(a) xqt) x(1) m wwww. Zm x(1) &6. Zm EI EI b( 3EI k=3 k= c) xp(t) 3E/ x3(k) xg(t) Figure 1 Model of the wing vibration of an airplane: (a) vertical wing vibration; (b) lumped mass/beam deflection model; (c) spring-mass model. Mode 1: Mode 2: Mode 3: For Mode 1: x11 x12 x13 = = X = EI ml3 EI ml3 EI m13 The three vibration mode shapes corresponding to the three natural frequencies of the airplane, normalised by setting the first element to unity, i.e. x1 = 1. rad/s rad/s rad/s For Mode 2: x21 x22 x23 = For Mode 3: *31 x32 *33