Physics - SHM Question with Solution | TestHub

The time period of a simple pendulum is given by $T=2\pi \sqrt{\frac{L}{g}}$.

This implies $T\propto \sqrt{L}$.

Given that the new length $L^{\prime }=3L$.

The new time period $T^{\prime }$ is given by:

$\frac{T^{\prime }}{T}=\sqrt{\frac{L^{\prime }}{L}}=\sqrt{\frac{3L}{L}}=\sqrt{3}$

$T^{\prime }=\sqrt{3}T$

Answer: $\sqrt{3}\mathrm{T}$