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Find the one dimensional particle motion in a given potential

  1. Nov 3, 2007 #1
    I'm not looking for a solution, but rather trying to understand the question.

    We've been given a series of potentials, U(x), and have been told to find the one-dimensional particle motion in them. For example:


    U(x) = V(tan^2(cx)), V>0

    My initial reaction was just to solve it for x(t), but after having found a(x), I'm not so sure that this is possible analytically... (I can't visualise a solution to -ma=2cV(tan(cx))(1+tan^2(cx))

    So perhaps the question is asking to find the period of the oscillatory motion? But it certainly doesn't look like that's what it's asking...
     
  2. jcsd
  3. Nov 3, 2007 #2
    Well I've tried to think of a nice trick using the chain rule or similar, but can't solve [tex] -\frac{1}{m}\frac{d}{dt}x(t)= U(x(t))[/tex]. Could it be you just have to qualitatively describe the resultant motion, or will all of your potentials result in oscillation?
     
  4. Nov 3, 2007 #3

    Astronuc

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    Staff: Mentor

    Well U(x) = V(tan2(cx)), V>0, has an equilibrium point about x = 0.

    tan2 x is an even function about x = 0.
     
  5. Nov 3, 2007 #4
    since 'a' is a function of x, you can use a = vdv/dx to get v as function of x and then v = dx/dt.
     
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