Many oscillatory systems are subject to damping effects that are
not exactly analogous to the linear frictional damping considered in Section 2.2.
Nevertheless, such systems typically exhibit an exponential decrease
in their average stored energy of the form
.
It is possible to define an effective quality factor for such oscillators as
, where
is the natural angular oscillation frequency.
For example, when the note “middle C” on
a piano is struck its oscillation energy decreases to one half
of its initial value in about 1 second. The frequency of middle C is Hz. What
is the effective of the system? [Modified from French 1971.]