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Which single measurement pair is sufficient to characterise either longitudinal oscillation completely, once its shape is known to be second order?

  • A.The trim speed and the altitude
  • B.The natural frequency and the damping ratio
  • C.The period and the peak amplitude
  • D.The time to half amplitude alone

Answer: B

A second-order mode is fully specified by its natural frequency and damping ratio, from which the period, the decay rate, the time to half amplitude and the cycles to half amplitude all follow. Peak amplitude describes how hard the mode was excited, not the mode itself, so pairing it with the period leaves the decay unknown. Time to half amplitude gives the product \( \zeta\omega_n \) but cannot separate the two factors. Trim speed and altitude are the flight condition at which the mode was measured, which determines the numbers without being them.

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