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Given force inputs and velocity outputs, the frequency response
of an ideal mass was given in Eq.(7.1.2) as
and the frequency response for a spring was given by Eq.(7.1.3) as
Thus, an ideal mass is an integrator and an ideal spring is a
differentiator. The modeling problem for masses and springs
can thus be posed as a problem in digital filter design given
the above desired frequency responses. More generally, the admittance
frequency response ``seen'' at the port of a general
thorder LTI
system is, from Eq.(8.3),

(9.14) 
where we assume
. Similarly, pointtopoint
``transadmittances'' can be defined as the velocity Laplace transform
at one point on the physical object divided by the drivingforce
Laplace transform at some other point. There is also of course no
requirement to always use driving force and observed velocity as the
physical variables; velocitytoforce, forcetoforce,
velocitytovelocity, forcetoacceleration, etc., can all be used to
define transfer functions from one point to another in the system.
For simplicity, however, we will prefer admittance transfer functions
here.
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