1 One single and unique time-constant for a linear second order dynamical system Dr. Marcelin Nini DABO, PhD. Abstract—Modern control engineering presents dynamical sys- tems as systems with a well-defined time-constant for first order ordinary differential equations (ODEs) and as systems without a time-constant for second order ODEs. In this paper, I present, for the first time, a new vision on control systems: there is only one single and unique time-constant for a second order dynamical system, whatever its damping ratio and natural pulsation, thanks to a deep observation and contemplation of solutions of second order ODEs. Thanks to this new approach, one can compute, with precision, temporal (or frequencial) per- formances for any given stable second order dynamical system. Also, it is absolutely possible to design a second order dynamical system with precision, by choosing the type of desired dynamics (critically damped, overdamped, underdamped) and the desired time-response or rise-time performance. Morever, a very simple criteria of identification for second order ODEs is presented. […]