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Quartic Oscillators

  1. Jun 25, 2009 #1
    1. The problem statement, all variables and given/known data

    The equation of motion for a particle of mass 1 in a quartic oscillator V(x)=0.25x^4 is x''+x^3=0. Suppose that the maximum amplitude of the oscillator is Xm(max). Find an expression for the time T that it takes to go from x=0 to x=Xm(max) and show that this time is inversely proportional to Xm(max).

    2. Relevant equations

    Xm(max) = sqrt(x^2+mv^2/k)

    3. The attempt at a solution

    V(x) is energy? E = 0.5mv^2 + V then d^2/dt^2(x) = -x^3 ? How to make the connection between the time T and these equations. Thanks very much.
     
  2. jcsd
  3. Jun 25, 2009 #2

    tiny-tim

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    Hi ZoroP! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    Hint: multiply by x' to give x'x'' + x3x' = 0, and then integrate. :wink:
     
  4. Jun 25, 2009 #3
    Thx tiny, then i get v*dv/dt + x^3 dx/dt = 0
    how to integral this? is this the same with v*dv = - x^3 dx?
     
  5. Jun 26, 2009 #4

    tiny-tim

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    Hi ZoroP! :smile:

    (just got up … :zzz:)

    (please use the X2 tag just above the Reply box :wink:)
    Yes, they're the same …

    so what do you get? :smile:
     
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