Fig.1(Critically Damped System)
ξis equal to one, or the damping coefficient
cis equal to critical damping coefficient "cc", then the system is said to be a critically damped system.
Now, let at
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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