  Non-Hermitian topological phenomena occur in mechanical systems described by
the Newton equation. A mechanical graphene, which is composed of mass points
and springs, shows symmetry-protected exceptional rings (SPERs) in the presence
of the friction. However, it remains unclear what physical properties or
phenomena the SPERs induce. Our numerical analysis reveals that the SPERs can
govern dynamics in the wavenumber space. Moreover, we propose how to extract
the dynamics in the wavenumber space for systems with the boundaries.
Furthermore, we also observe that connectivity of the SPERs changes depending
on the fiction, which is analogous to the Lifshitz transition of electron
systems.
