1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    [tex]U(x)=4x^2[/tex]
    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?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Find an equation for position vs time given potential vs position?
  1. Position vs Time Lab (Replies: 2)

Loading...