A three-story building can be modeled as a three-degree-of-freedom system, as shown in Figure 9.23, in which the horizontal members are rigid and the columns are massless beams acting as springs. Assume that m1 = 1200 kg, m2 = 2400 kg, m3 = 3600 kg, k1 = 500 kN/m, k2 = 1000 kN/m, and k3 = 1500 kN/m.
a. Derive the differential equations for the horizontal motion of the masses.
b. Solve the associated eigenvalue problem by hand. Plot the three modes and explain the nature of the mode shapes.
c. Solve the associated eigenvalue problem by using MATLAB.