This paper presents an approach to determine the time locations of a three-impulses sequence input shaper known as Unity Magnitude shaper (UM). The analytic design of UM shaper is already achieved for undamped systems and for low-damped ones. In this work, the analytic design for damped systems of such shaper is first developed for second order systems, then, extended to explicit fractional derivative systems. Graphical approaches are used to counter analytical difficulties.