Theoretically derive the equation for the period of a ring

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Theoretically derive the equation for the period of a ring pendulum. A ring pendulum is a ring with a notch set on a knife edge and pushed a small bit to oscillate at small amplitudes, so that it exhibits simple harmonic motion. We are to start with the equation for the period of rotary simple harmonic motion \(T = 2 \pi\sqrt{I/Lo}\)

Note: The moment of inertia of a body about any axis is equal to the moment of inertia it would have if the mass were all concentrated at the center of gravity plus the moment of inertia of the distributed mass about a parallel axis through its own center of gravity.

Reference no: EM13584723

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