### Dashpot

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].

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Ideal Mass

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Memoryless Nonlinearities