Definition:Overdamped

Definition
Consider a physical system $S$ whose behaviour can be described with the second order ODE in the form:
 * $(1): \quad \dfrac {\d^2 x} {\d t^2} + 2 b \dfrac {\d x} {\d t} + a^2 x = 0$

for $a, b \in \R_{>0}$.

Let $b > a$, so that the solution of $(1)$ is in the form:
 * $x = C_1 e^{m_1 t} + C_2 e^{m_1 t}$

for $m_1, m_2 < 0$.

Then $S$ is described as being overdamped.


 * Overdamped.png

Also see

 * Definition:Underdamped
 * Definition:Critically Damped