare

    am i right here?...i am a feeling i am wrong..but dun know how to aprroach this..
     
  2. jcsd
  3. Sep 1, 2008 #2

    tiny-tim

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    Hi hemetite! :smile:

    (have a squared: ² :wink:)

    I haven't checked whether your formula (1/2)kA² is right, but assuming it is …

    yes, that's fine! (though a bit long-winded :wink:) … now divide everything by (1/2)kA², and the result is … ? :smile:
     
  4. Sep 1, 2008 #3
    ..well...i am new here...i worry if i never explained thouroughly...you guys wont help me...hahaha...

    anyway...here goes

    =[(1/2)kA² - (1/2)k(0.97A)²] / [(1/2)kA²]

    = 0.0591

    should be correct now...
     
  5. Sep 1, 2008 #4

    tiny-tim

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    Sure is! :biggrin:
     
  6. Sep 1, 2008 #5
    hahaha....man ..i love this forum..

    people here are helpful and funny...
     
  7. Sep 1, 2008 #6

    tiny-tim

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    oi!
    :biggrin: so are the fish! :biggrin:
     
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