An aircraft engine has a rotating unbalanced mass \(m\) at radius \(r\). If the wing can be modeled as a cantilever beam of uniform cross section \(a \times b\), as shown in Fig. 3.39(b), determine the maximum deflection of the engine at a speed of \(N \mathrm{rpm}\). Assume damping and effect of the wing between the engine and the free end to be negligible.