Vibrations of a pendulum consisting of a bob suspended from a wire: the method of integral equations

Author:
Hyun J. Ahn

Journal:
Quart. Appl. Math. **39** (1981), 109-117

MSC:
Primary 70J05; Secondary 45J05

DOI:
https://doi.org/10.1090/qam/613954

MathSciNet review:
613954

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Abstract: The vibrations of a vertical pendulum consisting of a bob suspended from a wire are studied by the method of integral equations and the composite method, respectively. The composite method combines the minimum principles and the method of integral equations. This problem consists of the fourth-order differential equation and the boundary conditions dependent on the eigenvalue parameter. Lower bounds are established for the lowest natural frequencies by both methods. Numerical results are presented. Both theoretical and computational efficiencies are illustrated and the method of integral equations is stressed.

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DOI:
https://doi.org/10.1090/qam/613954

Article copyright:
© Copyright 1981
American Mathematical Society