Discussion
For \( C_{m_\alpha} = -0.8 \ \mathrm{rad^{-1}} \), dynamic pressure \( 3000 \ \mathrm{Pa} \), \( S = 30 \ \mathrm{m^2} \), \( \bar c = 2 \ \mathrm{m} \) and \( I_{yy} = 60\,000 \ \mathrm{kg\,m^2} \), the value of \( M_\alpha = C_{m_\alpha}\bar q S \bar c / I_{yy} \) is
Answer: C
Dimensionalising the moment coefficient:
\[ \begin{aligned} M_\alpha &= \frac{-0.8 \times 3000 \times 30 \times 2}{60\,000} \\ &= \frac{-144\,000}{60\,000} = -2.4 \ \mathrm{s^{-2}} \end{aligned} \]
so -2.4 per second squared, giving a one-degree-of-freedom frequency of \( \sqrt{2.4} = 1.55 \ \mathrm{rad/s} \). The -0.8 option is the coefficient itself, which has different units and cannot be used in the characteristic equation. -24 slips a factor of ten. -1.2 halves the answer, as though the chord had been omitted and the span used instead. The lesson is that frequency rises with dynamic pressure and falls with pitching inertia.
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