Hi,

I'm a little uncomfortable with your discussion. However, this may just be 
because it's a bit involved.

It should be obvious that if you have a regular stream of data points from a 
displacement sensor, you can plot the velocity (in arbitrary units) on the same 
graph by computing the difference in displacement between two points and 
plotting the points of the new curve "in between" the displacement points. You 
can then repeat the process on the velocity points to get acceleration.

The really important point, however, is to consider a simple pendulum, and 
realise that the acceleration is due to the force acting on the pendulum, which 
has nothing to do directly with the forces acting to move the pendulum support, 
but entirely on how far the pendulum mass is displaced from the "rest" position.

This is Prof Peters' point about acceleration.

I don't find the references to energy helpful. At the end of the day, the 
kinetic energy is eventually dumped into the damping.

If I understand force-feedback correctly, it can be crudely summarised by 
noting that whereas a simple pendulum swings, FFB holds the mass still and the 
simple analogue computer that comprises the fedback circuit swings instead, 
with the force applied to the mass (= acceleration) being measured at the 
output to the feedback coil (or equivalent) as the sensor output.

Kevin Brunt

On Wed, 09 Dec 2009 10:26:55 -0800 RSparks  wrote:

> Hello Randall,
> 
> Thanks for the informative posting relating sensors for seismometers.
> 
> Here is an example that might complement the discussion.
> 
> We all seem to agree that a coil/magnet sensor measures velocity and the 
> displacement sensor measures location, both relative to boom and case.  
> What I would like to add is that neither measurement completely defines 
> conditions at the instant of measurement.  The measurement of velocity 
> ignores location, and measurement of location ignores the component of 
> velocity.  What we should do is to measure BOTH components (two sensors 
> on each boom) at the same instant.  Of course this would result in two 
> data streams which would not be identical.  For any one sine wave, 
> maximum displacement would be measured when the velocity measurement was 
> zero,  and maximum velocity at a zero displacement measurement.
> 
>  If we want to relate the two measurements, we can easily see that the 
> distance traveled between any two DISPLACEMENT measurements is the 
> difference between the two measurements.  This difference is also 
> velocity when considered as distance per sample (which is distance per 
> unit time).  This can also be considered as the differential of the data. 
> 
>  On the other hand, if we want to convert our  VELOCITY readings to 
> distance, we would need to find the average velocity between each of two 
> measured velocities which would be the sum of the two velocities divided 
> by two, also considered as the integral of the data.  We can not expect 
> to simply integrate the velocity data and obtain distance because we 
> would be using the velocities measured at the distance points, not the 
> average velocity that actually caused the resulting measured  traveled 
> distance.
> 
>  Now assume that we want to calculate acceleration from the DISPLACEMENT 
> DATA.  We would first calculate velocity by taking the difference 
> between the two readings.  Then we would take the difference between two 
> of the velocity readings (a second differential of displacement) to find 
> the velocity change per time per time.  We would need at least three 
> data points to make this series of calculations.
> 
>  To find acceleration from the VELOCITY data, we can not simply find the 
> difference between two velocity readings (which is the velocity change 
> per time per time (the first differential) ) because we would be using 
> the velocities measured at distance points.  Instead, we should find the 
> average velocity between two points and then find the difference between 
> that average velocity and a previous average velocity to reach an 
> average acceleration.  Again, three data points would be required.
> 
> We should notice that both of these processes to find acceleration are 
> frequency sensitive and will suppress higher frequency data fluctuation's.
> 
> Finally, let us consider the STS device with a degenerative feedback 
> system installed.  Our two sensors would register nearly zero output 
> because the feedback system works to minimize both velocity and travel 
> of the boom.  As a result, energy as found in the kinetic energy of 
> velocity or energy in a spring is not allowed to be stored.  The reduced 
> storage energy can be expected to minimize the carry-over of energy from 
> one data sample to another, thus reducing  distortion of the true wave 
> form of the seismic disturbance.  When a displacement sensor is used to 
> generate the feedback signal, the resultant trace should still be a 
> displacement location.  When a velocity sensor is used to generate the 
> feedback signal, the resultant trace should still be a velocity trace 
> but the output should about 1.4 times higher than the externally damped 
> velocity output  because (nearly) all of the incoming energy is 
> available to generate a detectable reading (rather than being stored in 
> the boom as kinetic energy or in the spring as potential energy).
> 
>  Unfortunately, I do not have an STS device so I can not test this 
> explanation.  Perhaps you or others can enlighten us about the 
> correctness or failure of this conjecture.
> 
> Food for thought,
> 
> Roger


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