From the

quadratic formula, the two

poles are located at

and there is a zero at

and another at

. If the
damping

is sufficienly small so that

, then
the poles form a complex-conjugate pair:

Since

, the poles are always in the left-half
plane, and hence the analog RLC

filter is always stable. When the
damping is zero, the poles go to the

axis:

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