Dynamics of liquid water and its isotopes when adsorbed inside carbon nanotubes of different radii is studied by means of molecular dynamics simulations. Water molecules have been modeled with a flexible simple point charged (SPC) potential while carbon forces were accounted for with Lennard-Jones-type potentials. Diffusive behavior and,the librational, rotational, intra- and intermolecular motions of the constrained molecules have been investigated by means of the spectral densities computed from atomic velocity autocorrelation functions. The results show in all cases significant new vibrational bands and frequency shifts absent in bulk water.