Coulomb's Law and Simple Harmonic Motion

[gators1223]

Homework Statement

Two positive charges +Q are affixed rigidly to the x-axis one at x = -d and the other at x = +d. A third charge +q of mass mwhich is constrained to move only in the x-axis is displaced from th eorigin by a small distance s << d and then released from rest. Show that q+ will execute simple harmonic motion and determine the oscillation period T.

Homework Equations

Coulomb's Law F=kQ₁Q₂/r²
*possibly something else to relate this to SHM*

The Attempt at a Solution

I found the force from coulomb's law, F= -4kQqs/d³
but i really don't know how to relate this to SHM so i can derive an equation for period.

 

[kuruman]

Compare your expression for the force with the force exerted by a spring in a mass. How is the spring force related to the displacement of the mass from the equilibrium position?