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Period of small oscillations in central potential

  1. Dec 2, 2005 #1
    Hi,

    A particle is subjected to a central potential of:

    [tex]V(r) = -k\frac{e^{-\alpha r}}{r}[/tex]
    Where [tex]k, \alpha[/tex] are known, positive constants.

    If we make this problem one-dimensional, the effective potential of the particle is given by:
    [tex]V_{eff}(r) = -k\frac{e^{-\alpha r}}{r} + \frac{l^2}{2 m r^2}[/tex]
    Where the second term is the "centrifugal potential", [tex]l[/tex] is the absolute value of the angular momentum the particle has.

    Now suppose that this effective potential has a minimum at [tex]r_0[/tex], which is known, so that if placed there the particle will have a circular motion.

    The question is - what is the period of small oscillations (in the r-dimension) around the circular orbit?
    The answer needn't depend on the energy of the particle or its angular momentum.

    Thanks,
    Chen
     
  2. jcsd
  3. Dec 2, 2005 #2

    Tom Mattson

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    You know the rules: Post what you've got so far, and we'll help from there.
     
  4. Dec 3, 2005 #3
    I've solved it myself. Thank you very very much.
     
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