Hi everyone,

  A few weeks ago, I hatched a new idea for an old concept, the inverted 
pendulum, and made a demo model of it for study.  It consists of a graphite 
rod, 3 mm in diameter by 304 mm long, with 13 full turns of 1/8 diameter 
solder (20 grams) on top to provide the inertial mass.  The restoring force 
for this pendulum is provided by permanent magnets surrounding the graphite, 
and arranged to form a linear quadrupole field.  Graphite is diamagnetic, and 
is repelled by magnetic field gradients.  For a graphite rod immersed in a 
quadrupole field, this repulsive force is radially symmetric, and linearly 
proportional to the displacement of the rod from the magnet axis.  The 
restoring torque is proportional to the height of the magnet above the pivot 
point of the graphite rod.  By adjusting the height, one can get a long 
period pendulum, where the restoring torque is slightly stronger than the 
destabilizing gravity torque.

  Damping is provided by a sleeve made of 0.0045 inch thick aluminum foil 
salvaged from a deli pie plate.  Any amount of damping, from none to very 
over-damped, can be obtained by adjusting the penetration of the sleeve into 
the magnetic field.

  My present device is lacking the necessary position sensors, so I can tell 
you nothing about its performance as a tiltmeter type seismometer.  That will 
have to come later.  It should be able to sense horizontal ground motion and 
direction, if fitted out with a pair of othogonally oriented position 
sensors.

  I cut the top off of an empty LP gas bottle to form the support for the 
magnet.  The resulting cylinder is 8.25 inches tall and 2.75 inches O.D.  I 
put a bridge plate inside to form a resting place for the magnet.  The magnet 
and bridge are held in place by a coil spring between the magnet and inner 
wall.  The magnet can be easily axially aligned and centered, and can be 
adjusted up and down by sliding the spring, magnet, and bridge as a unit up 
and down within the cylinder.  A .375 inch hole was drilled in the bottom of 
the tank to allow the dully pointed tip of the graphite rod to pivot on the 
base plate.  No tilt adjustment is used.  Instead, the bottle is nudged about 
on the base plate until a point of balance is reached.  Fine adjustment is 
attained by very lightly tapping the base of the bottle with a pencil.  
Eventually, a top cover will be fabricated which will shield the pendulum 
from drafts and provide a structure for mounting the pickoffs. A small ball 
at the bottom end of the rod makes a better, more load bearing, pivot.  The 
graphite rod should be selected for straightness.  (You have to buy 12, so 
you can select the best.)

  The magnet is made up of 24 each 0.25 inch cube magnets of NdFeB.  Six 
magnets on each side form a 0.25 inch square opening of 1.5 inch length.  
Four spacers of 0.25 inch copper tubing hold the magnets in position as well 
as four 0.125 thick steel plates lap-jointed around the outside of the 
assembly.  The assembly is self-assembling (if you do it right) and self 
supporting, excepting for a tendency for the magnets to separate themselves 
axially.  Four brass bolts through the copper spacers keep the magnets 
axially confined.

  The natural period of this device is temperature sensitive, because the 
magnetic field is temperature sensitive.  Furthermore, the restoring force is 
a function of the square of the magnetic field, making the sensitivity even 
greater.  The very delicate balance of restoring force against gravity force 
causes the period to very temperature dependent.  Right now, the pendulum is 
set up on my basement floor on a base plate of Corian, set up for a period of 
5 seconds.  I will monitor the balance of the pendulum to see how well it 
remains centered over the next few days.

  The magnets were purchased from amazingmagnets.com and the graphite 
spectrographic grade rods from tedpella.com.

  I wish to acknowledge the help and advice of Chris Chapman and the 
encouragement provided by John Lahr, Meredith Lamb, and David Lamb in this 
endeavor.

Regards,  Bob McClure
Hi everyone,



  A few weeks ago, I hatched a new idea for an old concept, the inverted pendulum, and made a demo model of it for study.&
nbsp; It consists of a graphite rod, 3 mm in diameter by 304 mm long, with 13 full turns of 1/8 diameter solder (20 grams) on t
op to provide the inertial mass.  The restoring force for this pendulum is provided by permanent magnets surrounding the g
raphite, and arranged to form a linear quadrupole field.  Graphite is diamagnetic, and is repelled by magnetic field gradi
ents.  For a graphite rod immersed in a quadrupole field, this repulsive force is radially symmetric, and linearly proport
ional to the displacement of the rod from the magnet axis.  The restoring torque is proportional to the height of the magn
et above the pivot point of the graphite rod.  By adjusting the height, one can get a long period pendulum, where the rest
oring torque is slightly stronger than the destabilizing gravity torque.



  Damping is provided by a sleeve made of 0.0045 inch thick aluminum foil salvaged from a deli pie plate.  Any amount
 of damping, from none to very over-damped, can be obtained by adjusting the penetration of the sleeve into the magnetic field.




  My present device is lacking the necessary position sensors, so I can tell you nothing about its performance as a tiltme
ter type seismometer.  That will have to come later.  It should be able to sense horizontal ground motion and directi
on, if fitted out with a pair of othogonally oriented position sensors.



  I cut the top off of an empty LP gas bottle to form the support for the magnet.  The resulting cylinder is 8.25 inc
hes tall and 2.75 inches O.D.  I put a bridge plate inside to form a resting place for the magnet.  The magnet and br
idge are held in place by a coil spring between the magnet and inner wall.  The magnet can be easily axially aligned and c
entered, and can be adjusted up and down by sliding the spring, magnet, and bridge as a unit up and down within the cylinder.&n
bsp; A .375 inch hole was drilled in the bottom of the tank to allow the dully pointed tip of the graphite rod to pivot on the 
base plate.  No tilt adjustment is used.  Instead, the bottle is nudged about on the base plate until a point of bala
nce is reached.  Fine adjustment is attained by very lightly tapping the base of the bottle with a pencil.  Eventuall
y, a top cover will be fabricated which will shield the pendulum from drafts and provide a structure for mounting the pickoffs.
 A small ball at the bottom end of the rod makes a better, more load bearing, pivot.  The graphite rod should be selected 
for straightness.  (You have to buy 12, so you can select the best.)



  The magnet is made up of 24 each 0.25 inch cube magnets of NdFeB.  Six magnets on each side form a 0.25 inch square
 opening of 1.5 inch length.  Four spacers of 0.25 inch copper tubing hold the magnets in position as well as four 0.125 t
hick steel plates lap-jointed around the outside of the assembly.  The assembly is self-assembling (if you do it right) an
d self supporting, excepting for a tendency for the magnets to separate themselves axially.  Four brass bolts through the 
copper spacers keep the magnets axially confined.



  The natural period of this device is temperature sensitive, because the magnetic field is temperature sensitive.  F
urthermore, the restoring force is a function of the square of the magnetic field, making the sensitivity even greater.  T
he very delicate balance of restoring force against gravity force causes the period to very temperature dependent.  Right 
now, the pendulum is set up on my basement floor on a base plate of Corian, set up for a period of 5 seconds.  I will moni
tor the balance of the pendulum to see how well it remains centered over the next few days.



  The magnets were purchased from amazingmagnets.com and the graphite spectrographic grade rods from tedpella.com.



  I wish to acknowledge the help and advice of Chris Chapman and the encouragement provided by John Lahr, Meredith Lamb, a
nd David Lamb in this endeavor.



Regards,  Bob McClure