An aircraft wind tunnel model, having a pitch axis mass moment of inertia $\left(I_{y y}\right)$ of $0.014 \mathrm{~kg}-\mathrm{m}^{2},$ is mounted in such a manner that it has pure pitching motion about its centre of gravity, where it is supported through a frictionless hinge. If the pitching moment (M) derivative with respect to angle of attack $(\alpha)$, denoted by ' $\mathrm{M}_{a}$, is $-0.504 \mathrm{~N}-\mathrm{m} / \mathrm{rad}$ and the pitching moment (M) derivative with respect to pitch rate (q), denoted by 'M $_{\mathrm{q}}$, is $-0.0336 \mathrm{~N}-\mathrm{m} /(\mathrm{rad} / \mathrm{s}),$ the damping ratio of the resulting motion due to an initial disturbance in pitch angle is approximately_______________ (accurate to three decimal places).
An aircraft wind tunnel model, having a pitch axis mass moment of inertia $\left(I_{y y}\right)$ of $0.014 \mathrm{~kg}-\mathrm{m}^{2},$ is mounted in such a manner that it has pure pitching motion about its centre of gravity, where it is supported through a frictionless hinge. If the pitching moment (M) derivative with respect to angle of attack $(\alpha)$, denoted by ' $\mathrm{M}_{a}$, is $-0.504 \mathrm{~N}-\mathrm{m} / \mathrm{rad}$ and the pitching moment (M) derivative with respect to pitch rate (q), denoted by 'M $_{\mathrm{q}}$, is $-0.0336 \mathrm{~N}-\mathrm{m} /(\mathrm{rad} / \mathrm{s}),$ the damping ratio of the resulting motion due to an initial disturbance in pitch angle is approximately_______________ (accurate to three decimal places).