Brooke Clarke 2007 - 2019

Definition of Length
Earth's Rotation
Gravity (classical) Pendulum Patents


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.


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). 
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.  Concept used in inertial navigation related to gyroscopes.

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.

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, - " 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
also invented the lock-in-amplifier and Dicke radiometer (Wiki: Lock-in-amplifier)
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 -


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

Spendulum Kit


Kundo ATO electromagnetic pendulum clock.
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


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page created June 16 2007