Optimizing Physical Pendulum Oscillation: Finding d for Shortest Period

[oreosama]

Homework Statement

A physical pendulum is created from a uniform disk
of radius 12.0 cm. A very small hole (which does not
affect the uniformity of the disk) is drilled a distance d
from the center of the disk, and the disk is allowed to
oscillate about a nail through this hole. If the period of
oscillation is 1.00 s, find d



For the physical pendulum in Problem 6, find the
value of d that results in the shortest possible period of
oscillation, and find the corresponding period

Homework Equations

ωT = 2pi

ω = sqrt(mgd / I for phys pendelum)

The Attempt at a Solution

The first question involves using a quadratic which I've completely solved to be 3.35cm. The second part I know somehow utilizes derivative but I have no idea how.

 

[voko]

You need to find the equation that expresses the period as a function of d.

Then you need to minimize the function. Depending on the equation you obtain, you may or may not have to use calculus for that.