## 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

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Actually, the USGS short period 1Hz systems are adjusted for a bit less
than
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
overdamped
eventually.
One can see a graph of the displacement from a damped harmonic
oscillator
http://lectureonline.cl.msu.edu/~mmp/applist/damped/d.htm
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
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
Cheers,
John

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.
Regards,
Chris Chapman

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