Discussion
An aeroplane's phugoid is slightly divergent, with a real part of \( +0.02 \ \mathrm{s^{-1}} \). Its time to double amplitude is about
Answer: D
For a divergence, \( t_{2} = \ln 2/\sigma = 0.693/0.02 = 34.7 \ \mathrm{s} \), so about 35 seconds. That figure matters directly: MIL-F-8785C allows an unstable phugoid at Level 3 only if the time to double is at least 55 seconds, so this aeroplane fails even the lowest level and would need augmentation or redesign. 50 s and 20 s do not follow from the arithmetic. 69 s comes from using 1.386 in the numerator, which is the time to quadruple rather than to double.
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