A full-Lagrangian based Newton scheme for the dynamic analysis of MEMS is developed in this paper. In this scheme, both the mechanical and the electrical analysis is done on the original un-deformed geometry, unlike conventional semi-Lagrangian approaches which perform a mechanical analysis on the un-deformed geometry and the electrostatic analysis on the deformed geometry. The full-Lagrangian approach allows accurate computation of the inter-domain coupling term (mechanical to electrical) for the Jacobian-matrix of the Newton method which, otherwise, is a difficult task for the semi-Lagrangian methods. Dynamic characteristics of a transverse and a lateral comb drive have been simulated using the full-Lagrangian approach. Second super harmonic resonance is found to occur at half of the resonant frequency in these devices.