A uniform thin hoop of mass
M and radius
R hangs from a small fixed nail, able to swing freely in its own plane. A horizontal massless spring of spring constant
k connects the bottom of the hoop to a fixed vertical wall. In equilibrium, the center of the hoop is directly below the nail, and the spring is relaxed. The hoop is given a small angular displacement in its plane and released. What is the frequency
f of its small oscillations?