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 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

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:

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

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.

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 youa quite seriously underdamped system!Acritically damped systemexperiencesno 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 avery 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