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.
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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