Q. 1 Figure 1 shows a 2-story building, where the columns has flexural rigidities EI1 & EI2. The stiffness of each column on the lower floor is found from the following: 24�� ℎ' The stiffness of each column on the upper floor is one-third that of the lower floor, i.e. 8�� ℎ' Assume that m1 = 3 m, m2 = m, h1 = h2 = h. (a) Find the governing equations of motion and hence the natural frequencies of the building frame. (b) Find and also sketch the mode shapes of the frame. Figure 1Q. 2 A reciprocating engine is installed on the first floor of a new building to provide ventilation services, which can be modelled as a rigid rectangular plate resting on four elastic columns. The total mass of the engine and floor is 900 kg. At the rated speed of the engine, which is 600 rev/min, the engineers experienced large vibrations of the floor. It has been decided to reduce these vibrations by suspending a spring-mass system at the bottom surface of the floor as the absorber. Assume that the spring stiffness of the absorber is 900 kN/m, find the following: (a) The mass of the absorber to be attached to the floor. (b) The natural frequencies of the system after the absorber is added.