A uniform thin circular hoop of mass $m$ and radius $R$ has a small bead of mass $M$ firmly attached to it. The hoop is hung from a small fixed nail and undergoes small oscillations in its plane. Let $T_1$ be the period of small oscillations when the hoop is hung such that the bead is at the lowest possible point. Let $T_2$ be the period of small oscillations when the hoop is hung such that the bead is at the highest possible point (at the pivot). What is the ratio $T_1/T_2$?