The vibrational spectrum of water near a thermo-sensitive polymer poly(N-isopropylacrylamide) (PNIPAM) undergoing conformational transition through the lower critical solution temperature (LCST) is calculated using molecular dynamics simulations. The characteristic structural features observed at the atomic scale for these proximal water molecules in a solvated polymer chain while undergoing the conformational transition are strongly correlated to their vibrational densities of states. Comparison of the vibrational spectrum below LCST for the proximal water with the vibrational spectrum obtained for bulk water reveals a significant fraction of the hydrogen bonding between the proximal water molecules and the polymer side groups. Hydrogen-bonded bridges of water molecules are formed between two adjacent and alternate monomers. This network of hydrogen bonding results in formation of locally ordered water molecules at temperatures below the LCST. Analysis of the simulation trajectories confirms the presence of a quasi-stable solvation structure near the PNIPAM. The calculated vibrational spectra for proximal water above the LCST suggest significantly reduced hydrogen bonding with the polymer and indicate a reduction in the structural stability of proximal water around a collapsed polymer chain. Systematic trends in the observed peak intensities and frequency shifts at the low- and high-frequency ends of the spectrum can be correlated with the structural and dynamical changes of water molecules below and above the LCST transition, respectively, for various polymer chain lengths. The simulations reveal that, compared to bulk water, the libration bands are blue shifted and OH stretch bands red shifted for water in proximity to PNIPAM with 30 monomer units below the LCST. The simulations suggest that vibrational spectra can be used as a predictive tool for quantifying atomic-scale structural transitions in solvation of thermo-sensitive polymers such as PNIPAM.