Demonstrating Conical Pendulum Stable and Unstable States

This article analyzes and experimentally verifies the stability behavior of the equilibrium states of a conical pendulum. An analysis of the motion presents that the equilibrium states of the pendulum are determined by the pendulum angular speed. For a given pendulum length there exists a critical angular speed that determines stability conditions. Experimental results obtained using a variable speed rotator confirm the relationship between angular speed and equilibrium state conditions. An initially at rest pendulum has a stable equilibrium position that is vertically hanging straight down; however, it is shown that when gradually increasing the speed of a mechanical rotator to approach and surpass the pendulum critical speed, the initial stable equilibrium state becomes unstable. Furthermore, the pendulum, now in an unstable equilibrium, moves to a new stable equilibrium position that did not exist at speeds below the critical speed.