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Stable equilibrium question

  1. Dec 14, 2009 #1
    im so lost with this question, i have tried a lot and cannot solve it :

    A particle of unit mass moves on a straight line under a force having potential energy V (x) =
    x3=(x^4 + a^4) where  and a are positive constants. Sketch the graph of V (x).
    (a) Find the period of small oscillations about the position of stable equilibrium
    (b) Suppose the particle passes the origin, moving in the positive x-direction with speed v[0]. Show
    that the particle will subsequently pass the point x = a if and only if v^2[0] > =a. Find a further
    condition on v^2[0] for the particle to subsequently pass the point x = -a

    (square brackets represent a subscript)

    Thansk in advance----aa.
  2. jcsd
  3. Dec 15, 2009 #2


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    Homework Helper

    First, V (x) =
    x3=(x^4 + a^4) doesn't make sense. Which one is V(x) equal to:
    x3 or (x^4 + a^4)?

    For (a), force varies linearly with displacement according to F=-kx near the equilibrium point. (Can you see why?)

    (b) Sounds a lot like a conservation of energy problem!
  4. Dec 15, 2009 #3
    hi sorry about the messy question... i have added it as an attatchement. i managed to do the first part but cannot seem to do the the last part of part b.

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