The frequency response was determined for a second order servomechanism with backlash in the system. Frequency response for sinusoidal inputs were obtained by digital computer solutions of the equations of motion of the system which had inertia and viscous friction on both sides of the gear train. System parameters included input amplitude, magnitude of backlash, damping ratio and resilience of the gear teeth. The Control Data Corporation 1604 Computer was utilized and Fortran programming was employed. Results show the effects of the amount of backlash and the gear material resilience on the output to input ratios. The existance of sub-harmonic resonance was found with large values of backlash.