Model analysis of a hammer-string interaction

A hammer-string interaction of note C4 of a piano is investigated by use of a lumped-element model. The hammer is simulated by a mass-spring system with a nonlinear spring characteristic. The string is simulated by a large number of parallel resonant circuits, each of which consists of a mass, a linear spring, and a dashpot. The interaction period between the hammer and the string is approximately 3 msec for Vh(hammer speed) = 3 m/sec. This is approximately 80 percent of the period of note C4 (3.83 msec). During this period, the motion of the hammer appears as a half cycle of a sine wave. The motion of the string at the striking point is similar to the motion of the hammer, but it is wavier.