Discussion
The stick-fixed longitudinal characteristic equation of a conventional aeroplane is a quartic. For most configurations its roots appear as
Answer: A
The quartic normally factors into two oscillations: the phugoid, with a period of tens of seconds and a damping ratio of a few hundredths, and the short period, over in a second or two and damped between about 0.3 and 0.8. Their frequencies differ by a factor of thirty to a hundred, which is exactly why each can be studied with a two-degree-of-freedom approximation that ignores the other. Four real roots describe an aeroplane with no oscillatory longitudinal behaviour at all, which a conventional configuration does not have, and two positive ones would mean divergence. A repeated real pair is the critically damped special case, not the general one. Purely imaginary roots would mean undamped oscillation, so the aeroplane would ring forever after a gust.
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