Linear and time-invariant dynamic systems (L.T.I.) of second order, called overdamped, are characterized because their poles are real and differents. Usually the step response has been proposed in terms of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\xi, w_{0}$</tex> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K_{DC}$</tex> [1]–[3], which are called parameters of the transfer function, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$G(s)$</tex> ; others have set it in terms of time constants <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\tau_{1}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\tau_{2}$</tex> [4]–[6]. This article discusses the use of the dominant pole <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p1$</tex> and the relationship between the fastest pole and that one, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha:=p2/p1,\ p1 &lt; p2$</tex> , to state the expression of the system response signal, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$y(t)$</tex> . This approach leads to a formulation of the expression for the simplest system output signal, setting <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\xi$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$w_{0}$</tex> in terms of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p_{1}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha$</tex> . It should be noted that this approach allows determining certain characteristics of the signal from output to input step, for example, the determination of the settling time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t_{s}$</tex> , rise time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t_{r}$</tex> , fitting it with a polynomial for an easy calculation, also the time in which the change of concavity occurs with which the output corresponding to that instant of time is determined, there it is shown that this value is not greater than 27% of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K_{DC}$</tex> . Finally, the general expression for the impulse response is presented, parameterized by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p_{1},\ K_{DC}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha$</tex> . It is important to mention that the previous parameters cannot be obtained from the other known representations, with which from this work will have mathematical expressions to be able to completely analyze the overdamped second order systems, as the case for the first order systems, without having to simulate the output signal and obtain them from measurements on it.