Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Dynamics-Critical Damping Coefficient

  1. Nov 16, 2006 #1
    I have been reading Equations of Motion pertaining to "Damped Single Degree of Freedom Systems"

    There, the critical damping coefficient wherein the oscillation is completely eliminated from the system is defined by:

    Critical Damping Coefficient = 2 x m x (omega)

    where,
    m=mass
    omega=natural frequency of the system
    Natural frequency of the system= square root(k/m)

    k=stiffness of the system

    I want to know how the expression for critical damping coefficient obtained as 2 x m x (omega).

    Is it obtained through experiments/statistics??

    Please help
     
  2. jcsd
  3. Nov 16, 2006 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Remember how a spring acts if the "critical damping coefficient" is obtained.
    How is the spring moving then?
     
  4. Nov 16, 2006 #3
    Thanks for the response!!
    The spring will not oscillate if the critical damping coefficient is obtained.
    My question is how the expession of

    Critical Damping Coefficient = 2 x m x (omega) is obtained??
    Is it through experiments or statistics??

    where,
    m=mass
    omega=natural frequency of the system
    Natural frequency of the system= square root(k/m)

    k=stiffness of the system
     
  5. Nov 16, 2006 #4

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    "The spring will not oscillate if the critical damping coefficient is obtained.
    "

    Correct!
    So, if the system doesn't oscillate, what is its oscillation frequency equal to?
     
  6. Nov 16, 2006 #5
    if the system does not oscillate , oscillation frequence is zero
     
  7. Nov 16, 2006 #6

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Again correct!

    1. Now, for a given damping coefficient b, what is the general expression for the oscillation frequency of the system?

    2. How should we choose critical damping coefficient b* so that the oscillation frequency is, indeed, 0?
     
  8. Nov 16, 2006 #7
    1)for a given damping coefficient b, what is the general expression for the oscillation frequency of the system,

    omegad = omegan x sqrt (1-(b^2/2 x m x (omegan)^2))
    2)to keep the oscilaltion "zero"
    b=2 x m x (omegan)
     
  9. Nov 16, 2006 #8

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Again correct. You're finished.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Dynamics-Critical Damping Coefficient
  1. Critical Damping: T/4? (Replies: 6)

Loading...