PSN-L Email List Message

Subject: Re: Pendulum Q
From: Brett Nordgren Brett3mr@.............
Date: Tue, 23 Jan 2007 19:31:51 -0500

Dr. Peters,

I quite agree that uniform motion of an inertial frame of reference is not 
observable within it; for example the fact that we're moving at roughly 2 x 
10^20 nanometers per second around the sun should not interfere with our 
ability to make sensitive seismic measurements.

However, I am a bit confused about your comments on measuring ground 
motion.  I'd like to see if a thought-experiment approach might help me 
understand.  Let me borrow Einstein's thought-experiment box, the one with 
no windows that is big enough to let me get inside.  Sitting in the box, I 
coat the bottom with thought-experiment ice, the kind that has no 
friction.  Then I set a 1Kg brass weight on the ice in the center of the 
floor and wait for the thought-experiment earthquake to occur, which 
happens right on time.  Being that the quake is conveniently close, I 
observe that the mass appears to be moving, which I record with my video 
camera.  The question is, what am I observing when I plot the motion of the 
weight?  And then, can I tell anything about the nature of the motion of 
the box (i.e. ground velocity or acceleration) from analyzing the weight's 
apparent motion inside the box?  Also, I observe that , since there can be 
no (horizontal) force acting on the weight because of the ice, it will be 
seeing no (horizontal) acceleration at all.


At 09:47 AM 1/22/2007 -0500, you wrote:
>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 
>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 
>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.
>    Randall


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