As we noted earlier, ground and building motion during an earthquake has a complex, vibratory nature. All vibrating objects, including buildings, tend to eventually stop vibrating as time goes on. More precisely, the amplitude of vibration decays with time. Without damping, a vibrating object would never stop vibrating, once it had been set in motion. Obviously, different objects possess differing degrees of damping.
All buildings possess some intrinsic damping.
Today, some of the more advanced techniques of earthquake resistant design and construction employ added damping devices like shock absorbers to increase artifically the intrinsic damping of a building and so improve its earthquake performance.