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T, simple harmonic motion, gravity

  1. Feb 8, 2010 #1
    There are two masses both M +a and -a apart with respect to the origin on the y axis. A third mass, m, is x away from the origin. Due to gravity it will oscillate back and forth. What is T
    Also, how can I use conservation of energy to find the velocity of the third mass m when it reaches the origin if it started at rest?

    so far i got

    g=2Gmx/(x^2+a^2)^(3/2)


    and for the conservation of energy the PEi has to equal KEf
     
  2. jcsd
  3. Feb 9, 2010 #2

    rl.bhat

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    Homework Helper

    Hi kjavia, welcome to PF.
    Potential energy at any point along the x-axis is given by
    PE = GMm/(x^2 + a^2)^1/2.
    Equate this to KE at the origin and find v.
     
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