On the Normal Modes of Coupled Harmonic Oscillators

Francisco Fernández

doi:10.20944/preprints202311.0960.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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)

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 and more general because it is suitable for the treatment of problems with degenerate eigenfrequencies. We also discuss a problem that commonly appears in elementary courses on quantum mechanics that also requires the diagonalization of two symmetric matrices.

coupled oscillators; normal modes; degenerate frequencies

Physical Sciences, Theoretical Physics

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On the Normal Modes of Coupled Harmonic Oscillators

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