The low frequency vibrational modes of NO adsorbed on a Pt(111) surface have been investigated with helium atom scattering (HAS). At low coverages (Theta=0.03) NO forms a dilute phase of isolated molecules which have a characteristic frequency of (h) over bar omega=8.0 meV. Based on isotope exchange measurements this mode is assigned to the parallel frustrated translational mode (T-mode) of NO at on top sites. At saturation a well ordered p(2x2) structure (Theta=0.25) appears, for which two different dispersionless modes with frequencies of (h) over bar omega=9.5 meV and 12.3 meV were observed. Isotope substitution revealed that the higher frequency mode corresponds to a vibration of the NO molecules in specific threefold hollow sites, as shown by the asymmetric helium diffraction peak intensities. A lattice dynamical analysis identified the lower frequency mode as a back-folded substrate surface phonon, emphasizing that the surface phonon Umklapp processes must be properly identified in order to assign the low energy adsorbate vibrations correctly.