The figure below shows a two-story framed structure including two masses (m and m) and four identical columns. The column's modulus of elasticity is E and the column's cross-sectional area moment of inertia about its neutral axis is I. Each floor is supported by two columns. The connection type of each column is shown in the figure. An external force F is exerted on m2. For a welded-welded F13 column, the end deflection & of the column due to a concentrated load F is given by Sc pinned-welded column, the pinned end deflection Sp of the column due to a concentrated load F is given by Sp= F13 3E1 12EI' For a a) Find the equivalent spring constant k and k for pinned-welded columns and welded-welded columns. b) Draw a free-body diagram and derive the EOM for each floor. Use k and kp in your answer. c) State the EOMs in matrix form. Use kc and kp in your answer. d) Draw the equivalent spring-mass system. Pin x2 m2 F Pin Weld Weld x1 m1 Weld Pin Weld Weld