The conditions controlling the stable oscillation of graphite-based nanoelectromechanical systems (NEMS) are investigated under periodical harmonic driving force with numerical computational methods. The parameters of the system and control force which allow obtaining the sustained stable oscillation at a constant frequency are determined. The operating characteristics of the nano-oscillator are calculated and analyzed for the qual-length and unequal-length graphite sheets. Calculational results show that sustained stable oscillation of the graphite sheets can be realized by properly choosing the amplitude and the initial phase of the periodical harmonic driving force. The methods reported here are believed to have important implications in NEMS design.