An electric dipole of momentum `vecp` is placed in a uniform electric field. The dipole is rotated through a very small angle `theta` from equilibrium and is released. It executes simple harmonic motion with frequency `f=1/(2pi)sqrt((pE)/I)` where, I= moment of interia of the dipole.

Explanation

A dipole makes an angle 9 with an electric field from its equilibrium position. So, torque acting on it,
`vectau = vecp xx vecE`
`therefore tau = pEsintheta`
This torque rotates the dipole in clockwise direction
`therefore tau =-pEsintheta`
Here `theta` is very small.
`therefore sintheta =theta`
`therefore tau =-pEtheta`
but, `tau = 1alpha` and `alpha =-omega^(2)theta`
`1alpha = -pEtheta`, where `alpha` is the angular acceleration in S.H.M.
`therefore 1(-omega^(2)theta) = -pEtheta`
`therefore omega = sqrt((pE)/1)`
`therefore 2pif = sqrt((pE)/1) (therefore omega = 2pif)`
`therefore f=1/(2pi)sqrt((pE)/1)`