Coulomb's Law: Simple Harmonic Motion of a Charge Between Two Fixed Charges

[PatrickGeddes]

Two identical particles, each having charge +q, are fixed in space and separated by a distance d. A third particle with charge −Q is free to move and lies initially at rest on the perpendicular bisector of the two fixed charges a distance x from the midpoint between those charges (see figure below).

(a) Show that if x is small compared with d, the motion of −Q is simple harmonic along the perpendicular bisector. (Do this on paper. Your instructor may ask you to turn in this work.)

There is more to this problem but the first question I don't even know what is asking.

 

[PatrickGeddes]

Also, just looked at the second two questions, don't know where to start...
(b) Determine the period of that motion. (Use the following as necessary: π, q, Q, m for the mass of charge Q, d, and ke.)
T =

(c) How fast will the charge −Q be moving when it is at the midpoint between the two fixed charges if initially it is released at a distance a << d from the midpoint? (Use the following as necessary: π, q, Q, m for the mass of charge Q, d, and ke.)