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Homework Help: Heavily Damped Simple Harmonic System - How To Start?

  1. Mar 23, 2009 #1
    1. The problem statement, all variables and given/known data

    A heavily damped simple harmonic system is displaced a distance F from its equilibrium positio and released from rest. Show that in the expression for the displacement

    [tex]x=e^{-pt}(F\cosh qt + G\sinh qt)[/tex]





    that the ratio


    2. The attempt at a solution

    I've been thinking and thinking and thinking, but no luck. I'd really appreciate it if someone could just tell me where to start.

  2. jcsd
  3. Mar 23, 2009 #2


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    Homework Helper

    hi phyz,

    the differential equation of the damped harmonic oscillator is probably a good place to start...
  4. Mar 24, 2009 #3
    Hi lanedance!

    You mean I should simply calculate xdot and xddot and plug them into



    Let me give it a go :smile:
    Last edited: Mar 24, 2009
  5. Mar 24, 2009 #4


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    Science Advisor

    [tex]x'(t)= -pe^{-pt}(F\cosh qt+ G\sinh qt)+ e^{-pt}(qF\sinh qt+ qG\cosh qt)[/tex]

    Since it is released from rest, we have
    [tex]x'(0)=-pF+ qG= 0[/tex]
    That should be enough.
  6. Mar 26, 2009 #5
    Thank you! That did the trick :smile:
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