From Fig.F.33, we can see that the impedance of the parallel combination of the mass and spring is given by

(using the product-over-sum rule for combining impedances in parallel). The poles of this impedance are given by the roots of the denominator polynomial in :

The resonance frequency of the mass-spring oscillator is therefore

Since the poles are on the axis, there is no damping, as we expect.

We can now write reflection coefficient (see Fig.F.35) as

We see that dc ( ) corresponds to , and corresponds to .

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University