A uniform disk of mass $m$ and radius $r$ has a small hole drilled through it at distance $d$ from its center. The disk hangs from a flexible pivot passing through the hole and is given a small displacement perpendicular to the plane of the disk, so it oscillates perpendicular to that plane. The distance $d$ is chosen to make the period of oscillation as small as possible. What is this minimum period? The moment of inertia of a disk about the axis through its center and perpendicular to the plane is $I_{\text{disk}} = \frac{1}{2}mr^2$.