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Homework Help: Nonlinear second order ODE describing a force field

  1. Nov 10, 2012 #1
    Not sure if this topic belongs here, but here goes.

    1. The problem statement, all variables and given/known data

    From the AP physics C 1995 test there is a problem that gives the potential energy curve U(x). With [itex]F=-\frac{dU}{dx}[/itex] in one variable,


    Where a and b are constants. Now I need to get x(t)

    2. Relevant equations

    Dividing by mass and multiplying by x^2:


    Unfortunately I do not have the skills to solve this differential equation.

    3. The attempt at a solution

    [itex]x=y, \frac{-a}{mb}=b, \frac{ba}{m}=k, y'=u[/itex]


    I tried to eliminate the y'':




    And that doesn't really get me anywhere. Anyone with knowledge of nonlinear ODEs care to help? I tried Wolfram, but even with my Pro free trial it took to much computing time and never gave me a solution.

    Also since this wasn't required of the problem per se, and I just want to solve this, I'm not sure what forum it should be in.

  2. jcsd
  3. Nov 10, 2012 #2


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    Science Advisor
    Homework Helper

    hi thetasaurus! :smile:

    try the standard trick (from the chain rule) …

    d2x/dt2 = v dv/dx (where v = dx/dt)

    (btw, that's where 1/2 mv2 comes from :wink:)
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