A mechanical problem with complicated geometry

[wrobel]

Here I would like to draw colleagues attention to a class of problems that are simple from physics viewpoint but have pure geometric obstacles. I believe such problems can be discussed in basic courses of analytic geometry as well.

A coin of radius $r$ and of mass $m$ is put in a chute such that the plane of the coin can be horizontal. There is no slippery between the coin and the chute. The statement of the problem can be for example as follows: find a frequency of small oscillations.