In a message dated 2008/02/18, PETERS_RD@.......... writes:

> What I'm envisioning is not significantly different from the folded 
> pendulum in terms of the physics involved.
> Before describing it in more detail, let me respond to your comments, Chris.
>   Yes, one approach that has been used is to place a spring at the bottom to 
> 'soften' the restoring force of gravity acting on the pendulum.  Although in 
> principle o.k., in fact it has been shown to be unacceptable, due to the 
> dastardly properties of springs.  There is no need for such a spring to 
> accomplish the same result.

       I note that you have not commented using magnetic repulsion which has 
been shown to work!

>       In the case of the so-called folded pendulum, there are really two 
> pendulums--one that is 'usual', the other that is inverted. The usual one of 
> the pair behaves in normal manner; i.e., if disturbed, gravity restores it to 
> equilibrium. The inverted one behaves in just the opposite manner, and 
> provides for a much greater linear response than is possible by using positive 
> feedback by means of a spring at the bottom of a single pendulum.
>    Because one pendulum is trying to 'restore' to equilibrium whereas the 
> other one ('destoring') is trying to take the system away from equilibrium--the 
> net effect of these competing forces is a system with a longer period. It 
> can be taken all the way to infinite period and beyond (critical point in which 
> conversion from stable equilibrium to unstable equilibrium occurs).  Just 
> like any long period seismometer, the material properties limit how far one can 
> go in the direction of long-period until it becomes operationally 
> unacceptable (enough to make a preacher cuss).

       Several non-preachers have been cussing over the practicalities of 
trying to get a folded pendulum to work OK beyond 10 seconds. With four hinges, 
you seem to run into suspension stability / hysteresis problems.

>     The difference between what I've been discussing and the usual folded 
> pendulum without feedback is the following. Instead of two obvious pendulums 
> as with the folded, there is a single (usual) pendulum hanging from the drive 
> component of the
> feedback system which is itself functioning as the inverted pendulum. In 
> other words, the axis at the top of this drive component (holding the pivot for 
> the usual pendulum) is of approximately the same length as the primary 
> pendulum.
> As the pendulum swings to the right, its axis on the drive (inverted 
> pendulum) swings to the left. If the inverted pendulum were of infinite length 
> (horizontal motion as was first discussed as a feedback means) all that the drive 
> would accomplish is
> to excite the primary pendulum via acceleration.  On the other hand, for the 
> two pendulums swinging in precise phase opposition, the net effect is one of 
> a single pendulum with a longer period.
>     The phase opposition of the two pendulums is guaranteed in the case of 
> the folded pendulum because the two are rigidly connected.  Which pendulum is 
> more effective in controlling the period depends on how close the mass is on 
> the horizontal connecting boom to the one pendulum or the other.  Get too 
> close to the inverted pendulum and the system goes unstable (goes beyond the 
> critical point).

       Sure, but it seems to be difficult in practice and you still have an 
extremely high tilt sensitivity.

>    Where my idea differs from the traditional folded pendulum has to do 
> with the 'connection' between the two pendulums.
> There is no 'flexibility' of that connection in the traditional system.  
> With the feedback arrangement I've described, there is variable 'coupling' 
> determined by the nature of the feedback circuit's pole/zero architecture.  
> Control of the phase between the two units should be for engineers given to this 
> business 'what floats their boat'.

       OK. But you will have a driven support and a long period pendulum. 
What you will NOT have is the 1 second reference pendulum, so I where are getting 
the signal to drive the support?

>     I see again in one of Chris' statements the extreme difficulty most 
> everyone of us has when it comes to conceptual understanding of a seismometer. 
> Yes, Newton's first law says that an object at rest wants to remain at rest'.  
> This inertial property of matter is often misunderstood because not enough 
> attention is given to the part of the statement that I left off; i.e., 
> ...remain at rest unless acted upon by a force.

       Rather my point?

>     Einstein showed us that there doesn't have to be a force acting 
> directly on the seismic (inertial) mass. Indeed, it is the acceleration of the case 
> that is responsible for response. The mass is trying by Newton's first law to 
> remain in place as the
> case is moved. But it cannot remain fixed!  As the case moves, there is an 
> unbalanced force on the mass that results. With the pendulum, the mass trying 
> to stay at a fixed point and the case moved to a different point - means that 
> there is a deflection of the pendulum. There is no difference to be realized 
> from this and some force applied directly to the inertial mass with the case 
> unmoved. Einstein's principle of relativity says that we cannot distinguish 
> between the two.

       My understanding of Einstein's work would not entirely support this. 
You are driving the case and looking at the relative response of the pendulum. 
You are not driving the pendulum. It will have a lower dynamic energy. 

