T, simple harmonic motion, gravity

AI Thread Summary
The discussion centers on calculating the period of oscillation (T) for a mass m influenced by two other masses positioned symmetrically on the y-axis. The gravitational force acting on mass m is expressed as g = 2Gmx/(x^2 + a^2)^(3/2). To find the velocity of mass m when it reaches the origin, conservation of energy principles are applied, equating initial potential energy (PE) to final kinetic energy (KE). The potential energy at any point along the x-axis is given by PE = GMm/(x^2 + a^2)^(1/2). By using these equations, one can derive the velocity of mass m at the origin.
kjavia795
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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
 
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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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