  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.
