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The buzz phenomenon of a typical supersonic inlet is analyzed on the basis of numerical simulations and duct acoustic theory. Considering that the choked inlet could be treated as a duct with one end closed, a one-dimensional (1D) mathematical model based on the duct acoustic theory is proposed to describe the periodic pressure oscillation of the little buzz and the big buzz. The results of the acoustic model agree well with that of the numerical simulations and the experimental data. It could verify that the dominated oscillation patterns of the little buzz and the big buzz are closely related to the first and second resonant mode of the standing wave, respectively. The discrepancies between the numerical simulation and the ideal acoustic model might be attributed to the viscous damping in the fluid oscillation system. In order to explore the damping, a small perturbation jet is introduced to trigger the resonance of the buzz system and the nonlinear amplification effect of resonance might be helpful to estimate the damping. Through the comparison between the linear acoustic model and the nonlinear simulation, the calculated pressure oscillation damping of the little buzz and the big buzz are 0.33 and 0.16, which could be regarded as an estimation of real damping.