To simulate the effect of an earthquake on a rigid building

Question

To simulate the effect of an earthquake on a rigid building, the base is assumed to be connected to the ground through two springs: K_h for the translation al stiffness, and

Kr for the rotational stiffness. If the ground is now given a harmonic motion, Y_g = Y_c sin^ωt, set up the equations of motion in terms of the coordinates shown in Figure.