A hole of radius  $\frac{R}{4}$ is drilled from a disc of radius R and of mass m as shown. The disc of radius R can roll on the horizontal surface without slipping.

If it is slightly rolled and released from the shown situation then time period of oscillation nearly becomes  $T=6\pi \sqrt{\frac{5R}{g}}$

If is slightly rolled from the shown situation and released then the time period of oscillation nearly becomes  $T=3\pi \sqrt{\frac{5R}{g}}$

In the shown situation location of centre of mass is $\frac{R}{30}$   distance above O.

The moment of inertia of the disc about an axis passing through O and perpendicular to the plane of disc is $\frac{1}{2}m{R}^2$  approximately