PSN-L Email List Message

Subject: Re: New Lehman on line (almost)
From: John & Jan Lahr johnjan@........
Date: Tue, 01 Oct 2002 00:54:14 -0600

Actually, the USGS short period 1Hz systems are adjusted for a bit less
critical damping.  0.8 is, I believe, the damping factor.  Damping issues are discussed
in this message from Sean Morrissey.  I suppose one advantage to slight underdamping
in an amateur system would be to avoid overdamping.  It may be easier to see a small
overshot and return to zero, whereas both critically damped and overdamped
systems will both return to zero without crossing zero eventually.

One can see a graph of the displacement from a damped harmonic oscillator
on this page:

The equations to keep in mind are:

Omega (2 pi frequency) =  [sqrt(4mk  - b**2)]/2m

The damping factor is b/ [2 sqrt(mk)]

If the damping factor is zero (b = 0) then omega = sqrt(k/m)

If the damping factor is 1 (b = 2 sqrt(mk) ) damping is critical and
a displacement will return to zero exponentially.

If the damping factor is greater than 1, displacement will return
to zero at a slower exponential rate.

To see what a damping factor is 0.8 would look like, in the
applet above set m = k = 1 and b = 1.6.  There is a small overshoot
and then a return to zero.


At 08:13 PM 9/30/2002 -0400, you wrote:
In a message dated 30/09/02, shammon1@............. writes:

The standard rule is to pull the boom back a few inches and let it go. The boom
should loose 30% of its motion on each swing past center and come to rest
in 3 1/2 swings.

Hi Steve,

      I am puzzled as to where this *standard rule* is supposed to come from? But using it will give you a quite seriously underdamped system! A critically damped system experiences no oscillation at all. This is inherent in the maths.
      This is important if you apply post processing to the recorded signal with the assumption that it was critically damped to start with. It will also give problems with the amplitudes and frequencies calculated in FFT displays and may 'smear' P and S wave recordings.
      A procedure to get critical damping could involve deflecting the beam a very small amount (microns) and recording the amplifier output. You progressively increase the damping until the arm just returns to the balance position without having crossed the zero line. If you increase the damping further, the arm will simply take longer to get back to zero. If you use huge deflections like a few inches, you are likely to encounter non linear effects which do not apply to the tiny (hopefully!) signals that we normally record.  
      It is helpful if the recording displays just what the earth is doing. It is really not helpful if the system adds an oscillating tail to every transient.


      Chris Chapman

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