Figure 3 shows the lumped model of an airplane. The fuselage has mass M = 4 x 103 kg, and the two wings have mass m = 400 kg and stiffness k 105 N/m against the vertical displacements. = The coordinates y, y2 and y3 shown in Fig.3 are taken with respect to the equilib- rium configuration of the system. (a) Determine the mass and stiffness matrices. M 0 07 [40 0 0 4 0 4 0 0 0 0 0 Solution: M = y2 m m 0 m 2k 0 102 kg, K-k -k k (b) Determine the natural frequencies and mode shapes. Solution: W = 0, W = Y1 M Fig.3 -k k = V m 2 1-1/ 0 105 N/m m, 0 k 16 rad/s, w3 = --0-------0- m, 0 k Y3 k(M+2m) Mm m 17 rad/s, m