A pendulum in which a particle, attached by a string of constant length to a fixed point, moves in a circular path in a horizontal plane. Suppose that the string has length l and that the string makes a constant angle α with the vertical. The particle moves in a circular path in a horizontal plane a distance d below the fixed point, where d=l cos α. The period of the conical pendulum is equal to 2π√d/g.
http://www.ngsir.netfirms.com/englishhtm/ConicalPendulum.htm A visualization of the conical pendulum showing its forces.