We report the first analytic study of real time and frequency dependent behaviour at T= infinity of the 2D square lattice transverse Ising model. Our study, along with known results in the 1D case, in the mean field or infinity D case and in other studies, helps understand the experimentally obtained longitudinal dynamic structure factor of the induced moment ferromagnet LiTbF4 studied by Youngblood et al., and is consistent with the studies of Kotzler et al.