A model describing a dynamic system subjected to repetitive impulse was developed. The methodology presented addressed the specific case where the impulse repetition occurred at equal time intervals. The methodology was illustrated through an example, where a cryocooler induced repetitive impulse to a cryocooler cooled device. The analysis considered both a rigidly and a flexibly mounted cryocooler. Passive control was implemented by varying the coupling stiffness between the cryocooler and the cryocooler cooled system, the stiffness to ground and the mass of the cryocooler.