Discussion
Statement I: A negative value of the last coefficient E in the longitudinal quartic implies at least one real positive root.
Statement II: That condition corresponds to the loss of static longitudinal stability.
In the light of the above statements, choose the correct answer.
Answer: C
Both statements are correct, and together they are the neatest link between static and dynamic stability. With \( A \) positive, the product of the four roots equals \( E/A \); a negative \( E \) therefore forces an odd number of negative-product combinations, which for a real system means a real root in the right half plane and a pure divergence with no oscillation. The classical result is that \( E > 0 \) is the dynamic statement of the static stability criterion, so an aeroplane that has just lost static stability shows itself dynamically as an aperiodic pitch divergence rather than as a growing oscillation.
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