A thin hoop of radius R and mass M oscillates in its own plane hanging from a

Question:

A thin hoop of radius R and mass M oscillates in its own plane hanging from a single fixed point. Attached to the hoop is a small mass M constrained to move (in a frictionless manner) along the hoop. Consider only small oscillations, and show that the Eigen frequencies are

Find the two sets of initial conditions that allow the system to oscillate in its normal modes. Describe the physical situation for each mode.