An airfoil of mass \(m\) is suspended by a linear spring of stiffness \(k\) and a torsional spring of stiffness \(k_{t}\) in a wind tunnel, as shown in Fig. 5.43. The C.G. is located at a distance of \(e\) from point \(O\). The mass moment of inertia of the airfoil about an axis passing through point \(O\) is \(J_{0}\). Find the natural frequencies of the airfoil.

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k 00000 k C.G. ked FIGURE 5.43 Airfoil.