Periodic structures have received large interest due to their peculiar behavior: they have band gaps, that is portions of the frequency response along with any wave incoming in the structure is reflected. Numerous are the applications, like metamaterials and locally resonant structures. Nowadays, new possibilities could come from mechanical periodic structures that are connected to an electrical transmission line, periodic in turn. Starting from this idea, this paper analyses ideal a mono-atomic spring-mass chain, considering the springs connected to a periodic electric network, composed by inductances (and resistors): these simple examples will show how the frequency response is affected. In particular, the mutual influence between the electric and mechanical domain is highlighted, and the contribution of parameters on band gap positioning and design is explored. Details are provided about vibration modes and wave transmission.