Discussion
An aeroplane's phugoid and short-period frequencies are \( 0.07 \ \mathrm{rad/s} \) and \( 3.5 \ \mathrm{rad/s} \). The ratio of short-period to phugoid frequency is about
Answer: D
The ratio is \( 3.5 / 0.07 = 50 \). A separation of this order is typical, and it is the quantitative justification for treating the two modes independently: during one short-period cycle the phugoid variables have moved by about two per cent of their own cycle, so freezing them costs almost nothing. A ratio of 5 would be too close for the approximations to be safe, and is the kind of figure seen on an aeroplane whose short period has been slowed by a very aft centre of gravity. 500 and 25 both come from slipping a factor of ten or two in the division.
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