Background
Types
Definition of Length
Earth's Rotation
Gravity (classical) Pendulum Patents
Spendulum
Related
Links
Background
To a first order approximation
the period depends on the pendulum length and the acceleration
of gravity.
My interest in
Time & Frequency
got me looking at precision pendulum clocks. The
accuracy of the clock is determined by the pendulum.
In addition to clocks pendulums were used to measure gravity,
which required a precision clock mechanism.
When attempting to win the English prize for a way to find the
Longitude at sea, Harrison at first tried a clock based on a
dual pendulum, but gave up and switched to a balance wheel
because pendulums don't work well on ships. But they do
work when fixed to a rigid support.
Pendulums on this page are dynamic and make use of the period
of oscillation. Many pendulums that are used in a static
way like a plumb bob (gravity pendulum) or a weight at the end
of a string.
The
3036465
patent by Dicke is an all quartz system which should be better
than those that use metal. But I've recently heard that
the quartz exhibits "jumps" in it's crystal lattice that
causes the length to change slightly, changing the rate.
Types
When I made this web page I was mainly concerned with the
simple gravity pendulum, like used in clocks (where it's the
heart beat that when counted tells the time and gravity meters where the
period depends on g.
There are many types of pendulum (Wiki: Clock,
Time&Gravity,
Pendulum
(mechanics).
The Conical Pendulum (Wiki)
was also used to demonstrate the rotation of the earth. It
consists of a weight that moves in a circle instead of back
and forth in a straight line.
The
Bravais pendulum: the distinct charm of an almost forgotten
experiment.pdf
The Double pendulum (Wiki)
consists of a gravity pendulum with a second pendulum hung
form the main pendulum's bob. The motion of the lower
bob is chaotic (Wiki).
The Hengler (horizontal) pendulum was used as a seismometer,
see: Journal
of Seismology - Horizontal pendulum developemnt and the
legacy of Ernst von Rebeur
The Pendulum Astrolabe
uses a static 2-axis pendulum to determine the direction of
"down" and a prism to define the elevation angle (60.000000
degrees) where it is looking.
The Swinging
Sticks Kinetic Sculpture is based on a double pendulum.
Schuler Tuning (Wiki)
- simulates a pendulum that's equal in length to the Earth's
radius, i.e. a period of 84.4 minutes. A concept used in
inertial navigation related to gyroscopes. If a pendulum
had its swing increased so much that the bob was spinning in a
circle it would be called a gyroscope. The gyroscope and
pendulum are very similar.
Foucault Pendulum (Wiki).
There was one at Foothill College when I was there around
1962.
Academy
Pendulums - info@academypendulums.com - uses a
235 pound brass ball, so only for commercial applications.
A Foucault’s pendulum design, Horacio R. Salva, 8 July 2010, 5
pages (Salva.pdf)
- 27# & 16' 4.5 sec period, Copper ring, magnet on bottom
of bob to reduce elliptical orbit. "The heavier the
suspended orb and the longer the wire, the more limited the
elliptical drift."
The Coriolis force (Wiki)
is related to Gyroscopic precession (Wiki)
and so also to the Foucault pendulum?
Definition of Length
The first definition of the meter was that of a
Seconds Pendulum (Wiki)
at 45 degrees North latitude.
There was objection to the variability with latitude so the
definition of the meter was changed to be length of a physical
stick. Later it was changed to the distance light
traveled when measured with a Cesium beam clock.
The classic clock (Wiki)
relationship between pendulum length (hinge point to center of
oscillation (Wiki):
T = 2 * PI * SQRT(L/g) only works for small swings. For
small swings SIN(x) = x, where x is the angle in radians.
Earth's Rotation
Once the idea that the Earth might not be the center of the
universe started to be known and parallel idea was that the
Earth rotated. There were a number of experimental
attempts to demonstrate this starting in the 1700s.
