PSN-L Email List Message

Subject: Sensor Type (was Pendulum Q)
From: Roger Sparks rsparks@..........
Date: Mon, 22 Jan 2007 23:08:01 -0800

Randle,   Thanks for the thought provoking response.

I can understand what you are saying about direct coupled sensing of 
pendulums, but I think I am correct in saying that your comments are 
limited to sensors that actually extract some power from the pendulum 
motion.   A sensing system that (for instance) that counted area 
sweeping past a camera in a time period should not count as a direct 
coupled sensor.

I am using a magnetic/coil sensing system with a heavy damper.   The 
system is near or even more than critically damped.   My sensing magnet 
and coil are not providing much load on the pendulum, most of the energy 
captured by the pendulum is dissipated in the damper.   I certainly 
agree that my sensing system is really acceleration based as it does 
load and reduce the pendulum speed.   The sensor also acts to accelerate 
the pendulum from a standing start when a wave arrives.   These are two 
reasons to describe the system as an acceleration sensor.  

Despite these acceleration events, I have described my sensor as a 
velocity device.   I do this because maximum output of the sensor occurs 
when the pendulum is moving at maximum velocity.   Or at least that is 
what I believe is happening. 

I think of my pendulum as being set in motion by my direct coupled 
damper, direct coupled sensor, supporting spring, hinge, and surrounding 
air.   The sequence of events is: (1)earth moves; (2)damper, sensor, 
spring, hinge and air move; (3)pendulum responds to forces of 
acceleration from damper, sensor, spring, hinge, and air.   Once moving, 
the pendulum begins integrating all the instantaneous forces which will 
increase at different rates, and will not stop relative to earth until 
all the absorbed energy has been dissipated, which will not occur until 
some time period after the earth motion has stopped.   This time delay 
is dramatic if one watches an in-car pendulum while stopping the car.

There seems to be some logic in classifying a sensor by when peak output 
is reached relative to pendulum velocity as measured against earth.   A 
strain gage mounted on the side of a flexible pendulum arm should be a 
pure acceleration measure.   A magnetic system can be closely coupled an 
be an acceleration system, or could be lightly coupled with very little 
effect on the velocity of the pendulum.   A capacity measuring position 
indicator would have a negligible force couple to the pendulum but not a 
zero force because a conductor or dielectric will be pulled into the 
space between the fixed plates proportional to the applied voltage. With 
negligible coupling, capacity sensors would be position indicators.   
Direct coupled sensors appear to cover nearly the entire range between 
sensing acceleration and sensing displacement.

Amateur seismology is certainly a good way to experiment and learn 
physics.   Thanks to you and several other very knowledgeable people for 
making this hobby very worthwhile and enjoyable.

Best wishes,


psn-l-digest-request@.............. wrote:

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Subject: Re: Digest from 01/21/2007 00:00:40
From:    Randall Peters 
Date:    Mon, 22 Jan 2007 09:47:19 -0500

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Roger, I have respnded to your request for help; i.e.,
"This brings up a very important point--what is the pendulum sensor
reading?   Is it acceleration, velocity, or displacement?  I need help here. "

With all the confusion as to how a seismometer functions, one has to wonder if Einstein was
the only one who ever acquired a complete conceptual
mastery of inertia. His principle of relativity states that the ``laws of physics remain the
same for any non-accelerating frame of reference''. In
practical terms, this equivalence of inertial reference frames means that it is impossible
to detect uniform motion on the basis of measurements
conducted inside a box, such as a seismometer. Thus the only feature of motion having any
importance whatsoever to a seismometer is acceleration
of the case that supports its inertial mass M. It is very common to erroneously believe that
any type motion of the case will be met with displacement
of M relative to the case, because of the inertia of M. Be sure to understand that the only
property of the motion that is ``resisted'' by M is the
acceleration. Thus the acceleration is the only thing that can be directly measured!!
Velocity and position, the other kinematic variables so frequently
discussed in seismology, can only be inferred from the acceleration measurement. Unlike the
quintessential acceleration, they cannot be directly
measured, even though they are frequently specified.
    The output from a seismometer is directly proportional to acceleration, as long as the
acceleration takes place at a frequency
lower than the natural (eigen) frequency of the instrument, and additionally, it is
operating with damping that is near critical. When the frequency of
the drive is higher than the natural frequency of the instrument, the response of the
instrument is attenuated by the ratio of the square of the drive
frequency to the square of the eigenfrequency. If one is talking about the ground
displacement, as opposed to the acceleration, just the opposite
behavior is found. For those who want to believe that a seismometer responds directly to
ground displacement, complete confusion results.
    It is also important to note that the horizontal seismometer, such as a pendulum,
responds to more than one type of acceleration. From ``inside the
box'' of the instrument there is no way to distinguish between these two forms of
acceleration, which are (i) horizontal acceleration of the instrument,
and (ii) changes in orientation of the box (tilt) relative to the direction of the local
field of the earth g of the earth, having the magnitude of 9.8 m/s2.


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