Abstract: A positioning apparatus includes a platen and a head independently movable relative to the platen. First and second coils having a particular phase relationship are disposed relative to each other on the head are independently energized to produce first and second electromagnetic forces. These electromagnetic forces have varying characteristics for moving the head relative to the platen and constant characteristics for maintaining the head in a substantially fixed relationship to the platen. Abrupt changes from the variable to the constant characteristics of the applied electromotive forces allow inertial forces to impart a decaying oscillation of the head about the positional origin determined by the constant characteristics of the applied electromotive force.Oscillation of the head relative to the platen produces first and second back-electromotive force sinusoids in the first and second coils, respectively.