An electric dipole of dipole moment P is placed in a uniform electric field E is stable equilibrium position. Its moment of inertia about the centroidal axis is I. If it is displaced slightly from its mean position find the period of small oscillation.

$T=2 \pi \sqrt{\frac{I}{PE}}$

When displaced at an angle θ, from its mean position the mean position the magnitude of restoring torque is 

$\tau=-P E \theta$

For small angular displacement $\sin \theta \approx \theta$

$\tau=-PE \theta$

The angular acceleration is,

$\alpha=\frac{\tau \theta}{I}=-\left(\frac{pE}{I}\right) \theta=-\cos ^2 \theta$

Where $\omega^2=\frac{P E}{I}$

∴ $T=2 \pi \sqrt{\frac{I}{PE}}$