A note on the periodic solutions to a relativistic Micro-Electro-Mechanical System

A recent result shows that there exists d(0)>0 such that an idealized mass-spring model of electrostatically actuated relativistic Micro-Electro-Mechanical System (MEMS) has at least two, at least one, or no periodic solution, according to d >d(0), d=d(0), or d<d(0), respectively. Here d represents the initial distance between two parallel capacitor plates. In this paper, it is further proved that the model has exactly two classes of periodic solutions. The first class of periodic solutions uniformly tends to 0 at the rate d(-1/2) as d tends to +infinity, while the second one uniformly tends to +infinity at the rate d.