Is it possible to make a pendulum bob undergo uniform circular motion in a vertical plane?

00:48 Hint given | 01:50 Solution starts | 06:23 Answer | 06:28 Animation

Watch the inner end of string move along the plotted curve. Change parameters and see the effect on the path.

Animation of solution on Desmos

Question N1L3: Concepts used in solution

Centripetal acceleration | F=ma |

Problem statement

A small bob of mass m is attached to one end of a light string of length l. How should the other end of the string be moved such that the bob undergoes uniform circular motion along a circle of radius l, in a vertical plane under gravity?