Answer
1.64 seconds
Work Step by Step
Substituting the value of $I=\frac{4}{3}mL^2$ into the equation, we find that the following equation gives the period of the meter stick:
$T = 2\pi\sqrt{\frac{\frac{4}{3}mL^2}{mgL}}$
Recall, the length is equal to half of the length of the meter stick, which is half of a meter. Thus, we find:
$T = 2\pi\sqrt{\frac{\frac{4}{3}mL^2}{mgL}}$
$T = 2\pi\sqrt{\frac{\frac{4}{3}L}{g}}$
$T = 2\pi\sqrt{\frac{\frac{4}{3}(.5)}{9.81}}=\fbox{1.64 seconds}$
