A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E, as shown in figure. Its bob has mass m and charge q. The time period of the pendulum is given by:

A

$$2\pi\sqrt{\frac{L}{\sqrt{g^2 + \frac{q^2E^2}{m^2}}}}$$

B

$$2\pi\sqrt{\frac{L}{g + \frac{qE}{m}}}$$

C

$$2\pi\sqrt{\frac{L}{g - \frac{qE}{m}}}$$

D

$$2\pi\sqrt{\frac{L}{\sqrt{g^2 - \frac{q^2E^2}{m^2}}}}$$