Yet another meaning for

is as follows [

20, p. 326]

where the

resonator is freely decaying (unexcited).

**Proof. **The total stored energy at time

is
equal to the total energy of the remaining response. After an

impulse
at time 0, the stored energy in a second-order resonator is

The energy dissipated in the first

period
is

, where

Assuming

as before,

so that

Assuming further that

, we obtain

This is the energy dissipated in one cycle. Dividing this into the
total stored energy at time zero,

, gives

whence

as claimed. Note that this rule of thumb requires

, while
the one of the previous section only required

.

**Next Section:** Lossless Analog Filters**Previous Section:** Decay Time is Q Periods