Calculating Period of Oscillation for a Colliding System

[SMG75]

Below is a problem that I am trying to work through in preparation for an upcoming exam. I worked through part A with no problems, but I am struggling with part B. Could someone point me in the right direction?

Homework Statement

A gob of clay with mass m falls from rest a distance h before striking and sticking to the edge of a uniform cylinder of mass M and radius r. The cylinder is free to rotate about a horizontal axis through its center.

2A) What is the initial angular velocity of the cylinder with the gob of clay attached?
2B) Now assume that after the collision, the system experienced a small amount of friction such that after a long time, the system comes to undergo small periodic oscillations, as shown. Ignoring friction, calculate the period of the oscillation.

Thanks.

 

[kuruman]

2B) Now assume that after the collision, the system experienced a small amount of friction such that after a long time, the system comes to undergo small periodic oscillations, as shown. Ignoring friction, calculate the period of the oscillation.

Thanks.

"As shown" where?

 

[SMG75]

Ah, right. I forgot to attach the diagram. It won't let me for some reason. I will try to describe it. It shows the cylinder on its side, so it just looks like a circle. The axis of rotation is in the center of that. The clay is stuck to the bottom edge, and it is making small oscillations in that manner. Any help?

 

[kuruman]

Does "physical pendulum" ring a bell?