# The trying trough

A small bead is attached to the perimeter of a hoop of radius $$\textbf{r}$$. The mass of the hoop and the bead are the same. The hoop is placed in a cylindrical trough of radius $$\textbf{R}$$ ,such that the bead is at the top of the hoop. Find the greatest value of the ratio $$\frac{R}{r}$$ such that the hoop-bead system performs SHM when displaced slightly to one side.

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