A moving coil actuator that moves in a rapid back-and-forth motion is constructed with a magnet assembly that concentrates the magnetic flux in a region of limited length and with a coiled electric conductor that includes two separated regions of densely wound coil, the assembly and conductor arranged such that only one of the coil regions resides in a concentrated flux region at either end of the actuator stroke. This is achieved with either a single region of concentrated flux or two spatially separated regions of concentrated flux. In either case, the force constant, i.e., the motor force generated in each coil per unit of current through the coil, is non-linear, with a maximal force at each end of the stroke and a minimal force at the stroke mid-point. The result is an efficient use of the electric current and relatively small amounts of materials of construction, and accordingly less weight for the actuator to carry during its travel and its changes of direction.