PSN-L Email List Message

Subject: serious pendulum misconceptions
From: Randall Peters PETERS_RD@..........
Date: Tue, 19 Feb 2008 08:13:55 -0500

Just because a physical pendulum has a long period does not mean it is useful as a
For two decades I have been using such an instrument to study internal friction.  The period
such a pendulum approaches very long values (easily beyond 20 s), by causing the center of
mass to
get ever closer to the axis of rotation.  The way this is done, of course, is to put mass
above the axis
as well as below it as in the simple pendulum  The long periods of oscillation are possible
only for
a structure that is very rigid, having a large quality factor in the absence of externally
imposed damping.
     The reason this long period pendulum is not a useful seismometer is very easy to
understand from
the physics of extended bodies.  When you apply a force to an extended body, as opposed to a
mass, the acceleration that results involves both translation and rotation.  If the force
acts exactly through
the center of mass, the result is strictly translation; i.e., rotation is not possible
because the moment arm
responsible for torque has vanished.
    In the case of the pendulum, the acceleration of the case is equivalent (in terms of
response) to a force
in the opposite direction to the acceleration acting directly on the pendulum through the
center of mass.
As the center of mass approaches the axis, there is no torque with which to produce
rotation.  Without rotation
there is no response.  Thus the instrument is not a viable seismometer, even though it is a
wonderfully useful
tool for studying the influence of defect structures.
    What this demonstrates is just one more example of the critical need to understand
conceptually the
physics involved, if one is to build a useful instrument.  That physics continues to be
'clouded', even by the 'analogy'
you mention Chris--about pucks on a table.  The demonstrations that you observed were cases
appropriate to the discussion of seismic behavior) in which the frequency character of
disturbance was much higher
than the natural frequency of the analogous seismometer (puck/spring arrangement).  The unit
was therefore
functioning as the 'vibrometer' that I mentioned earlier.  The vibrometer works on the basis
of the fact
(low eignfrequency of the instrument compared to frequency of acceleration disturbance) that
there is
insignifcant motion of the mass (puck) over the time intervals
of external (case) disturbance.  This is not the regime for which are trying so hard to
improve instrument performance.
That regime is at the opposite end of the excitation frequency spectrum.  When the case of a
seismometer is
accelerated at very low frequencies of the earth's motion, there is absolutely no way one can
think of the inertial
mass remaining at rest!!!!!  The mass is connected to something (whether spring or pendulum
rod) that serves as
a device to keep it centered in the case and which is responsible for the seismometer being a
oscillator.  If it were not an oscillator, then there would be no reason to provide eddy
current dampers using rare earth magnets.  Simply stated, the inertial mass MUST be part of
an oscillator
IF it is to be a seismometer.  If it oscillates, then the mass cannot remain at rest, and
there is a repeat interval of time
associated with the motion, called the period of oscillation.  The finite value of this
period is what in turn causes an
upper limit on the sensitivity that is governed by the square of the period of oscillation.
The reason there is a limit to the amount of relative motion between mass and case
(instrument sensitivity) is the FACT that the inertial mass DOES move.
There is ABSOLUTELY no way it CANNOT!
    On a different subject:
Chris you mention what I believe to be indeed true--publishable results out to (and beyond)
2000 s could change a
great deal in the world of seismmology.  It is a virtually unexplored regime.  Let me give
you an example.  I was just yesterday looking at the
differences between the N-S and E-W channels of my VolksMeter here in Macon.  Because the
concrete cylinder that
is part of the monolithic pier goes 20 ft into the ground, there is a significant reduction
in the thermoelastic tilt that is
otherwise seen for instruments sitting on a slab on top of the earth.  What is really
interesting about the two channel
records, for 1 sample per minute over 24 h is the following.  Sometimes the two channels are
almost completely
correlated.  Whatever is tilting the pier is the same in both N-S and E-W direction.  But
there are days in which
this is not at all true.  A correlation plot shows fascinating loop-the-loops that seem to
cycle over a period of several days.  Is this something local to middle Georgia, or does it
have global features?  The answer to this important question can only be provided by
networked sensors.  What I find remarkable is that a simple pendulum has the potential to do
experiments which cry out for data collection.  Anybody who believes that science is in the
process of just 'tying up loose ends' to mature understand of nature (whether in physics or
any other discipline) is hopelessly naive.  It is mind boggling to
me the extent to which seismology has only 'scratched the surface' with regard to a true
understanding of
earth's complex motions. One of the reasons so little understanding has been gained derives
from the 'delta function' mentality concerning sensor type for instruments.

[ Top ] [ Back ] [ Home Page ]