Is it reasonable to approximate the swinging building (base of the building) during an earthquake to a simple harmonic motion? I am thinking of making a model of swinging building during earthquake and study the methods to minimize the swinging. 

So does it even makes sense to approximate the swinging buildings (the base of the building) to simple harmonic motion? if not then what kind of motion does the buildings do.
By the definition of simple harmonic motion (restoring force proportional to displacement), no. You need to take into account damping.