Given:
The period of a pendulum,
[tex]T=2\pi\sqrt{\frac{L}{g}}[/tex]
To find:
The equation to find the acceleration due to gravity.
Explanation:
On taking the square of the equation,
[tex]T^2=4\pi^2(\frac{L}{g})[/tex]
On multiplying g on both sides of the equation,
[tex]\begin{gathered} T^2g=\frac{4\pi^2L}{g}\times g \\ \implies T^2g=4\pi^2L \end{gathered}[/tex]
On dividing both sides of the equation by T²,
[tex]\begin{gathered} \frac{T^2}{T^2}g=4\pi^2\frac{L}{T^2} \\ \implies g=\frac{4\pi^2L}{T^2} \end{gathered}[/tex]
Final answer:
The equation to calculate the acceleration due to gravity is
[tex]\begin{equation*} g=\frac{4\pi^2L}{T^2} \end{equation*}[/tex]
