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Oscillator (not shm)

  1. Feb 28, 2010 #1
    1. The problem statement, all variables and given/known data
    For a certain oscillator the net force on the body with mass {m} is given by F_x = - cx^3.
    a) What is the potential energy function for this oscillator if we take U = 0 at x = 0?
    b) One-quarter of a period is the time for the body to move from x = 0 to x = A. Calculate this time and hence the period.

    2. Relevant equations
    a) [tex]U = \int F dx[/tex]
    b) [tex]E = \frac{1}{2}(mv^{2} + kx^{2})[/tex]

    [tex]T = \int\frac{dx}{v(x)}[/tex]

    3. The attempt at a solution

    ok, the first part is pretty straight forward. just integrating w.r.t x yields [tex]\frac{1}{4}cx^{4}[/tex]

    [tex] E = constant = \frac{1}{4}cA^{4} = \frac{1}{2}mv^{2} + \frac{1}{4}cx^{4}[/tex]

    solve to get v as function of x: [tex]v(x) = \sqrt{\frac{c}{2m}(A^{4}- x^{4})}[/tex]

    then integrating of interval x = 0 to x = A:

    [tex]T = 4 \int\frac{dx}{v(x)}[/tex]

    [tex] = 8A^{2}\sqrt{\frac{2m}{c}}[/tex]

    but it's wrong it just so wrong… please help
    thanks!
     
    Last edited: Mar 1, 2010
  2. jcsd
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