Let's check our result by comparing the

transfer function from the
input

force to the force on the

mass in both the discrete- and
continuous-time cases.

For the discrete-time case, we have

where the last simplification comes from the mass

reflectance relation

. (Note that we are using the standard

traveling-wave notation for the

*adaptor*, so that the

signs are swapped relative to element-centric notation.)
We now need

.
To simplify notation, define the two coefficients as

From Figure

F.30, we can write

Thus, the desired transfer function is

We now wish to compare this result to the

bilinear transform of the
corresponding analog transfer function. From Figure

F.27, we
can recognize the mass and

dashpot as

*voltage divider*:

Applying the bilinear transform yields

Thus, we have verified that the force transfer-function from the
driving force to the mass is identical in the discrete- and
continuous-time models, except for the bilinear transform

frequency
warping in the discrete-time case.

**Next Section:** Oscillation Frequency**Previous Section:** A More Formal Derivation of the Wave Digital Force-Driven Mass