Floating table
A supplement to the solutions of the theoretical problem Nº2 at 9th European Physics Olympiad, held between June 13 and 17 2025 in Sofia, Bulgaria.
Grab a point B, which is a point on the rigid upper part of the table and drag it around, to visualize the motion of the table. Red lines represent chains, blue lines represent the 2 parts of the rigid frame (the bottom one, fixed to the floor, and the upper one, to which the table plate - represented by the yellow line - is attached). C is the center of mass of the table (the frame and the chains have negligible mass when compared to the mass of the plate).
When the plate moves, its center of mass moves and leaves a trace behind. The position, where the table plate is horizontal, is a stable equilibrium position where the potential energy is minimal, as can be concluded from the trace of C.