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

  • Thread starter Parisa Panahi
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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
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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 .
 

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  • #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:
 
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