Suspend a metal ball from a fixed support using a rubber band and twist it many times around its vertical axis. When the ball is released, standing waves are formed on the rubber band. Investigate this phenomenon and study how the wave depends on relevant parameters.

Background reading from IYPT reference kit

*G. Zurlo, J. Blackwell, N. Colgan, and M. Destrade. The Poynting effect. Am. J. Phys. 88, 12,1036-1040 (2020), arXiv:2004.09653 [condmat.soft], https://doi.org/10.1119/10.0001997 *P. Ciarletta and M. Destrade. Torsion instability of soft solid cylinders. IMA J. Appl. Math. 79, 804-819 (2014), arXiv:2009.09790 [condmat.soft], https://doi.org/10.1093/imamat/hxt052 *J. Diani, B. Fayolle, and P. Gilormini. A review on the Mullins effect. Eur. Polymer J. 45, 3, 601-612 (2009), https://doi.org/10.1016/j.eurpolymj.2008.11.017

TYPT Supplementary References

University Physics Vol. 1 Ch. 15 Oscillations, Ch. 16 Waves. https://openstax.org/details/books/university-physics-volume-1

• https://openstax.org/books/university-physics-volume-1/pages/15-introduction
• https://openstax.org/books/university-physics-volume-1/pages/16-introduction

Nayfeh, A. H., & Mook, D. T. Nonlinear Oscillations. Wiley, 1979. https://archive.org/details/NonlinOscNayfeh/mode/2up Graff, K. F. Wave Motion in Elastic Solids. Dover, 1991. https://archive.org/details/wavemotioninelas00graf/page/n3/mode/2up

OBSERVATION

We have:

• A metal ball (mass m) suspended from a fixed point by a rubber band of length L, linear density μ, and elastic modulus E.
• The rubber band is twisted many turns about the vertical axis.
• When released, the torsional energy stored in the twisted band converts into:
  • Rotational motion of the ball
  • Elastic wave motion along the band

This creates standing waves that are visible as patterns along the rubber band.

SIMPLE MODEL (THIS IS AN EXAMPLE. YOU MAY HAVE YOUR OWN)

ADVANCE MODEL (THIS IS AN EXAMPLE. YOU MAY HAVE YOUR OWN)