Dynamics-Critical Damping Coefficient

[jrm2002]

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

 

[arildno]

Remember how a spring acts if the "critical damping coefficient" is obtained.
How is the spring moving then?

 

[jrm2002]

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

 

[arildno]

"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?

 

[jrm2002]

if the system does not oscillate , oscillation frequence is zero

 

[arildno]

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?

 

[jrm2002]

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)

 

[arildno]

Again correct. You're finished.