A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric…

Two forces will be acting on the mass $m$, gravity force and force by the electric field.

Thus, the effective force $=\mathrm{ }\mathrm{ }\sqrt{{\left(\mathrm{q}\mathrm{E}\right)}^2+{\left(\mathrm{m}\mathrm{g}\right)}^2}$
From force equation, ${\mathrm{g}}_{\mathrm{e}\mathrm{f}\mathrm{f}}=\sqrt{{\mathrm{g}}^2+{\left(\frac{\mathrm{q}\mathrm{E}}{\mathrm{m}}\right)}^2}$
Time period of the pendulum is $\left(\mathrm{T}\right)=2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{{\mathrm{g}}_{\mathrm{e}\mathrm{f}\mathrm{f}}}}$
$=2\mathrm{\pi }\mathrm{ }\sqrt{\frac{\mathrm{L}}{\sqrt{{\mathrm{g}}^2+{\left(\frac{\mathrm{q}\mathrm{E}}{\mathrm{m}}\right)}^2}}}$