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The elementary impedance element in mechanics is the dashpot which may be approximated mechanically by a plunger in a cylinder of air or liquid, analogous to a shock absorber for a car. A constant impedance means that the velocity produced is always linearly proportional to the force applied, or , where is the dashpot impedance, is the applied force at time , and is the velocity. A diagram is shown in Fig. 7.1.
In circuit theory, the element analogous to the dashpot is the resistor , characterized by , where is voltage and is current. In an analog equivalent circuit, a dashpot can be represented using a resistor .
Over a specific velocity range, friction force can also be characterized by the relation . However, friction is very complicated in general [419], and as the velocity goes to zero, the coefficient of friction may become much larger. The simple model often presented is to use a static coefficient of friction when starting at rest () and a dynamic coefficient of friction when in motion ( ). However, these models are too simplified for many practical situations in musical acoustics, e.g., the frictional force between the bow and string of a violin [308,549], or the internal friction losses in a vibrating string [73].