Calculating Period of Oscillation for a Colliding System

AI Thread Summary
The discussion revolves around a physics problem involving a gob of clay colliding with a rotating cylinder, leading to periodic oscillations. The user successfully solved part A, which involves calculating the initial angular velocity after the collision. However, they are struggling with part B, which requires calculating the period of oscillation for the system, assuming small friction. The user mentions a diagram that illustrates the setup but is unable to attach it, prompting a request for clarification on the concept of a "physical pendulum." The conversation seeks assistance in understanding how to approach the calculation of the oscillation period in this context.
SMG75
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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.
 
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SMG75 said:
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?
 
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?
 
Does "physical pendulum" ring a bell?
 

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