Parts mating often requires the use of compliant motions, which cause an object in the grasp of a robot to slide along obstacles in its environment. This paper is about the interface between a compliant motion programming system and a compliant motion control system. We propose that in this interface the robot can be modeled as a damped spring. This model allows the programming system to specify and reason about compliant motions without worrying about low-level control details. The utility of the damped spring model is demonstrated by applications in teaching and planning of compliant motion strategies.