#### WD Mass-Spring Oscillator at Half the Sampling Rate

Under the bilinear transform, the maps to (half the
sampling rate). It is therefore no surprise that given
(), inspection of Fig.F.35 reveals
that any alternating sequence (sinusoid sampled at half the sampling
rate) will circulate unchanged in the loop on the right, which is now
isolated. Let
denote this alternating sequence.
The loop on the left receives
and adds
to
it, *i.e.*,
.
If we start out with and
, we obtain
, or

which agrees with the spring, as it must.

**Next Section:**

Linearly Growing State Variables in WD Mass-Spring Oscillator

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DC Analysis of the WD Mass-Spring Oscillator