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As the centre of gravity is moved progressively aft towards and beyond the neutral point, the short-period roots

  • A.Move away from the origin along the imaginary axis
  • B.Stay fixed while only the phugoid roots move
  • C.Become more heavily damped without any change of frequency
  • D.Move towards the origin, and eventually one root crosses into the right half plane

Answer: D

Aft loading reduces pitch stiffness, so the short-period roots migrate towards the origin: the frequency falls, the damping ratio rises because the real part is roughly preserved, and at the neutral point the stiffness reaches zero. Past it, \( E \) changes sign and a root crosses into the right half plane, giving the aperiodic pitch divergence that defines the aft limit. Moving away from the origin is what a forward shift does. The phugoid is comparatively insensitive to centre of gravity, so it is the short period that moves, not the other way round. Damping ratio and frequency cannot change independently here, since both depend on the same stiffness.

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