How is the formula for critical damping obtained in mechanical vibration?

  • Thread starter Parisa Panahi
  • Start date
In summary, the formula for critical damping in mechanical vibration is obtained by setting the damping coefficient to the value where the system reaches its fastest settling time without oscillation. This is achieved by solving the equation of motion using the quadratic formula and finding the roots that correspond to critical damping. This formula is crucial in designing systems that require minimal oscillation and quick settling time, such as shock absorbers and earthquake-resistant buildings.
  • #1
Parisa Panahi
How did you find PF?
Google search
Hi, I was reading mechanical vibration, free vibrations.
and I don't know how to obtain critical damping.
there is a formula in the attached file, but I don't understand it :(
I would appreciate it if you tell me how did we obtain this formula .
 

Attachments

  • forum.PNG
    forum.PNG
    21.1 KB · Views: 41
Physics news on Phys.org
  • #3
Parisa Panahi said:
How did you find PF?: Google search

Hi, I was reading mechanical vibration, free vibrations.
Welcome to PF.

The New Member Introduction forum is just for brief intro posts. Please post your question in the main technical forums, probably under the Physics/Mechanics forum. Thanks.
 
  • #5
berkeman said:
Welcome to PF.

The New Member Introduction forum is just for brief intro posts. Please post your question in the main technical forums, probably under the Physics/Mechanics forum. Thanks.
thank you :thumbup:
 
  • Like
Likes berkeman

Similar threads

Equations of motion of a 2-DoF Free damped vibration system
Replies
7
Views
2K
Beam boundary condition problem
Replies
12
Views
1K
Textbook 'The Physics of Waves': Lifetime of SHM Oscillators
Replies
5
Views
487
Inverse Kinematics: Oscillators and Multi-Bar Links
Replies
2
Views
909
I Justify Assumption of Exponential Response to Free Vibration Problem
Replies
6
Views
989
Find the resistive constant in a critically damped system
Replies
14
Views
2K
Damped Oscillatory Motion with Varying Bump Timing for Control
Replies
13
Views
2K
How Can I Vibrate Materials at Different Frequencies Using DC Current?
Replies
1
Views
290
B How are critical values in statistical tests obtained?
Replies
9
Views
1K
Engineering What kinds of jobs can a vibration engineer with this experience?
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top