Research to improve performance in resonant MEMS sensors has concentrated on novel designs, fabrication techniques, actuation and sensing mechanisms, often based on macroscale designs and phenomena which have been studied extensively. This dissertation is about one such actuation mechanism, called parametric excitation, based on the phenomenon of parametric resonance, to enable performance improvement in an electrostatically actuated MEMS ring resonator modulation can be conveniently achieved using electrostatic actuation which is a widely preferred actuation mechanism for MEMS.