The magnetization dynamics of perpendicularly magnetized FePt films is studied using both magnetic-field-induction and all-optical methods. A critically damped trajectory was observed in this system, where the precession ended within subnanoseconds after a single large oscillation. Using the Landau-Lifshitz-Gilbert (LLG) calculation with an experimental configuration, the effective anisotropy and damping constant were obtained. A damping constant of approximately 0.2 was determined after both a magnetic field and a laser pulse were used. The laser-induced real-space trajectory was well explained by the modified LLG calculation taking into account the demagnetization and time-dependent anisotropy.