Answer
$1.532 \ s$
Work Step by Step
We know the following equation for period:
$T= 2\pi \sqrt{\frac{I}{mgcL}}$, where k is the percent as a decimal down the initial rod that you are. Thus, we see that $c=.25$. Using the equations for the moments of inertias, we find:
$T = 2\pi \sqrt{\frac{\frac{1}{12}mL^2+ \frac{1}{16}mL^2}{mgcL}}$
$T = 2\pi \sqrt{\frac{\frac{1}{12}L+ \frac{1}{16}L}{.25g}}$
Since L=1, we find:
$T = 2\pi \sqrt{\frac{\frac{1}{12}+ \frac{1}{16}}{.25g}}=1.532 \ s$
