Beat (acoustics)/Differential equations

Beat (acoustics) /Phase beats /Literature search /Just fifth displace stretch /Exact phase beats /Differential equations subpages drafts

Proposed style of this section

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 ${\dot {x}}_{j}=dx_{j}/dt$ would be best (with $j=1,2.$ ) 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

w:Linear differential equation: #Homogeneous_equation_with_constant_coefficients

Nonlinear

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