The dynamic behavior of system which influenced by the coupling between the single electron spin and carbon nanotube mechanical resonator was theoretically analyzed. By means of a master equation, average phonon occupation number as functions of the frequency detuning under the case with and without qubit-oscillator coupling was investigated via a semiclassical approach. The variation of average phonon occupation number as functions of the frequency detuning under the case with and without rotating-wave approximation was compared for different coupling strength. For coupling system, average phonon occupation number occurs a splitting phenomenmon when resonance, simultaneously, a bistable state was observed near the splitting peak. By analysing the average phonon occupation number of the carbon nanotubes resonator, it was found that rotating-wave and non-rotating-wave approximation can coincide with each other very well under the weak coupling strength. However, the non-rotating-wave approximation term must be considered in the ultrastrong coupling system due to the rotating-wave approximation is no longer effective.