Fig.1(Critically Damped System)
ξ
is equal to one, or the damping coefficient c
is equal to critical damping coefficient "c_{c}", then the system is said to be a critically damped system.Now, let at
$t = 0$ : $x = X_0$
$t = 0$ : $\mathring x =0$
Substituting these values in equation (1):
From above equation (5), it is seen that as time t
increases, the displacement x
decreases exponentially.
The motion of a critically damped system is aperiodic (aperiodic motion motions are those motions in which the motion does not repeat after a regular interval of time i.e non periodic motion) and so the system does not shows vibrations.
For critically damped systems, if a system is displaced from its initial position, it will try to reach its mean position in a very short time.
Critically damped systems are generally seen in hydraulic doors closer as it is necessary for the door to come to its initial position in a very short time.
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