Find the period of oscillation of a little charged ring

[anynamewilldo]

Homework Statement

Find the period of oscillation, T, of a little charged ring that is free to move along a vertical wire when placed equi-distant between two like charges above and below it. Small displacement only. Treat the “little” ring like a point charge and use the binomial expansion for small “x” to reduce the net force on the ring to a linear Hooke’s law style force.

Homework Equations

T= 2pi*sqrt(m/k)
E = k*dq/r^2
F = ma

The Attempt at a Solution

Since there are two charges and a point essentially you can calculate the electric field at a point p on the wire. Afterwards you can use F = ma at the field since F = qE = ma.

Am, I wrong about my thinking here. I really just want some help setting this up as in how I should start.

 

[Simon Bridge]

Also assume the "wire" is an electrically neutral insulator, but it sounds reasonable so far.
Keep going.