Physics - SHM Question with Solution | TestHub

A simple pendulum consists of a point mass attached to an inextensible string and suspended from a support.

The formula to calculate the time period $\left(T\right)$ of a simple pendulum is given by

$T=2\mathrm{\pi }\sqrt{\frac{\mathcal{l}}{\mathrm{g}}}.......................\left(1\right)$

where, $\mathcal{l}$ is the length of the pendulum and $g$ is the acceleration due to gravity.

Simplify equation (1) to obtain the relation between the time period and the length.

$\begin{array}{rcl}{T}^{\mathit{2}}& \mathit{=}& \frac{\mathit{4}{\pi }^{\mathit{2}}}{g}\mathit{\times }𝓁\\ T^2& \propto & \mathcal{l}............................\left(2\right)\end{array}$

Equation (2) suggests that the graph between the square of the time period versus the length of the pendulum is a straight line passing through the origin.