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Oscillation of a cylinder on a cylindrical surface.

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A small uniform cylinder of radius R rolls without slipping along the inside of a large fixed cylinder of radius r (r>R). Show that the period of Oscillation of the rolling cylinder is equivalent to that of a simple pendulum whose length is 3(R-r)/2.

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The period of small oscillation for a cylinder of radius R inside a curved cylindrical surface of radius r.

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