T, simple harmonic motion, gravity

[kjavia795]

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

 

[rl.bhat]

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.