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Homework Help: Find an equation for position vs time given potential vs position?

  1. Nov 7, 2013 #1
    1. The problem statement, all variables and given/known data
    If I was given the potential energy equation
    How would I find the equation for position vs time? I know the graph for position vs time for this equation is a sin curve because the book tells me so.

    [itex]v = 0 [/itex] and [itex]x = 0 [/itex] when [itex]t = 0 [/itex]

    2. Relevant equations
    [tex]\frac{d}{dx} U(x) = -F(x)[/tex]

    3. The attempt at a solution
    Taking the derivative of the potential energy equation would yield an equation of force. [tex]-F = 8x [/tex]

    Using Newton's second law, we get: [tex]ma = -8x [/tex]

    Replace acceleration with velocity and we get: [tex] m \frac{dv}{dt} = -8x [/tex]

    I know I would integrate here twice somehow to find position in terms of time, but I'm not entirely sure how. In addition, I don't see how this position equation would have a sin function, as the book shows it should. I was hoping to find a way to solve this or learn a different approach here.

    Thanks in advance.
    Last edited: Nov 7, 2013
  2. jcsd
  3. Nov 7, 2013 #2
    Could you use conservation of energy here?
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