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Abstract
Symmetric spring mass networks of finite degree of freedom have been analysed for modes of vibration by the group representation theory. A working outline of the theory has been presented. By associating the unit base vectors with each mass point of the network and by operating on them by the symmetry operators of the system, a reducible representation is generated. The number of irreducible representations contained in the reducible representation are then calculated on the basis of group representation theory. By the use of projection operators the symmetry adapted basis vectors are determined. The energy matrices are obtained in a quasi-diagonal form by Wigner's theorem. The Lagrangian is expressed in the symmetry adapted coordinate system and the frequencies along with their corresponding modes are evaluated from the resulting equations of motion.
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