This paper reports a micromagnetic study of single-domain-grain dynamics in a thin-film magnetic recording medium which is used in the hard disk drive industry today. The behavior of the magnetization-vector of an individual grain is modeled by a modified Landau-Lifshitz (MLL) equation with the damping torque originating from the coupling between the magnetization and stresses of the intrinsic and extrinsic magnetic anisotropy. An analytic two-parameter formula governing the magnetization-vector reversal as a function of precession frequency is derived from the equation of magnetization energy loss. This equation depends on material-dependent parameters which are deduced from ferromagnetic resonance measurements. The results show a characteristic feature of magnetization reversal, a transient quasi-stationary state. This state is generally a property of multilayered thin-film recording media and can cause shortening of the relaxation time to the picosecond regime.