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A modified Landau‐Lifshitz equation is solved for a single‐domain sphere and an infinitely‐wide thin single‐domain sheet of ferromagnetic material neglecting anisotropy. The external magnetic field is switched from one direction to its opposite instantaneously at the initial time and the behavior of the magnetization vector is investigated thereafter. It is shown that there is a critical value of the damping constant corresponding to the minimum value of the (repetitive) magnetization reversal time. If the damping constant is larger than the critical value, the magnetization vector moves slower; if it is smaller, the magnetization vector moves faster but oscillates so that it takes longer time until it comes to a rest at the final position. The critical values of the Landau‐Lifshitz damping constant λ are γM for the sphere and 0.013γM for the thin sheet, where γ and M are the gyromagnetic ratio and the magnetization, respectively. The computed minimum switching time for the thin sheet of 4–79 molybdenum Permalloy is of the order of 10-9 sec.