Mechanism For Oscillation of Cylinder

[FallenApple]

Homework Statement

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Begin with a solid cylinder of mass M and radius R. A hole is bored through this cylinder with radius r < R/2, parallel to the axis of the cylinder and with the surface of the hole touching the cylinder’s axis. This modified cylinder then rolls on a horizontal surface under the influence of gravity. If the cylinder starts from rest with the orientation given by θ = θ0, |θ0| ≪ 1 find the subsequent motion.

Homework Equations

euler lagragne and SHO equations.

The Attempt at a Solution

The solution is in the above. I just don't know what is the mechanism for causing the oscillations in the first place.

Is it the fact that there is a hole in it? Would a cylinder without a hole oscillate?

Also, how is it that the gravitational potential energy can be treated as being solely contained by hollow and not the rest of the object?

And also, how is it that potential energy is stored as theta increases? Is the ground acting as a spring?

 

[DrClaude]

What happens to the center of mass as the cylinder rolls?

 

[FallenApple]

It will go up. Moves counterclockwise up while the hollow moves counter clockwise down?

 

[DrClaude]

It will go up. Moves counterclockwise up while the hollow moves counter clockwise down?

Correct. If you think about the problem from the point of view of the motion of the center of mass, I think you can answer your questions.