The simplest transducer both for sensing motions and for exerting forces is an electromagnetic (electrodynamic) device where a coil moves in the field of a permanent magnet, like in a loudspeaker (Fig. 14). The motion induces a voltage in the coil; a current flowing in the coil produces a force. From the conservation of energy it follows that the responsivity of the coil-magnet system as a force transducer, in Newtons per Ampere, and its responsivity as a velocity transducer, in Volts per meter per second, are identical. The units are in fact the same (remember that 1 N m = 1 Joule = 1 V A s). When such a transducer is loaded with a resistor and thus a current is permitted to flow, then according to Lenz's law it generates a force opposing the motion. This effect is used to damp the mechanical free oscillation of passive seismic sensors (geophones and electromagnetic seismometers).
We have so far treated the damping as if it were a viscous effect in the mechanical receiver. Actually, only a small part hm
of the damping is due to mechanical causes. The main contribution (in
passive seismometers) normally comes from the electromagnetic
transducer which is suitably shunted for this purpose. Its contribution