The first attempts involved firing cannons straight up
expecting to see the cannon ball land to the West or
dropping a perfect sphere to see it fall to the West, but
these experiments did not work out.
Leon Foucault used a pendulum (Wiki)
to demonstrate the Earth's rotation. Eight years later
he used a gyroscope
to make the same demonstration.
Gravity (classical) Pendulum Patents
Also see my gravity meters
web page, many of which are a form of pendulum.
205808
Electric Gravity Escapement for Pendulums, J.F. Pratt, Jly 1878,
- the impulse is by gravity not electromagnet, not gravity meter
2151317
Clock system,
Dicke
Robert H, Mar 21, 1939, 368/56, 968/562, 368/184, 368/207
- corrects self starting synchronous motor clocks.
2377618
Electric clock, Dicke
Oscar H, Dicke
Robert H, Jun 5, 1945,
368/52,
200/186,
318/119,
968/522,
318/127,
318/132,
200/208 - runs on AC while
present and auto switches to internal time base if power fails
280463
Gravity Escapement for Clocks J.H. Gerry, Jly 1883
-
"
287181
Gravity Escapement for Clocks, D. Shive, Oct 1883 - "
288027
Compensating Pendulum, A.S. Crane, Nov 1883 - temperature
compensation
2992526
Timepiece mechanism, Dicke
Oscar H, Jul 18, 1961
, 368/186, 74/504, 74/528, 116/308, 968/122 - synchronized time
and rate setting
301873
Escapement for Clocks, 1884 - "
383539
Pendulum for Clocks 1888
403999
Gravity Clock Escapement 1889
508530
Mercurial Compensation Pendulum, S. Riefler, Nov 1893, - temp
comp
519421
Gravity Escapement for Clocks, H. Conant, May 8 1894, -
531935
Apparatus for Demonstrating Laws of Gravity and Mechanics, J.S.
Hemenway, Jan 1895, -
625674
Gravity Machine, W.H. Hawkes, May 1899, 73/382R - measures
distance of falling objects to determine gravity
626807
Gyrating-pendulum Escapement, F. Gundorph - clock
720426
Apparatus for Demonstrating Laws of Gravity and Mechanics, J.S.
Hemenway,
739245
Gravity Escapement for Clocks,
842130
Pendulum, A.W. Barnard, Jan 1907, - weighing scales
1097637
Gravity Escapement for Clocks,
1317072
Device for Measuring Accelerations, J. Carlier, Sep 1919, -
spring & mass to some electrical change
1537395
Electric Clock, H.E. Warren, May 1925, - gravity escapement
1559192
Apparatus for Demonstrating Gravity Acceleration, B.
David, Oct 1925,
1792013
Apparatus for Determining the force of Gravity at sea, February
10, 1931, 73/382R ; 250/230; 250/231.1; 250/235; 359/201
dual pendulum
1797044
Electric Clock, March 17, 1931, 368/166 ; 185/40A; 368/149;
968/454 - novel way to impulse the pendulum
1868769
Pendulum for Measuring Time, Max Schuler, July 26, 1932, 368/179
; 968/306 -
radius of gyration P=
SQRT(theta/m), theta = moment of inertia, m = mass
period = 2 * PI * SQRT( (2*P) / g)
uses helium or hydrogen to conduct heat instead of vacuum -
lower thermal gradients
1987786
Pendulum for Gravity Determination, January 15, 1935, 73/382R ;
368/182; 968/105
the use of screws located at key
geometrical points so that if they turn it will not effect the
period
"minimum pendulum" i.e. cg = (L of theoretical pendulum)
/ 2
1995305 -
March 26, 1935, 73/382R ; 331/155; 331/156; 331/157; 340/870.3;
367/180; 73/514.29
a weighted wire vibrates at a
ferquency up to 10 kHz depending on g
2077390
Frequency Comparing Device for Determining the Force of Gravity,
April 20, 1937, 73/382R ; 324/76.39; 324/76.41; 346/45; 346/7;
73/1.45; 968/770 - uses tuning fork & pendulum
2089745
Gravity Instrument, August 10, 1937, 73/382R - resilient
suspension, isosynchronous movement?, temperature compensation
2097156
Gravity Pendulum, October 26, 1937, 73/382R - elastic pendulum
2500433
Pendulum clock,
Theodore
K Riggen,
Bendix
Aviation Corp, 1950-03-14, - "...an object of the present
invention to provide a novel mechanical movement involving
pendulum motion having a long period of vibration in which the
elements are of small physical dimensions."
