Experimental observation of exceptional points in coupled pendulums

Abstract

The concept of exceptional point (EP) is demonstrated experimentally in the case of a simple mechanical system consisting of two linearized coupled pendulums. Exceptional points correspond to specific values of the system parameters that yield defective eigenvalues. These spectral singularities which are typical of non-Hermitian system means that both the eigenvalues and their associated eigenvectors coalesce. The existence of an EP requires an adequate parameterization of the dynamical system. For this aim, the experimental device has been designed with two controllable parameters which are the length of one pendulum and a viscous-like damping which is produced via electromagnetic induction. Thanks to the observation of the free response of the coupled pendulums, most EP properties are experimentally investigated, showing good agreements with theoretical considerations. In contrast with many studies on EPs, mainly in the field of physics, the novelty of the present work is that controllable parameters are restricted to be real-valued, and this requires the use of adequate search algorithms. Furthermore, it offers the possibility of exploiting the existence of EPs in time-domain dynamic problems.