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A non-oscillatory longitudinal root lies at \( -0.5 \ \mathrm{s^{-1}} \). The time constant of the resulting subsidence is

  • A.2.0 s
  • B.0.5 s
  • C.1.39 s
  • D.0.69 s

Answer: A

The time constant is the reciprocal of the magnitude of the real root, \( \tau = 1/0.5 = 2.0 \ \mathrm{s} \), so the disturbance falls to about 37 per cent of its initial value in two seconds. 0.5 s is the root itself read back as a time. 1.39 s is the time to half amplitude, \( \ln 2/0.5 \), which is a different and equally useful measure but not the time constant. 0.69 s halves that again. Keeping the three apart matters in flight test reporting, since requirements are written sometimes in time constants and sometimes in times to half amplitude.

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