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Maximum speed of overdamped oscillator without crossing origin

  1. Oct 3, 2012 #1
    1. The problem statement, all variables and given/known data
    An overdamped oscillator with natural frequency w and damping coefficient g starts out at postion x0 > 0. What is the maximum initial speed towards the origin it can have without crossing the origin?


    2. Relevant equations
    x(t) for overdamped oscillator


    3. The attempt at a solution
    x(t) for a general overdamped oscillator has been solved already. However if I only know x0 > 0 and nothing else, how do I go about determining the maximum speed. I can't see how this problem will workout and I can't get it started. Thanks for any help
     
  2. jcsd
  3. Oct 3, 2012 #2

    tiny-tim

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    Hi MeMoses! :smile:
    Just find the answer as a function of xo :wink:
     
  4. Oct 3, 2012 #3
    Edit: My idea made no sense. So how do find this maximum v0?
     
    Last edited: Oct 3, 2012
  5. Oct 3, 2012 #4

    tiny-tim

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    what is your x(t) equation?
     
  6. Oct 3, 2012 #5
    I get x(t) = Ae**((-g-z)t) + Be(-(g-z)t) with z=sqrt(g**2 - w**2). At t=0 I get x0 = A + B
     
    Last edited: Oct 3, 2012
  7. Oct 3, 2012 #6

    tiny-tim

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    Hi MeMoses! :wink:
    (hmm … i'm not sure how that's supposed to be read :confused: … but anyway …)

    So what is the maximum value of x(t) (presumably at t = ∞) ?

    And what is the intitial speed? :smile:
     
  8. Oct 3, 2012 #7
    Sorry i type that from my phone. The lim x(t) as t approaches infinity is 0, it will always go to 0 eventually but how do I know if it crosses the origin or not and how can I find the initial speed using what you told me? Edit: also how can I solve the coefficients?
     
    Last edited: Oct 3, 2012
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