A particle slides on the inside surface of a frictionless cone. The cone is fixed with its tip on the ground and its axis vertical. The half-angle at the tip is ? (see Fig.). Let r(t) be the distance from the particle to the axis, and let ?(t) be the angle around the cone. Find the equations of motion. If the particle moves in a circle of radius r0, what is the frequency, ?, of this motion? If the particle is then perturbed slightly from this circular motion, what is the frequency, ?, of the oscillations about the radius r0? Under what conditions does ? = ??

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