This paper investigates electrostatically actuated nanoelectromechanical (NEMS), to include Casimir effect, resonator response near natural frequency. Both electrostatic force and Casimir force are nonlinear. The method of multiple scales is used in a direct approach of the problem in the case of small actuation, damping, and Casimir effect. Two approximation problems resulting from the direct approach are solved. The phase-amplitude relationship is obtained. Numerical results for uniform NEMS cantilever resonators for possible sensing applications are provided.

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