2732717
Gravity Meter, January 31, 1956, 73/382R - rotating and swinging
in the normal manner to determine the direction of anomaly
2794134
Mechanical Generators of Isosynchronous Oscillations, May 28,
1957, 310/39 ; 368/165; 968/472
2820338
Constant Periodic Motion Device, J. Rabinow, January 21, 1958,
368/134 ; 324/96; 368/166; 368/181; 73/652; 968/457
vacuum chamber surrounding
pendulum is a second pendulum
Prolific inventor, China Lake work on Sidewinder missile.
2974265
Electric clock, Thoma Fritz, Kieninger and Obergfell, March 7,
1961, 318/132 368/157 310/32 446/484 968/463,
Junghans
Kundo ATO Electronic Clock
3036465
Gravity Meter,
Robert H.
Dicke, May 29, 1962, 73/382R ; 73/514.29 - >= 20 cps, Q
>1,000,000
optical pick up and
electrostatic drive, mostly fused quartz parts
founder of Princeton Applied Research
3103819
Gravimeter, Blisagme, September 17, 1963, 73/382R ; 73/514.15 -
inverted reed pendulum w/variable periods, rotated
3173297
Pendulum Apparatus for Relative Gravity Determination, March 16,
1965, 73/382R - dual anti-phase pendulums
3290874
Gravity Pendulum Clock Escapement, December 13, 1966, 368/134 ;
368/165; 368/170; 968/105; 968/435
electric motor driven spring
wind & automatic correction for non plumb case
3242734
Pendulum for Gravity Determination, March 29, 1966, 73/382R ;
33/391 - 1/2 sec period, vacuum, temp control, small swing
3336806
Gravity Meter, August 22, 1967, 73/382R - rotating weights &
strain gauge
3386327
Metronome, June 4, 1968, 84/484 ; 968/819 - for keeping time for
music
3424006
Superconducting Gravimeter,
Robert H.
Dicke, January 28, 1969, 73/382R -
super conducting magnet and
floating object. object moves up or down as gravity
varies and is read out by interferometer
3429184
Gravity Meter, February 25, 1969, 73/382R ; 359/529; 359/577 -
Falling retro reflector
3449956
Force measuring instrument,
Goodkind
John M,
Prothero
William A, Jun 17, 1969, 73/382.00R, 73/514.18
levitating superconducting gravimeter - maybe
the ultimate in performance -
GWR Instruments
three mutually perpendicular differential
capacitors are used to position a sphere and to measure it's
position.
W.A. PROTHERO, A CRYOGENIC GRAVIMETER, Ph,D.
dissertation, University of California, San Diego (1967);
3501958
Gravity Meter, March 24, 1970, 73/382R - 2 pendulums identical
periods when static, but different when dynamic
3520125
Pendulum clock,
Kuhn
Hans Arthur, Jul 14, 1970, 368/65, D10/130, 968/104,
368/323, 368/170, 968/21 - falling liquid powered
3704626
Interferometric method and apparatus for measuring gravity
gradients,
Stone
Richard S (
Little
Inc A), Dec 5, 1972, 73/382.00R, 356/28.5, 359/529
3769710
Electronic Celestial Navigation Means,November 6, 1973, 33/320 ;
244/175; 250/203.6; 33/323; 33/355R; 701/220; 701/222 - star
tracker related to the
MD-1
3960344
Precision mobile gravity survey and guidance system, June 1,
1976, 244/182 ; 244/177; 324/330; 368/136; 368/181; 700/303;
701/121; 702/144; 73/178R
"The pendulum will have a second oscillation
frequency at a second aircraft speed with respect to the Earth's
surface
due to the change in the Earth's spin-induced
centrifugal force on the pendulum."
