In this article, we derive error estimates for the Galerkin approximation of a general linear
second order hyperbolic equation. The results can be applied to a variety of cases, for example,
vibrating systems of linked elastic bodies. The results generalize the work of Baker  and also
allow for viscous type damping. Splitting the proofs for the semi-discrete and fully discrete cases
not only simplifies the proofs but less restrictive regularity assumptions are required.