Assignment:
The foundation of the building in Problem below undergoes the horizontal motion y(t) = yo sin wt. Derive the system response.
The one-story structure shown in Fig. can be modeled in the first approximation as a single-degree-of-freedom system by regarding the columns as massless beams clamped at both ends and the roof as a rigid slab. Derive the equation for the horizontal translation of the slab and determine the natural frequency. The mass of the slab is denoted by M and the flexural rigidity of the columns by EI.
Provide complete and step by step solution for the question and show calculations and use formulas.