Vibration of M.D.O.F system
All the real structures are actually infinite degree of freedom systems. However, for the purpose of studying their dynamic behaviour we can idealize them into single or multi degree of freedom systems. If mass of the structure can be lumped at different locations in the structure then the dynamic behaviour consists of same number of modes of vibration. Such structure is called a multi degree of freedom system. Typically in a multi-storey building, masses of different elements can be lumped at centre of mass at each slab level.
To find out natural frequencies and natural mode shapes of multidegree of freedom system. To find out response of each floor to a given ground motion.