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Damped Oscillator Equation

  1. Dec 8, 2012 #1
    the damped oscillator equation:

    (m)y''(t) + (v)y'(t) +(k)y(t)=0

    Show that the energy of the system given by

    E=(1/2)mx'² + (1/2)kx²

    satisfies:

    dE/dt = -mvx'


    i have gone through this several time simply differentiating the expression for E wrt and i end up with

    dE/dt = x'(-vx')

    im at a brick wall. Am i doing something wrong? Any help is much appreciated! Thanks
     
  2. jcsd
  3. Dec 8, 2012 #2
    I have also assumed that y and x are interchangeable variables here, as no other information has been provided
     
  4. Dec 8, 2012 #3

    Mute

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    I don't see anything wrong with your calculation. In fact, double check the units for your expressions - I don't think the suggested answer "##m\gamma \dot{x}##" even has the same units as ##dE/dt##.
     
  5. Dec 9, 2012 #4

    pasmith

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    That must be wrong: it requires that [itex]E = C - mvx[/itex] for some constant C, which is not the case.

    That is the right expression for dE/dt.
     
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