2 - Pitch Divergence

Given the c.g. and e.a. at 35% chord
\begin{align*}
e &= 0.06 \\
\gamma &= 8 \\
I^*_f &= 0.001 \\
R &= 20 \mathrm{\;ft} \\
c &= 1 \mathrm{\;ft} \\
\omega_{\theta_0} &= 14 \mathrm{\;Hz}\\
\Omega &= 420 \mathrm{\;RPM}
\end{align*}
For a stable blade,
\begin{equation}
\frac{x_I - x_A}{R} < \frac{16}{3\gamma}\nu_\beta^2 I^*_f \nu_\theta^2
\end{equation}
The aerodynamic center is assumed to be at 1/4-chord, and \(x_I = 0\) giving the left-hand side
\begin{equation}
\frac{0.1\times1}{20} = 0.005
\end{equation}
the rotating flap frequency is
\begin{equation}
\nu_\beta^2 = 1+\frac{3}{2}e = 1.09
\end{equation}
the rotating torsion frequency is
\begin{equation}
\nu_\theta^2 = 1 + \frac{\omega_{\theta_0}^2}{\Omega^2} = 1 + \left(\frac{14}{\frac{420}{60}}\right)^2 = 1 + 4 = 5
\end{equation}
giving the right-hand side
\begin{equation}
\frac{16}{3\times8}\times1.09\times0.001\times5 = 0.0036\bar{3}
\end{equation}
therefor
\begin{equation}
0.005 \nless 0.00363
\end{equation}
and the blade is unstable in pitch divergence at 420 RPM.