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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