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Homework Help: One dimensional wave

  1. Apr 15, 2010 #1
    1. The problem statement, all variables and given/known data

    A particle of mass m moves in one dimension subject to the potential energy given by:

    U(x) = -Uoe-(x/l)2

    where Uo is a positive constant with units of energy. Supposing that at time t=0 the mass has zero velocity and is located at position 0.01l, what is the position of the mass for all subsequent times?

    2. Relevant equations


    3. The attempt at a solution

  2. jcsd
  3. Apr 15, 2010 #2
    Looks like an instanton to me. Anyways, dont you just do the normal lagrangian/hamiltonian methods here? Its just a classical problem, right?
  4. Apr 15, 2010 #3
    This is a second year engineering physics course on Vibrations and Waves, that does not expect any knowledge of Lagrangian method (I barely know) and Hamiltonian method (don't know).
  5. Apr 15, 2010 #4
    Sorry that was basically overkill, I had different idea in mind when i looked at it quickly before.

    Sketch the potential, where does the mass start out? Is it reasonable to approximate the potential by one that you know well?
  6. Apr 15, 2010 #5
    Thanks Jrosen! You have really helped me on this problem.

    I got something like:

    x = 0.01l cos (wt)

    where w^2 = k/m

    where k = U'' = 4(x/l)2 Uo e-(x/l)2
  7. Apr 15, 2010 #6
    It wasn't so bad was it? That looks right to me, harmonic oscillator all the way. In the future try to realize if you are patient and think it through a little you will figure it out. Don't be in a hurry to get the answer, enjoy the process of figuring it out for yourself!
  8. Apr 16, 2010 #7
    I just noticed you wrote your spring constant as a function of x, but that wouldn't be right, would it?
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