12. Consider the three degree-of-freedom system shown in Fig.4; it consists of three equal masses m and a foundation connected in series by three equal springs k. The absolute displacements of the masses are X1, X2, and x3. The stiffness coefficients are thus K1 = 4k, K22 = 6k, K33 = 3k, K12 = K21 = -k, K23 = K32 = -k, and K13 = K31 = 0. Determine the frequencies of the system. iny min m Fig.4

12. Consider the three degree-of-freedom system shown in Fig.4; it consists of three equal masses m and a foundation connected in series by three equal springs k. The absolute displacements of the masses are X1, X2, and x3. The stiffness coefficients are thus K1 = 4k, K22 = 6k, K33 = 3k, K12 = K21 = -k, K23 = K32 = -k, and K13 = K31 = 0. Determine the frequencies of the system. iny min m Fig.4