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Smart polymers have the ability to respond to slight changes in the environment. They recover their initial state as soon as the stimulus is removed. Temperature sensitive polymers are the most widely studied smart polymers. Here the stimulus is 'temperature'. Poly N-Isopropylacrylamide is one such temperature-sensitive polymer. It exhibits a sharp phase transition close to 32 C0. In the present work normal mode analysis with full dispersion curves within the first brillion zone have been calculated for Poly N-Isopropylacrylamide using Wilson GF matrix method as modified by Higg. The frequency distribution curves (density-of states) are derived from dispersion curves which in turn gives the heat capacity as a function of temperature.