Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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


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