  We explore the topological aspect of dynamics in a micro-electro-mechanical
system (MEMS), which is a combination of an electric-circuit system and a
mass-spring system. A simplest example is a sequential chain of capacitors and
springs. It is shown that such a chain exhibits novel topological dynamics with
respect to its oscillation modes. On one hand, when it undergoes free
oscillation, the system is governed by the Su-Schrieffer-Heeger model, and the
topological charge is given by a winding number. Topological and trivial phases
are differentiated by measuring the dynamics of the outermost plate. On the
other hand, when it undergoes periodical motion in time, the system is governed
by an inversion-symmetric-trimer model, and the topological phases are
characterized by an inversion-symmetry indicator. There emerge topological edge
states, which are well signaled by measuring electromechanical-impedance
resonance. Our results will open an attractive field of topological MEMS.
