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Overdamped oscillator solution as hyperbolic function?

  1. Apr 4, 2017 #1
    1. The problem statement, all variables and given/known data
    Here is the equation for the general solution of an overdamped harmonic oscillator:
    x(t) = e-βt(C1eωt+C2e-ωt)

    2. Relevant equations
    β decay constant
    C1, C2 constants
    ω frequency
    t time

    3. The attempt at a solution
    I know (eωt+e-ωt)/2 = coshωt and (eωt-e-ωt)/2 = sinhωt but how do I implement this if there are constants? I tried to solve for the constants, but I just get a nasty expression in terms of x(o) and v(0) for each C (where v is the velocity) and this doesn't help with rewriting the functions.
     
  2. jcsd
  3. Apr 4, 2017 #2

    ehild

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    Gold Member

    Write eωt and e-ωt in terms of the hyperbolic functions cosh(ωt) and sinh(ωt).
     
  4. Apr 5, 2017 #3
    Yes I know that is the goal but how do I do it if there are two constants that are different in front of each e term?
     
  5. Apr 5, 2017 #4
    Nevermind I did it
     
  6. Apr 5, 2017 #5
    Thank you
     
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