The behavior of relaxation oscillations in the presence of a nonlinear loss was used to determine the relevant parameters of an intracavity frequency-doubled and mode-locked Nd : YAG laser. The acousto-optic mode locker was used in a controlled manner to excite the relaxation oscillations which allowed the measurement of the damping time and frequency. Laser output power at 0.53 μm and damping time is consistent with recent theory.