Micro-electromechanical system (MEMS) resonator is decidedly utilized in a
diversity of areas, including time referencing, movement sensing, signal filtration, mass
detecting, and further numerous applications. The aim of this article is to use the multiple scales
approach to derive analytical formulas for MEMS resonator vibration response. The properties
of the complicated nonlinear system at various AC and DC voltages are investigated to be
extremely well captured by modeling the dynamics of the micro-beam using multiple scales
technique. The resulting Jacobian matrix eigenvalues are tested to verify the stability ranges of
these solutions; hence, the jump phenomenon that occurs in experimental performance is
interpreted. To study the influence of resonator characteristics on the nonlinear dynamical
behavior of such a beam, several response plots are presented. Finally, a numerical solution is
obtained with the fourth order Rung-Kutta method to verify the studied model's overall behavior.