The bob of a simple pendulum of length ' $L$ ' has a mass ' $m$ ' and charge ' $q$ '. The pendulum is…
The bob of a simple pendulum of length ' $L$ ' has a mass ' $m$ ' and charge ' $q$ '. The pendulum is suspended between the plates of a charged parallel plate capacitor. The direction of electric field is shown in figure. The period of oscillations of the simple pendulum is (acceleration due to gravity $g>q E / m$ )
Electric force, $\mathrm{F}_{\text {electric }}=\mathrm{qE}$
The effective force,
$\begin{aligned}
& \mathrm{mg}_{\text {eff }}=\mathrm{mg}-\mathrm{F}_{\text {electric }} \\
& \mathrm{g}_{\text {eff }}=\mathrm{g}-\frac{\mathrm{qE}}{\mathrm{m}}
\end{aligned}$
The period of oscillation for a simple pendulum,
$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{L}}{\mathrm{g}}}$
Time period when pendulum is suspended between the plates,
$\begin{aligned}
& \mathrm{T}=2 \pi \sqrt{\frac{\mathrm{L}}{\mathrm{g}_{\text {eff }}}} \\
& \mathrm{T}=2 \pi\left[\frac{\mathrm{L}}{\mathrm{g}-\frac{\mathrm{qE}}{\mathrm{m}}}\right]^{\frac{1}{2}}
\end{aligned}$
