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A particle of mass m slides in a frictionless semi—circular depression in the ground of radius 1 0f 2 R. Find the angular frequency of small amplitude oscillations about the particle’s equilibrium position, assuming that the oscillations are essentially one-dimensional, so that the particle passes through the lowest point of the depression during each oscillation cycle.

A particle of mass m slides in a frictionless semi—circular depression in the ground of radius
1 0f 2 R. Find the angular frequency of small amplitude oscillations about the particle’s equilibrium
position, assuming that the oscillations are essentially one-dimensional, so that the particle passes through the lowest point of the depression during each oscillation cycle.

 
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