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Oscillations are emhasized.

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An ice cube can slide around the inside of a vertical circular hoop of radius R. It undergoes small-amplitude oscillations if displaced slightly from the equilibrium position at the lowest point.

Find an expression for the period of these small-amplitude oscillations. Give your answer in terms of R and constants g and pi.

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Let mg be wieght of the cube.
Let o be the centre of the circular loop.
Let P be the point of location of the ice cube. Then OP is a radius of the circle.
Let the direction of the vertical gravitational force mg make an angle x (angle x is small) with OP produced.

Please draw a circle representing the loop with centre O. Let ON be a radius with point N vertically below O. P is a point where the ice cube is located, a small distance away from N and to the right of N. Angle NOP = x. x is small. Draw a ...

Solution Summary

The period of small-amplitude oscillations is given in terms of radius and pi.