Abstract

Citation

Researchers should cite this work as follows:

• Pendril, A. (2023). 2015-Pendrill-Eager-Free fall and harmonic oscillations analyzing trampoline jumps. SIMIODE, QUBES Educational Resources. doi:10.25334/G3KZ-R145

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Article Context

Description

Pendrill^. Ann-Marie and David Eager. 2015. Free fall and harmonic oscillations: analyzing trampoline jumps. Physics Education. 50(1): 1-9.

http://iopscience.iop.org/article/10.1088/0031-9120/50/1/64/meta . Accessed 29 March 2023.

(This is an author-created, un-copyedited version of an article published in Physics Education 50 64-70 (2015). IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at doi:10.1088/0031-9120/50/1/64  .)

  Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion, including free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is obtained in terms of maximum normalised force from the trampoline and the harmonic frequency. A simple expression is obtained for the ratio between air-time and harmonic period, and the maximum g-factor. The results are compared to experimental results, including accelerometer data showing 7g during bounces on a small trampoline in an amusement park play area. Similar results are obtained in a larger garden trampoline and even stronger forces have been measured for gymnastic trampolines.

Visual of data from accelerometer is rendered and parameters are estimated for model comparison.

Keywords:  free fall, trampoline, jump, accelerometer, data, second order, differential equation, model