$$\require{cancel}$$
Consider a dipole oscillating in an electric field (figure III.3). When it is at an angle $$\theta$$ to the field, the magnitude of the restoring torque on it is $$pE \sin \theta$$, and therefore its equation of motion is $$I\ddot \theta = -pE\sin \theta$$ where I is its rotational inertia. For small angles, this is approximately $$I\ddot \theta = -pE\theta$$ and so the period of small oscillations is
$\label{3.3.1}P=2\pi\sqrt{\frac{I}{pE}}.$