Abstract: The method of moments is applied to the bistable Duffingoscillators driven by Gaussian white noise and weak periodic force, and theconverging rate of the method is found dependent on the damping size,namely, with the same nonlinear parameter, it converges quicker if thedamping coefficient is larger. Since the method of moments can make usdisclose more general characteristic than only using numerical simulations,the results derived from the method of moments along with the numericalsimulation results can make us to find relations between stochasticresonance and stochastic dynamical behavior. With the method of moments, themono-peak and double-peak resonant structures in the system are disclosedwith the spectral amplification factor for different drive frequencies forthe case of the larger damping coefficient. To explain the derived resonantstructure, the dependence of nonzero frequency peaks peaked out fromfluctuating spectral density on noise intensity is investigated, and thedouble-peaked resonance is found to be resulted from the intrawellvibrations and the above potential barrier vibrations, which is amodification to the previous result. The study confirms there are threepossible resonant sources, i.e. interwell jump, intrawell vibration andabove-barrier vibration in the considered system, and the results haveimportance in statistical mechanics.