Eur. Phys. J. Plus (2022) 137: 9
https://doi.org/10.1140/epjp/s13360-021-02239-5

Regular Article

Frequency level repulsion and exchange of normal-mode shapes at avoided crossings in 1D dissimilar coupled elastic resonators

¹ Instituto de Física, Benemérita Universidad, P.O. Box J-48, Autónoma de Puebla, 72570, Puebla, Pue., Mexico
² Universidad Politécnica del Estado de Morelos, 62550, Jiutepec, Morelos, Mexico

^b jtorresg@upemor.edu.mx

Received: 4 August 2021
Accepted: 28 November 2021
Published online: 13 December 2021

Abstract

We report the experimental measurement of the exchange of torsional normal-mode shapes around an avoided crossing of levels in an elastic system consisting of two dissimilar coupled aluminum resonators. The length of both resonators is varied while keeping the total length of the system fixed, which allows both avoided crossings between any of the independent states of both resonators and a good resolution in the experimentally obtained frequencies. The relative contribution of the independent states to the normal-mode shapes is compared with the two-level quantum case, and remarkable similarities are found for avoided crossings between identical independent states. In contrast, discrepancies are found for avoided crossings between different independent states of both resonators.