Discussion
Flight test gives the lateral roots as \( -0.12 \pm 1.20j \), \( -2.50 \) and \( -0.02 \). The Dutch roll damping ratio and the roll time constant are
Answer: B
The complex pair is the Dutch roll and the large real root is the roll subsidence:
\[ \begin{aligned} \omega_n &= \sqrt{0.12^{2}+1.20^{2}} = 1.206 \\ \zeta &= \frac{0.12}{1.206} = 0.10 \\ \tau_R &= \frac{1}{2.50} = 0.40 \ \mathrm{s} \end{aligned} \]
so 0.10 and 0.40 s. The small root at \( -0.02 \) is the spiral, here just stable with a time constant of 50 seconds. The second option reports the real part as a damping ratio and the roll root as a time constant without inverting it, and the third takes the spiral root for the roll mode.
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