Discussion
A Dutch roll trace shows successive peaks of \( 6.0 \) and \( 4.5 \) degrees of sideslip. The damping ratio is about
Answer: C
From the logarithmic decrement:
\[ \begin{aligned} \delta &= \ln(6.0/4.5) = 0.288 \\ \zeta &= \frac{\delta}{\sqrt{4\pi^{2}+\delta^{2}}} = \frac{0.288}{6.29} = 0.046 \end{aligned} \]
so about 0.046, a poorly damped mode that would fail most Level 1 requirements and calls for a yaw damper. 0.29 is the decrement itself, which differs from the damping ratio by a factor of about \( 2\pi \). 0.75 is the ratio of the peaks. 0.25 does not follow from the arithmetic at all.
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