Discussion
Why is a Dutch roll of adequate damping ratio still objectionable if its frequency is very low?
Answer: D
Decay is governed by the product \( \zeta\omega_n \), so a low frequency stretches the absolute time to decay even when the ratio itself looks acceptable. A damping ratio of 0.1 at 0.3 rad/s takes over twenty seconds to halve, which passengers experience as a persistent wallow. That is precisely why specifications constrain the product and the frequency separately rather than the ratio alone. Low frequency does not make a mode aperiodic, tells us nothing about the spiral, and does not affect roll control.
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