>    One can think about the response in the following way.  When the case 
> moves, the inertial mass tries to remain fixed, but it cannot remain that way 
> ostensibly for longer than 1/4th the period of the mechanical oscillator of 
> which it is a part.  After
> all, if the system did not oscillate, we're engaging in complete foolishness 
> to talk about sensitivity being proportional to the square of the natural 
> period.

       Again, one of my concerns. If you drive the case of a 1 Hz pendulum at 
10Hz, 20 Hz you will get a direct amplitude response. The pendulum will not 
be able to respond. It is the pendulum in the gravitational field which 
oscillates / fails to respond.

>     One can acceptably estimate the amount of relative motion between mass 
> and case as follows (I'm trying to avoid detailed math for those of you who 
> are frightened by it) Allow me just one foundational feature that you must 
> accept on faith if you
> can't follow the math.  For an object moving at constant acceleration, the 
> distance travelled goes like the square of the time during which it 
> accelerates.  Since acceleration of the inertial mass cannot be avoided as the result 
> of case movement, we see immediately that the amount of motion (instrument 
> sensitivity) is proportional to the square of the period of the instrument.
> Why, because for only about 1/4th of the period of the system can the mass 
> be assumed to be moving with a 'constant' acceleration.
>     For those who want to believe that the inertial mass does not accelerate 
> (total misunderstanding of the physics of Newton's laws applied to a 
> seismometer) - think about the following. The inertial mass is incapable of 
> functioning without oscillatory
> motion (even though we try with critical damping to suppress the transient 
> parts).  Oscillation means 'back and forth', which in turn means acceleration 
> that is also back and forth oppositely directed to displacement. There can be 
> no displacement of the inertial mass relative to the case without a 
> corresponding acceleration of the inertial mass. It is not at rest, and never can be 
> totally at rest! To place one's emphasis on the displacement as opposed to 
> the acceleration is to 'get the cart before the horse'.  Acceleration is 
> fundament; displacement is not!

       We used to have a first year dynamics demonstration apparatus. It was 
a horizontal glass sheet supported by four horizontal hinge links at the 
corners. On the top, there were four sprung wires attached around the edges. The 
dynamic 'pucks' were short brass cylinders with a chamber in the top for dry 
ice. The dry ice (CO2) sublimated slowly and provided the gas drive for the 
bearing on the circular base (The glass was polished flat and the bottom of the 
puck was also lapped flat.) In operation, there was ~zero friction between the 
pucks and the glass. There was a stationary illuminated white perspex sheet 
underneath with a coarse grid ruled on it.
       In operation, you could sit two pucks on the glass and then move the 
glass in either X or Y direction and the two pucks stayed fixed in space 
relative to the grid. If no force or acceleration is applied to the mass, it just 
doesn't move. To 'fire' one puck at the other, you put the target one in the 
centre of the glass sheet, put the other one up against the spring wire at one 
end and pushed the glass sheet. The motion of the two pucks was then independent 
of any motion of the glass sheet until one or both bounced off the sprung 
wires at the edges. You could fit an O ring to one puck to demonstrate different 
coefficients of restitution. Cold rubber doesn't bounce too well.

       I suspect that you could make a fairly good demonstration horizontal 
seismometer this way. Use a couple of small magnets to provide the centralising 
force and detect the relative motion of the puck and the baseplate. If you 
used two pairs of magnets or bar magnets, you could probably get ~single axis 
motion?  Or maybe a thin leaf spring? It should be fairly easy to get a 20 
second period or longer. You could damp the system magnetically if you made the 
puck from copper or fitted a Cu disk to the top. Maybe use battery 'pointer' 
lasers and mirrors to project the motion onto a wall or ceiling?

>     How many variants of this discussion are necessary before folks finally 
> GET IT (the physics).  Hey, you amateurs are not the only confused ones.  
> Many of the professional seismologists with whom I've interacted do not have a 
> conceptual understanding of how a seismometer works.  It they did, they 
> wouldn't 'worship the god of velocity sensing'.

       Don't be too hard on them. Not all seismologists have the physics 
training to design or to understand a seismometer. And once a particular 'system' 
has been adopted (for good historical reasons) and thousands of seismometer 
years of data collected, it would take a huge effort to change the system. 
Remember that digital recording is only maybe 25 years old and we are still 
updating older systems.
       But wanting to, being able to and finding useful / publishable results 
at periods out to 2,000 seconds could just change all this. I suspect that if 
we are ever to be able to predict the severe quakes, this is the region to 
try to do it, where the crust is being cycled by the Earth tides twice a day. 
That and determining the precise location, depth and timing (or cessation) of 
nearby small quakes. 
       
       Regards,

       Chris   
In a me=
ssage dated 2008/02/18, PETERS_RD@.......... writes:



What I'm envisioning is not sig=
nificantly different from the folded pendulum in terms of the physics involv=
ed.

