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This problem consists of a sequence of ideas concerning the configuration of hoop and pole as shown in the diagram below.
A rigid hoop of radius $r$ is attached to a vertical pole. A light ideal spring of unstretched length $L$ and spring constant $k$ is attached at one end at the point of contact of the hoop to the pole. A bead of mass $m$ is attached to the other end of the spring and the bead and spring are threaded onto the hoop, so they can slide around its circumference. |