FYKOS Year 26 Series 5 Problem 3 — sunbathing · FYKOS 26 #26.5.3
Physics · mechanics · optics
Problem
Two half cylinders are lying on top of each other as shown in the picture. The radius of the smaller one is r and that of the larger one is R. Given r, what is the condition on R so that the system is stable?
Bonus: If the parameters are chosen so that the system is stable, what will be the period of oscillations of the top half cylinder after it has been slightly shifted from the equilibrium position?