Oscillations of an Elastic Pendulum

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This Demonstration considers the motion of an elastic pendulum. In the case that the spring frequency is double the pendulum frequency, the motions exhibit a resonance. There is nonlinear coupling between the spring motion and the lateral pendulum motion. Two subsystems can exchange energy, which depends on the initial conditions.

Contributed by: Volodymyr Holovatsky and Yana Holovatska (February 2019)
(Chernivtsi National University, Ukraine and Chernivtsi Liceum #1)
Open content licensed under CC BY-NC-SA



[1] A.Vitt and G. Gorelik, "Oscillations of an Elastic Pendulum as an Example of the Oscillations of Two Parametrically Coupled Linear Systems," Zhurnal Tekhnicheskoy Fiziki, 3(2–3), 1933 pp. 294–307.

[2] R. Carretero-Gonzalez, H.-N. Nuñez-Yepez and A. L. Salas-Brito, "Regular and Chaotic Behavior in an Extensible Pendulum," European Journal of Physics, 15(3), 1994 pp. 139–148. doi:10.1088/0143-0807/15/3/009.

[3] M. C. de Sousa, F. A. Marcus, I. L. Caldas and R. L. Viana, "Energy Distribution in Intrinsically Coupled Systems: The Spring Pendulum Paradigm," Physica A: Statistical Mechanics and Its Applications, 509(1), 2018 pp. 1110–1119. doi:10.1016/j.physa.2018.06.089.


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