Reciprocating workpiece device with a drive system seeking the resonance of the driven system portion thereof

A dental hygiene device for cleaning teeth, comprising:

• a drive assembly coupled with a driven assembly in such a manner to produce a drive signal for the driven assembly comprising force pulses, resulting in a drive frequency which gradually increases from zero in operation of the dental hygiene device, wherein the drive assembly includes a battery powered DC motor;
• and
• the driven assembly having a brushhead mounted thereon with a return spring assembly, the driven assembly having a resonant frequency, and wherein as the drive frequency increases from zero, the drive frequency will approach the resonant frequency of the driven assembly, at which point the energy produced by the motor is transferred into movement of the brushhead, such that the tips of the bristles of the brushhead move at a velocity greater than approximately 1.5 meters per second, sufficient to produce a cleansing action on the teeth.