Before describing it in more detail, let me respond to your comments, Chris.=


  Yes, one approach that has been used is to place a spring at the bott=
om to 'soften' the restoring force of gravity acting on the pendulum. =20=
Although in principle o.k., in fact it has been shown to be unacceptable, du=
e to the dastardly properties of springs.  There is no need for such a=20=
spring to accomplish the same result.




       I note that you have not commented usi=
ng magnetic repulsion which has been shown to work!



     =20=
In the case of the so-called folded pendulum, there are really two pendulums=
--one that is 'usual', the other that is inverted. The usual one of the pair=
 behaves in normal manner; i.e., if disturbed, gravity restores it to equili=
brium. The inverted one behaves in just the opposite manner, and provides fo=
r a much greater linear response than is possible by using positive feedback=
 by means of a spring at the bottom of a single pendulum.

   Because one pendulum is trying to 'restore' to equilibrium wher=
eas the other one ('destoring') is trying to take the system away from equil=
ibrium--the net effect of these competing forces is a system with a longer p=
eriod. It can be taken all the way to infinite period and beyond (critical p=
oint in which conversion from stable equilibrium to unstable equilibrium occ=
urs).  Just like any long period seismometer, the material properties l=
imit how far one can go in the direction of long-period until it becomes ope=
rationally unacceptable (enough to make a preacher cuss).




       Several non-preachers have been cussin=
g over the practicalities of trying to get a folded pendulum to work OK beyo=
nd 10 seconds. With four hinges, you seem to run into suspension stability /=
 hysteresis problems.



    The differen=
ce between what I've been discussing and the usual folded pendulum without f=
eedback is the following. Instead of two obvious pendulums as with the folde=
d, there is a single (usual) pendulum hanging from the drive component of th=
e

feedback system which is itself functioning as the inverted pendulum. In oth=
er words, the axis at the top of this drive component (holding the pivot for=
 the usual pendulum) is of approximately the same length as the primary pend=
ulum.

As the pendulum swings to the right, its axis on the drive (inverted pendulu=
m) swings to the left. If the inverted pendulum were of infinite length (hor=
izontal motion as was first discussed as a feedback means) all that the driv=
e would accomplish is

to excite the primary pendulum via acceleration.  On the other hand, fo=
r the two pendulums swinging in precise phase opposition, the net effect is=20=
one of a single pendulum with a longer period.

    The phase opposition of the two pendulums is guaranteed i=
n the case of the folded pendulum because the two are rigidly connected.&nbs=
p; Which pendulum is more effective in controlling the period depends on how=
 close the mass is on the horizontal connecting boom to the one pendulum or=20=
the other.  Get too close to the inverted pendulum and the system goes=20=
unstable (goes beyond the critical point).




       Sure, but it seems to be difficult in=20=
practice and you still have an extremely high tilt sensitivity.



   Where my idea diff=
ers from the traditional folded pendulum has to do with the 'connection' bet=
ween the two pendulums.

There is no 'flexibility' of that connection in the traditional system. =
; With the feedback arrangement I've described, there is variable 'coupling'=
 determined by the nature of the feedback circuit's pole/zero architecture.&=
nbsp; Control of the phase between the two units should be for engineers giv=
en to this business 'what floats their boat'.




       OK. But you will have a driven support=
 and a long period pendulum. What you will NOT have is the 1 second referenc=
e pendulum, so I where are getting the signal to drive the support?



    I see again=20=
in one of Chris' statements the extreme difficulty most everyone of us has w=
hen it comes to conceptual understanding of a seismometer. Yes, Newton's fir=
st law says that an object at rest wants to remain at rest'.  This iner=
tial property of matter is often misunderstood because not enough attention=20=
is given to the part of the statement that I left off; i.e., ...remain at re=
st unless acted upon by a force.




       Rather my point?



    Einstein sho=
wed us that there doesn't have to be a force acting directly on the seismic=20=
(inertial) mass. Indeed, it is the acceleration of the case that is responsi=
ble for response. The mass is trying by Newton's first law to remain in plac=
e as the

case is moved. But it cannot remain fixed!  As the case moves, there is=
 an unbalanced force on the mass that results. With the pendulum, the mass t=
rying to stay at a fixed point and the case moved to a different point - mea=
ns that there is a deflection of the pendulum. There is no difference to be=20=
realized from this and some force applied directly to the inertial mass with=
 the case unmoved. Einstein's principle of relativity says that we cannot di=
stinguish between the two.




       My understanding of Einstein's work wo=
uld not entirely support this. You are driving the case and looking at the r=
elative response of the pendulum. You are not driving the pendulum. It will=20=
have a lower dynamic energy. 



