Discussion
For a short-period mode with \( \zeta = 0.6 \), the number of cycles to half amplitude is closest to
Answer: B
Using \( N_{1/2} = 0.110\sqrt{1-\zeta^{2}}/\zeta = 0.110 \times 0.8/0.6 = 0.147 \), the amplitude halves in about a seventh of a cycle. In other words the mode is gone before it completes its first swing, which is why a well-damped short period is described as a crisp response rather than an oscillation. 1.5 is a factor of ten out. 0.60 is the damping ratio quoted back. 2.75 is the answer for a damping ratio of 0.04, which belongs to a phugoid; the contrast between the two figures is the clearest single illustration of how differently the two modes behave.
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