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Critical Damping and Related Terms
Since the poles of the transfer function
are [20, p. 624]
![$\displaystyle p_0 \eqsp \sigma_0 \pm j\omega_0 \eqsp -\alpha \pm j\sqrt{\omega_p ^2-\alpha^2} \eqsp -\alpha \pm \sqrt{\alpha^2 - \omega_p ^2}, \protect$](img1913.png) |
(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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