Electric Dipole in Simple Harmonic Motion

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Homework Statement

An electric dipole in a uniform horizontal electric field is displaced slightly from its equilibrium position, where theta is small. The separation of the charges is 2a, and each of the two particles has mass m. Assuming the dipole is released from this position, show that its angular orientation exhibits simple harmonic motion with a frequency

f=1/(2*pi)*sqrt(q*E/(m*a))

Homework Equations

The Attempt at a Solution

The problem that I'm having is that I don't know how to start it. I know that I need to get it to a formula that looks like Hooke's law to show that it's simple harmonic and get k=qE/a, but how would I start the problem. I don't really want a solution, but a small push would be nice.

So far, I said that E=k*q^2/(4a^2) for the external field as it was in equilibrium when theta equals 0, but how would I incorporate theta when it's changed?

 

[Doc Al]

So far, I said that E=k*q^2/(4a^2) for the external field as it was in equilibrium when theta equals 0

No, the external field is given as E. (It's in equilibrium when theta = 0 since the torque is zero at that point.)

Hint: Find the restoring torque as a function of theta.