Article
Version 2
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On the Normal Modes of Coupled Harmonic Oscillators
Version 1
: Received: 14 November 2023 / Approved: 14 November 2023 / Online: 15 November 2023 (10:38:12 CET)
Version 2 : Received: 18 November 2023 / Approved: 20 November 2023 / Online: 21 November 2023 (10:04:52 CET)
Version 2 : Received: 18 November 2023 / Approved: 20 November 2023 / Online: 21 November 2023 (10:04:52 CET)
How to cite: Fernández, F. On the Normal Modes of Coupled Harmonic Oscillators. Preprints 2023, 2023110960. https://doi.org/10.20944/preprints202311.0960.v2 Fernández, F. On the Normal Modes of Coupled Harmonic Oscillators. Preprints 2023, 2023110960. https://doi.org/10.20944/preprints202311.0960.v2
Abstract
We discuss in detail a well known method for obtaining the frequencies of the normal modes of coupled harmonic oscillators that is based on the simultaneous diagonalization of two symmetric matrices. We apply it to some simple illustrative examples recently chosen for the presentation of an alternative approach based on a set of constants of the motion. We show that the traditional method is simpler, even in the case of equal frequencies. We also discuss a problem that commonly appears in elementary courses on quantum mechanics that also requires the diagonalization of two symmetric matrices.
Keywords
coupled oscillators; normal modes; degenerate frequencies
Subject
Physical Sciences, Theoretical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Commenter: Francisco Fernández
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