## PSN-L Email List Message

Subject: long-period pendulums
From: Randall Peters PETERS_RD@..........
Date: Fri, 09 Nov 2007 13:15:30 -0500

```I noticed the interest in period lengthening of a compound pendulum, as though any such change toward long period would be an advantage.  Unfortunately, this is not the case.  I have spent the biggest part of my career studying internal friction using the rod-pendulum-types in which there is a mass located
above the axis as well as below.  Although the period can be made very long, it does not result in an increased sensitivity in accord with what is experienced with the simple pendulum  This style of pendulum is an entirely different system than the folded pendulum, which I have also researched.  As a
compact unit, the folded pendulum can be made very sensitive.
There can be an advantage to the use of the long-period rod pendulum, but not in the traditional seismic sense.  I wrote a paper titled "Compound pendulum to monitor hurricanes and tropical storms", online at
http://arxiv.org/abs/physics/0610092
and which uses such a pendulum.
For those who want to understand the physics behind my preceding comments, this paper provides the details.
To appreciate the lack of sensitivity (to anything other than really, really low frequency drive, including tilt), consider the following.
Imagine a rod in which the axis approaches the center of mass.  The period thus approaches infinity; so you might expect it to have really great sensitivity.  The problem with the rod pendulum is it becomes very sensitive to internal structural change while having little sensitivity to high frequency
seismic activity.
In fact, the sensitivity at frequencies above the very low eigenfrequency is virtually zero.  The reason is obvious.  If you accelerate an extended object with a force that goes through the center of mass, it does not rotate.
Thus it cannot serve as a seismometer.  Guess you know already that some mechanical systems can be intuitively hard to understand if not downright baffling!  Before I was able to really appreciate what was happening with this pendulum, as relates to seismic sensing, I had to thoroughly describe it with the
tools of physics; i.e., mathematics.  Only afterwards was I able to conceptually appreciate its properties.
There was a comment about the VolksMeter.  How can it, through 'period extension' operate well in spite of a pendulum less than a meter in length.  The key is in what is done digitally.  The raw data output is not good for teleseismic viewing, where sensitivity is a must.  But the integral of that data
alters the response of the instrument (same as is done in the Shackleford-Gunderson).  The Bode plot falls off with frequency, allowing the 20 s period teleseisms to be seen above noise in many cases, for M 6 or more.  It is not a case in which the increased SNR derives from the pendulum; rather it derives
from the electronics employed.  Even force-balance commercial units rely on electronics to give great response even though the eigenfrequency of the non-feedback instrument is too high for good performance.  There the tailoring of both lower corner frequency and damping is accomplished by means of the
negative feedback employed.

Randall

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