Definition:Critically Damped

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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:

$x = C_1 e^{-a t} + C_2 t e^{-a t}$


Then $S$ is described as being critically damped.


CriticallyDamped.png


Also see


Sources