What is the Den Hartog Criteria for Tuned Mass Dampers?

[Dustinsfl]

Homework Statement

I have been searching online but I am unable to find a site that explicitly states the Den Hartog criteria for a tuned mass damper.

What is the Den Hartog criteria?

Homework Equations

The Attempt at a Solution

 

[jedishrfu]

Is this a good reference?

http://fire.nist.gov/bfrlpubs/build98/PDF/b98039.pdf

 

[Dustinsfl]

Is this a good reference?

http://fire.nist.gov/bfrlpubs/build98/PDF/b98039.pdf

It has
$$
\mu = m/M
$$
Is $M$ total mass of the system prior to the damper or is the total mass plus the damper mass of m?

 

[jedishrfu]

Look at figure 1, it shows M and m are distinct masses so M is not in fact M+m

 

[Dustinsfl]

Look at figure 1, it shows M and m are distinct masses so M is not in fact M+m

I am not sure on how I would design a tuned mass damper from the paper though. I am trying to design one for a system with $M = 55$ kg and a tuned mass damper weighing $5.5$ kg. The natural frequency of the system is $\omega_n = 12.061$ and the forcing function has $\omega = 183.26$.