A simple conical pendulum swings from a rigid support in a circular motion. The string is light and the mass is small. The period of the pendulum is the period of the circular motion.
Resolving the two forces that act on the mass (mg and the tension force) in vertical and horizontal directions gives ...
The period T is given by ...
... which gives at once ....
The period of a simple conical pendulum is the same as the period for small oscillations of a simple linear pendulum, with the length of the string l replaced by the height h.
A driven conical pendulum is filmed from above. Note the slight foreshortening in the horizontal direction because of the camera position. The position-time graphs in the x and y directions show at once that the circular motion is the combination of two simple harmonic motions displaced by 90°.