Two point masses, each equal to M, are placed a distance `2a` apart. Show that a small mass m placed midway between them on the line joining them will be in equilibrium and if it is slightly displaced from this position along the line perpendicular to the line joining the masses, it will execute simple harmonic oscillations. Calculate the frequnency of these oscillations.

Answer

`1/(2pi) sqrt((2GM)/(a^(3)))`