A particle of mass or moves under the inuence of gravity on the inner surface of a smooth cone of half-angle a. The axis of the cone is vertical with its vertex downward. Determine the condition on the angular velocity to such that the particle can describe a horizontal circle at a height )1 above the vertex Gravity is acting vertically downward. Also show that if the particle is displaced slightly from this circular path. it will undergo oscillations about the path within a period ( 2" Xi)? com 39