Motion of Pendulum Interrupted by a Peg

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This Demonstration shows the movement of a simple pendulum whose swing is interrupted by a peg.


The pendulum is a bob of arbitrary mass connected to a pivot at by a perfectly flexible, massless string of length 1. A peg is located directly below the pivot at a distance . The initial angle between the string and the vertical is .

To keep the string taut and prevent the bob from falling down, we have as limiting conditions for the height of the interrupting peg: and for the initial angle: .


Contributed by: Erik Mahieu (December 2011)
Open content licensed under CC BY-NC-SA



Each complete period is a sequence of four quarter-periods: two for a pendulum of length 1 and initial angle when the bob is to the right of the vertical and two for a pendulum of length and initial angle when the bob is to the left. The quarter-periods are determined by solving the appropriate ODE and escaping the solution using Mathematica's built-in "EventLocator" method.

An interesting article on the subject is C. E. Mungan. "Maximum Bob Height of an Interrupted Pendulum." United States Naval Academy Physics Department. (2006)

See also the Demonstration by Enrique Zeleney, "Interrupted Pendulum".

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