To be able to perform a basic aeroelastic study of the aircraft prototype he is planning to manufacture, a homebuilder has idealized his aircraft as a rigid fuselage of mass 1200kg with two wings built-in, each represented as a flexible member of mass per length 50kg/m,6m semi-span and flexural rigidity 500000Nm2. For sake of simplicity, he further assumes that the series representation for the bending deformation of the wings is a combination of a rigid body heave and a flexible 'branch' shape, namely z(y,t)=q0t+(sy)2q1t. Obtain an estimate for the frequency of the free-free bending mode of the aircraft. Hints - Use a matrix form of analysis, so as to reach an eigenvalue problem - Make use of Lagrange's equations - The mass matrix is not diagonal because the assumed shape for the wing deformation is not a free-free mode shape and therefore is not orthogonal to the rigid body shape. - Using the Rayleigh-Ritz method, the bending deformation becomes z(y,t)=J=1Nj(y)qj(t)