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Homework Help: Determing U(x) from Force

  1. Oct 20, 2005 #1
    A particle is under the influece of a force F=-kx+kx^3/(a^2), where k and a are constants and k is positive. Determine U(x) and discuss the motion. What happens when E=1/4 (k a^2)?

    I know F = - grad U, but how do I use this fact to set up the problem?
    Can someone help me to get started?

  2. jcsd
  3. Oct 20, 2005 #2


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    This is a one-dimensional problem, so no need for gradients. Just F=-dU/dx

    So start by finding (a) U(x).
  4. Oct 20, 2005 #3


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    In one-dimension, that's F(x) = -dU(x)/dx. Now what can you do to express U(x) in terms of F(x) ?

    Edit : Started before Galileo's post was up...now redundant as it's saying the same thing.
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