Beat (acoustics)/Differential equations

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Proposed style of this section

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 ${\dot {x}}_{j}=dx_{j}/dt$ 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

• w:Matrix differential equation
• w:Characteristic equation (calculus)

• b:General Mechanics/Coupled Oscillators
• b:Circuit_Theory/Laplace_Transform#Determining_electric_current_in_circuits

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

• w:Relaxation oscillator
• w:Limit cycle
• w:Hodgkin–Huxley model
• w:Phase-locked loop
• w:Arnold_tongue#Mode_locking
• w:Method_of_averaging#Example:_Van_der_Pol_Equation
• w:
• w: