In order to study the load response of two degree of freedom (2DOF) system, to get the response parameters, the experimental platform of the response parameters of 2DOF free vibration was designed. The impact of various factors on the experimental data were analyzed, and a method was presented to get physical parameters identification of free vibration based on curve fitting method. A 2DOF system was formed by two elastic beams with 1DOF unit coupled by spring，timedomain data were collected by LMS vibration tester after couping of the system. The response parameters of free vibration were gotten from the curve fitting of timedomain data by using LevenbergMarquardt plus Universal Globe Optimization （LMUGO）method of 1stOpt. The results show that LMUGO can fit the experimental response data excellently by relying on its strong optimization ability and robustness, calculate the response parameters, which is a powerful tool to deal with curve fitting. The validity of the fitting method is proved by the evaluation method, such as the correlation coefficient, the minimum residuals and etc.