Development of mechanics of a rocking problem

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The discussion focuses on developing the mechanics of a problem involving an inverted glass resting on a table with a mass on top. When the glass is rotated so that only one corner touches the table and then released, the goal is to determine the vertical force acting on the mass as the glass comes into full contact with the table. The setup assumes the glass is rigid with negligible mass, and the contact is modeled as a linear spring with stiffness K. The participant has already established that the lateral velocity and vertical acceleration of the mass are directly proportional and seeks to explore the relationship between these two variables further. The inquiry aims to deepen the understanding of the dynamics involved in this specific rocking problem.
Hector92
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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
 
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I have found the lateral velocity and vertical acceleration of the top mass and are directly proportional to each other. I want to find out the relationship between two
 

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