   One can think abou=
t the response in the following way.  When the case moves, the inertial=
 mass tries to remain fixed, but it cannot remain that way ostensibly for lo=
nger than 1/4th the period of the mechanical oscillator of which it is a par=
t.  After

all, if the system did not oscillate, we're engaging in complete foolishness=
 to talk about sensitivity being proportional to the square of the natural p=
eriod.




       Again, one of my concerns. If you driv=
e the case of a 1 Hz pendulum at 10Hz, 20 Hz you will get a direct amplitude=
 response. The pendulum will not be able to respond. It is the pendulum in t=
he gravitational field which oscillates / fails to respond.



    One can acce=
ptably estimate the amount of relative motion between mass and case as follo=
ws (I'm trying to avoid detailed math for those of you who are frightened by=
 it) Allow me just one foundational feature that you must accept on faith if=
 you

can't follow the math.  For an object moving at constant acceleration,=20=
the distance travelled goes like the square of the time during which it acce=
lerates.  Since acceleration of the inertial mass cannot be avoided as=20=
the result of case movement, we see immediately that the amount of motion (i=
nstrument sensitivity) is proportional to the square of the period of the in=
strument.

Why, because for only about 1/4th of the period of the system can the mass b=
e assumed to be moving with a 'constant' acceleration.

    For those who want to believe that the inertial mass does=
 not accelerate (total misunderstanding of the physics of Newton's laws appl=
ied to a seismometer) - think about the following. The inertial mass is inca=
pable of functioning without oscillatory

motion (even though we try with critical damping to suppress the transient p=
arts).  Oscillation means 'back and forth', which in turn means acceler=
ation that is also back and forth oppositely directed to displacement. There=
 can be no displacement of the inertial mass relative to the case without a=20=
corresponding acceleration of the inertial mass. It is not at rest, and neve=
r can be totally at rest! To place one's emphasis on the displacement as opp=
osed to the acceleration is to 'get the cart before the horse'.  Accele=
ration is fundament; displacement is not!




       We used to have a first year dynamics=20=
demonstration apparatus. It was a horizontal glass sheet supported by four h=
orizontal hinge links at the corners. On the top, there were four sprung wir=
es attached around the edges. The dynamic 'pucks' were short brass cylinders=
 with a chamber in the top for dry ice. The dry ice (CO2) sublimated slowly=20=
and provided the gas drive for the bearing on the circular base (The glass w=
as polished flat and the bottom of the puck was also lapped flat.) In operat=
ion, there was ~zero friction between the pucks and the glass. There was a s=
tationary illuminated white perspex sheet underneath with a coarse grid rule=
d on it.

       In operation, you could sit two pucks o=
n the glass and then move the glass in either X or Y direction and the two p=
ucks stayed fixed in space relative to the grid. If no force or acceleration=
 is applied to the mass, it just doesn't move. To 'fire' one puck at the oth=
er, you put the target one in the centre of the glass sheet, put the other o=
ne up against the spring wire at one end and pushed the glass sheet. The mot=
ion of the two pucks was then independent of any motion of the glass sheet u=
ntil one or both bounced off the sprung wires at the edges. You could fit an=
 O ring to one puck to demonstrate different coefficients of restitution. Co=
ld rubber doesn't bounce too well.



       I suspect that you could make a fairly=20=
good demonstration horizontal seismometer this way. Use a couple of small ma=
gnets to provide the centralising force and detect the relative motion of th=
e puck and the baseplate. If you used two pairs of magnets or bar magnets, y=
ou could probably get ~single axis motion?  Or maybe a thin leaf spring=
? It should be fairly easy to get a 20 second period or longer. You could da=
mp the system magnetically if you made the puck from copper or fitted a Cu d=
isk to the top. Maybe use battery 'pointer' lasers and mirrors to project th=
e motion onto a wall or ceiling?



    How many var=
iants of this discussion are necessary before folks finally GET IT (the phys=
ics).  Hey, you amateurs are not the only confused ones.  Many of=20=
the professional seismologists with whom I've interacted do not have a conce=
ptual understanding of how a seismometer works.  It they did, they woul=
dn't 'worship the god of velocity sensing'.




       Don't be too hard on them. Not all seis=
mologists have the physics training to design or to understand a seismometer=
.. And once a particular 'system' has been adopted (for good historical reaso=
ns) and thousands of seismometer years of data collected, it would take a hu=
ge effort to change the system. Remember that digital recording is only mayb=
e 25 years old and we are still updating older systems.

       But wanting to, being able to and findi=
ng useful / publishable results at periods out to 2,000 seconds could just c=
hange all this. I suspect that if we are ever to be able to predict the seve=
re quakes, this is the region to try to do it, where the crust is being cycl=
ed by the Earth tides twice a day. That and determining the precise location=
, depth and timing (or cessation) of nearby small quakes. 

       

       Regards,



       Chris