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.
If our notes and videos are helpful to you, kindly support us by making a donation from our support page so we can continue making more content for students like you.
Go to support page
All comments that you add will await moderation. We'll publish all comments that are topic related, and adhere to our Code of Conduct.
Want to tell us something privately? Contact Us
Comments: