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Critical Damping and Related Terms
Since the poles of the transfer function
are [20, p. 624]

(E.9) 
we have that the poles are complex only when
. Equivalently, the
damping ratio
must be less than 1. Since real
poles do not resonate, we have
for any resonator. The case
is called critically damped, while
is called
overdamped. A resonator (
) is said to be
underdamped, and the limiting case
is simply
undamped (
and the poles are on the
axis at
).
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