Beat (acoustics)/Differential equations

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Proposed style of this section

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Coupled oscillators
 
mass spring system

The article should be accessible to students with one year of calculus. On the linear equations, I would like to start with two coupled pendulums as shown in the figure. I think the   would be best (with  ) The students might not know what matrices are, so write them in non-matrix form and just show them the matrices with a link to matrices on wikipedia (or wikibooks or wikiversity.)

We need a figure showing the equivalent of the linearly coupled linear pendulums to horizontally oscillating masses on spring. That way we can use k and m in solving the problem (instead of g and l for a simple pendulum)

The van der pol oscillator will give them a hint as to the complexity of nonlinear systems.

Linear

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Nonlinear

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  • w:Van der Pol oscillator
  • International Journal of Non-Linear Mechanics, 29, pp. 737-753, 1994 Averaging Method for Strongly Nonlinear Oscillators with Periodic Excitations. R. Valéry Roy, R. Val'ery Roy link1 link2]

Tsatsos, Marios. "the Van der Pol equation." arXiv preprint arXiv:0803.1658 (2008)

King, H., U. Deker, and F. Haake. "Renormalized perturbation theory of the Van der Pol oscillator." Zeitschrift für Physik B Condensed Matter 36.2 (1979): 205-208.

Other

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