Oscillations in an electric field

[evangoor]

Homework Statement

Two positive point charges Q are held fixed on the x-axis at x=a and x=-a. A third positive point charge q, with mass m is them placed on the the x-axis away from the origin at a coordinate x such that lxl<<a. The charge q, which is free to move along the x-axis, is then released. Find the frequency of oscillation of the charge q.

Homework Equations

So I started with the force equation for charges where F_E=1/(4∏ε₀)*q_qq₂/r²
I figured I need to get it into a form of Hooke's law where F=-kx. So I could then use the equation f=1/(2∏)*\sqrt{k/m}

The Attempt at a Solution

So I wrote the force equations which each of the fixed charges would exert on the point charge and added them together resulting in F=Q*q/4∏ε₀*-4ax/(a²-x²)². From here I did not see how I could get it into a form of Hooke's law. At this point I am at a loss of what path to take. Help would be greatly appreciated.

 

[TSny]

Since |x| << a, approximate the denominator.