In this talk we will show an application of the theory of Herglotz-Nevannlina functions for the linear viscoelastic problem, the dielectric problem and the conductivity problem in the time domain. Specifically, by using the analyticity of the Dirichlet-to-Neumann map which relates the applied field on the boundary to the corresponding measured field on the boundary one can determine bounds on the response of the body for any moment of time. Such bounds are tighter the more information regarding the body is incorporated. By tailoring the time-dependent applied field so that the bounds incorporating the volume of the inclusion are extremely tight at specific moments of time, one can then use them in an inverse fashion to determine the size of the inclusion.