Answer
$T = 2\pi~\sqrt{\frac{L}{g}}$
Work Step by Step
We can write the equation for the period of a physical pendulum:
$T = 2\pi~\sqrt{\frac{I_{support}}{mgL_{cm}}}$
For a simple pendulum, $I_{support} = mL^2$
For a simple pendulum, $L_{cm} = L$
We can derive the equation for the period of a simple pendulum:
$T = 2\pi~\sqrt{\frac{I_{support}}{mgL_{cm}}}$
$T = 2\pi~\sqrt{\frac{mL^2}{mgL}}$
$T = 2\pi~\sqrt{\frac{L}{g}}$