4115996
Self actuating pendulum system, September 26, 1978, 368/181 ;
968/105; 968/453 - synchronous motor on pendulum with offset
weights
4219940
Angular accelerometer stabilized pendulum, September 2, 1980,
33/366.24 ; 73/514.02 -
"A signal representative of the relative
angular velocity between the pendulum and the angular
accelerometer is fed back to a torquing system
which maintains the pendulum's orientation
along the local gravity vector."
4295372
Gravity measurement apparatus for ships, October 20, 1981,
73/382G ; 73/178R -
4445371
Gravity meter and method, May 1, 1984 - the frequency is
generated by oscillations in a magnetic vibrator formed by
magnets having vertically opposed magnetic poles.
4615022
Symmetrically-suspended vertical-swing long-period pendulum
means, September 30, 1986, 367/179 ; 181/122; 33/1HH; 33/391;
73/652 - long period
seismometer
4628735
Vibrating beam accelerometer, December 16, 1986, 73/514.29
- comprises a pendulum and a force transducer
4649748
Accelerometer, March 17, 1987, 73/514.19 ; 73/514.23; 73/653 - a
pendulum fixed to the other end of said flexible hinge,
torquers for producing a torque proportional
to acceleration applied from the base table to the pendulum and
a displacement
detecting apparatus for electrically
detecting a relative displacement between the fixed portion of
the base table and the pendulum
4723232
Pendulum indicator horological device, February 2, 1988, 368/76
; 368/179; 368/223; 40/426; 40/485; 968/214; 968/388; 968/395 -
just as pointer to hours or minutes
5112126
Apparatuses and methods for making geophysical measurements
useful in determining the deflection of the vertical, May 12,
1992,
356/141.5 ; 33/283; 33/304; 33/306; 33/309;
356/148; 356/149; 356/250 -
Preferably, the device for finding the
instrument spatial angle uses a system of gyroscopes.
Preferably, the device for finding the
deflection spatial angle uses a pendulum.
5268881
Compensator for a mechanical pendulum clock, December 7, 1993,
368/134 ; 368/137 - motor adjusts center of mass of bob to
regulate rate
5351122
Absolute gravity inline measuring apparatus incorporating
improved operating features,
James
E. Faller,
William
J. Hollander,
Timothy
M. Niebauer (
Micro-G
Solutions, Inc. Web
page,
FG5,
A10)), Sep
27, 1994, 356/496, 356/28.5 -
Spendulum
Got this from Grand
Illusions in the UK.
YouTube: Grand
Illusions: Tim's
Autoparametric Resonance, 2:20 -
Comes with documents:
The Spring-Pendulum or "Spendulum' c2020 by Grand Illusions
Why does a mass on a string sometimes misbehave? M.
G. Olsson, Dept of Physics, Univ of Wisconsin, Madison, WI
6 April 1976
American Mathematical
Society: Modelling
the journey from elementary word problems to
mathematical research, Chris Sangwin, Oct. 24,
2011 - see: Approximate Models with Approximate
Solutions pg 1439
This is similar to, but different from, the Wilberforce
Pendulum (Wiki,
YouTube).
Related
Gyroscopes
Kundo ATO electromagnetic
pendulum clock.
Navigation
Optics
Projection (Shadow) ceiling
clocks
Quartz Wall Clocks
Self Winding (Pendulum) Clock Co: page
No.1 & page No.2 & Patents
Steller Time
Time & Frequency
Tuning Forks
Zendulum
Links
PRC68,
Alphanumeric
Index of Web pages,
Contact,
Products for Sale
page created June 16 2007