#### Exercises in Wave Digital Modeling

**Comparing digital and analog frequency formulas.**This first exercise verifies that the elementary ``tank circuit'' always resonates at exactly the frequency it should, according to the bilinear transform frequency mapping , where denotes ``analog frequency'' and denotes ``digital frequency''.- Find the poles of Fig.F.35 in terms of .
- Show that the resonance frequency is given by
- Recall that the mass-spring oscillator resonates at
. Relate these two resonance frequency formulas
via the analog-digital frequency map
.
- Show that the trig identity you discovered in this way is true.
*I.e.*, show that

- Find the poles of Fig.F.35 in terms of .

**Previous Section:**

Energy-Preserving Parameter Changes (Mass-Spring Oscillator)