Abstract

Citation

Researchers should cite this work as follows:

• Fay, T. H. (2023). 2003-Fay-Graham-Coupled spring equations. SIMIODE, QUBES Educational Resources. doi:10.25334/HT0Q-AM30

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Fay, T.H. and S. D. Graham. 2003. Coupled spring equations.  Int.J. Math. Educ. Sci. Technol. 34(1): 65-79.  

See https://www.tandfonline.com/doi/abs/10.1080/0020739021000029258 . Accessed on 27 March 2023.

ABSTRACT Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described. For the linear model using Hooke’s Law, the motion of each weight is described by a fourth order linear differential equation. A nonlinear model is also described and damping and external forcing are considered. The model has many features that permit the meaningful introduction of many concepts including: accuracy of numerical algorithms, dependence on parameters and initial conditions, phase and synchronization, periodicity, beats, linear and nonlinear resonance, limit cycles, harmonic and subharmonic solutions. These solutions produce a wide variety of interesting motions and the model is suitable for study as a computer laboratory project in a beginning course on differential equations or as an individual or a small-group undergraduate research project.

This is a great source of experiment ideas and questions.

KEYWORDS: spring, spring mass, coupled springs, model, system, differential equation, periodic, phase portrait, forcing function, forcing, oscillation,