Now let's consider a tworesonance
guitar bridge, as shown in
Fig.
9.6.
Figure 9.6:
Synthetic input
admittance of a passive, linear, dynamic system using a pair of
resonating twopole filters, a pair of zeros between the resonances,
and a zero near dc.

Like all mechanical systems that don't ``slide away'' in response to a
constant applied input
force, the bridge must ``look like a
spring''
at zero frequency. Similarly, it is typical for systems to ``look
like a
mass'' at very high frequencies, because the drivingpoint
typically has mass (unless the driver is springcoupled by what seems
to be massless spring). This implies the driving point admittance
should have a zero at dc and a
pole at infinity. If we neglect
losses, as frequency increases up from zero, the first thing we
encounter in the admittance is a pole (a ``resonance'' frequency at
which energy is readily accepted by the bridge from the strings). As
we pass the admittance peak going up in frequency, the phase switches
around from being near
(``spring like'') to being closer to
(``mass like''). (Recall the
graphical method for
calculating the
phase response of a
linear system
[
449].) Below the first resonance, we may say that the system
is
stiffness controlled (admittance phase
),
while above the first resonance, we say it is
mass controlled
(admittance phase
). This qualitative description is
typical of any lightly damped, linear, dynamic system. As we proceed
up the
axis, we'll next encounter a nearzero, or
``antiresonance,'' above which the system again appears ``stiffness
controlled,'' or springlike, and so on in alternation to infinity.
The strict alternation of
poles and zeros near the
axis is
required by the
positive real property of all passive
admittances (§
C.11.2).
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