In this talk, we analyze the stabilization of damped and viscoelastic linear wave equations evolving on a bounded domain, subject to an inhomogeneous Neumann manipulation on a portion of the domain`s boundary. Compared to their homogeneous counterparts, these models present additional features and challenges. This is due to the fact that, in the present context, the rate at which the energy of the solutions changes depends directly on the boundary trace of the temporal derivative. Due to regularity issues, it is not clear in advance how these quantities should be controlled based on the given data. However, we establish global existence and prove the uniform stabilization of solutions, with decay rates characterized by the Neumann input. We support our theoretical results with numerical simulations satisfying the given assumptions. We supplement these with additional simulations in which the data do not necessarily satisfy the required assumptions for decay. The latter offer essential physical insights into how energy might change in the presence of improper boundary data.