A free piston and free displacer (FPFD) Stirling cryocooler has been widely used for the cooling infrared and cryo-sensor. The thermodynamic performance of the free piston and free displacer type (FPFD) Stirling cryocooler is highly dependent on the operating frequency of the linear compressor and the natural frequency of the displacer. In this study, to find optimal relation between operating and natural frequency of the displacer the dynamic characteristics of the displacer in the expansion space of the Stirling cooler was investigated by experiment. The experimental results show that the Stifling cryocooler has maximum cooling capacity at the operating frequency of about 0.8 times of the natural frequency of displacer. Therefore the operating frequency of the Stirring cryocooler should be determined by natural frequency of the linear compressor and displacer.