1. The problem statement, all variables and given/known data (see attachment for figure) A small object is mounted to the perimeter of a hoop of radius r. The mass of the object and the hoop is same. The hoop is placed into a fixed semi-cylinder shaped rough trough of radius R, such that small mass is at top. Find the least r/R ratio such that the object performs simple harmonic motion. 2. Relevant equations 3. The attempt at a solution I honestly have no idea on how should I begin to solve this problem, this is very different from the SHM problems I have done. Any help is appreciated. Thanks!