We describe the results of a simulation of a model of a random chain embedded as a self-avoiding walk on a diamond lattice. The dynamic model is the same as that of Kirkwood. The equation-of-motion method that we use permits such functions as S(k,) the dynamic structure factor, to be calculated as easily as the density of states. We describe the method in some detail and present results on the density of states and S(k,) for chains of 1000 monomers. The results show that a depression appears in the density of states around =0 when the chain is disordered. We discuss the possible origin of this hole and its possible significance for studies of polymer conformation.