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Unusual harmonic oscillator.

  1. Oct 16, 2009 #1
    1. The problem statement, all variables and given/known data
    A particle of mass m moves (in the region x>0) under a force F = -kx + c/x, where k and c are positive constants. Find the corresponding potential energy function. Determine the position of equilibrium, and the frequency of small oscillations about it.


    3. The attempt at a solution
    I found the potential energy function by integrating -F(x)dx, and the position of equilibrium by putting F=0. I'm having difficulty even starting the third part, I think I have to do it like one does the damped harmonic oscillator. Any help would be greatly appreciated, thanks in advance.
     
  2. jcsd
  3. Oct 16, 2009 #2
    Hehe, nice question!

    Here's a big big hint:
    Work out the potential energy function while setting your plane of reference at the equilibrium point. Look at the expression you get, and examine what happens when [tex]x\rightarrow x_{eq}[/tex]

    Differentiate the energy function to find the force, and solve for the oscillations.
     
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