development of mechanics of a rocking problem

Hi
I want to develop mechanics of a problem which is as follows.

Suppose there is an inverted glass (cylinder) lying on a table. Now suppose there is a mass (or coin) on the top of glass. If we provide an initial rotation to the glass such that only one corner of glass is in contact with table (no overturning) and then release it. Now when the glass will come in full contact with table then the coin will lift vertically. I want to find out the vertical force (acceleration) acting on the top mass or coin using mechanics.

(Suppose glass or cylinder is rigid and with insignificant mass. Only mass acting is the top mass (m). No shear slip. Contact of glass base and table can be represented by a linear spring with stiffness K).

Thanks and Regards