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Homework Help: Seperation constant giving a harmonic dependence. (Seperation of variables)

  1. Jan 31, 2012 #1
    1. The problem statement, all variables and given/known data
    http://img18.imageshack.us/img18/8970/bose.png [Broken]

    3. The attempt at a solution
    I'm on part b) where it asks which seperation constation gives a harmonic time dependence. From part a) I deduced the equation [itex]\frac{d^{2}T}{dt^{2}}[/itex][itex]\frac{1}{T}[/itex] = a constant. I'm choosing the constant [itex]k^{2}[/itex] and my question is does it matter if the constant is negative or positive? I have seen in textbooks that a positive constant gives the solution T(t) = Aexp(-kt) + Bexp(kt) whereas a negative one would be Acos(kt) + B sin(kt). Are both solutions equivalent or does only one of them give a harmonic time dependence (My guess would be the sin/cos one is the proper answer for this question.)
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Jan 31, 2012 #2


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    Science Advisor
    Homework Helper

    hi xago! :smile:
    yes, you're right … harmonic has to be periodic, and only sin/cos will be periodic :smile:

    (exp will be either runaway or decay :redface:)
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