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The magnetic dynamics of a total recording system composed of a single pole head and a perpendicular recording medium with a soft underlayer was performed by a three-dimensional micromagnetic model. In this paper, the effect of the magnetic damping constant of the soft underlayer (SUL) on the signal-to-noise ration (SNR) was systematically studied for the case of abrupt change in head field. For this purpose, the different damping constants (α) of 1.0, 0.1, 0.03, and 0.01 were studied in a conventional SUL. In all cases, SNR rapidly decreased with decreasing α of SUL. The longer range magnetic fluctuation in the SUL for smaller damping constant affects the shift of the transition region of the bits more. For comparison, we have shown SNR for the same media with a head field rise time was considered.