Electric Charge and Coulomb's Law

Fusilli_Jerry89

1. Homework Statement
Two positive charges +Q are held fixed a distance d apart. A particle of negative charge -q and mass m is placed midway between them, then is given a small displacement perpendicular to the line joining them and released. Show that the particle describes simple harmonic motion of period sqrt((epsilon not)m((pi)^3)(d^3))/(qQ).

2. Homework Equations

3. The Attempt at a Solution

SO I calculated the resultant force on the Q charge at any point and found it to be [((sqrt(2))qQ)]/[4pi(epsilon not)(r^2)). I then saw that F=-kz and T = 2pi*sqrt(m/k).
After plugging everything in and seeing that z was neglible when compared to d/2, I came up with several different answers all the same as sqrt((epsilon not)m((pi)^3)(d^3))/(qQ) only I had coefficients in the numerator and denominator. I have no idea what I am doing wrong? Also, how do you prove it is simple harmonic motion?

Here's what I did:

I said that r is approx. equal to d/2. and z is rsin(theta). After I pug this all in to T = 2p*sqrt(m/k) I get T = sqrt([16(pi^3)(epsilon not)m(r^3)sin(theta)]/[sqrt(2)qQ]).
I don't get what I am doing wrong. Plz help...thx.

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