Abstract
We have intimated already that a weight on a spring and an oscillating circuit are the same object so far as oscillation theory is concerned. They are both described by a single well-known differential equation and are characterized by the same phase space, that is by a plane containing the trajectories of a family of ellipses lying one inside the other. This would seem to be a trivial statement. “However, it is not trivial that it is trivial,” L.I. Mandel’ shtam remarked. “That is, it is not trivial that the analogy between the oscillations of a weight on a spring and the charges or current within a circuit has come so far that it is now an accepted method of argument amongst physicists even though these phenomena belong to two quite different branches of science.” [1] The philosophy and content of this chapter concerns this analogy, and we consider the properties of a linear oscillator, this being the basic model in the linear theory of oscillations and waves.
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References
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© 1989 Kluwer Academic Publishers
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Rabinovich, M.I., Trubetskov, D.I. (1989). Linear Oscillators. In: Oscillations and Waves. Mathematics and Its Applications (Soviet Series), vol 50. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1033-1_1
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DOI: https://doi.org/10.1007/978-94-009-1033-1_1
Publisher Name: Springer, Dordrecht
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