### Impedance Networks

The concept of impedance is central in classical electrical
engineering. The simplest case is *Ohm's Law* for a resistor
:

*dashpot*, Ohm's law becomes

*mechanical resistance*.

^{2.14}

Thanks to the *Laplace transform* [449]^{2.15}(or *Fourier transform* [451]),
the concept of impedance easily extends to masses and springs as well.
We need only allow impedances to be *frequency-dependent*. For
example, the Laplace transform of Newton's yields, using the
*differentiation theorem* for Laplace transforms [449],

*i.e.*, .) The

*mass impedance*is therefore

*spring*having spring-constant is given by

The important benefit of this frequency-domain formulation of
impedance is that it allows every interconnection of masses, springs,
and dashpots (every RLC equivalent circuit) to be treated as a simple
*resistor network*, parametrized by frequency.

As an example, Fig.1.11 gives the impedance diagram
corresponding to the equivalent circuit in Fig.1.10.
Viewing the circuit as a (frequency-dependent) resistor network, it is
easy to write down, say, the Laplace transform of the force across the
spring using the *voltage divider* formula:

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Equivalent Circuits