Some application areas such as musical synthesis, animation or more generally, instrumental arts, have specific requirements for the "haptic rendering" of small movements that go beyond the thresholds that usual simulators and haptic interfaces allow. The quality of a simulator is specifically brought by the dynamical properties of its components: haptic interface, simulator and control system. For such type of applications, variations of objects intrinsic properties and mutual combinations are relevant aspects which bring about global properties of an entire object domain as well as restitute specific object properties. As a general aim, rather than to minimize the technical effects to reach transparency, we intent to characterize them by physical metaphors conferring to haptic medium the role of a tool. This standpoint leads to firstly analyze the natural human-object interaction as a simplified evolving system and then considers its synthesis in the case of the interactive physical simulation. By means of a frequential method, this approach is presented for some elementary configurations of the simulator.