# Talk:Pendulum

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## Which formula for the true period should be used?

The "Period of oscillation" section gives the series expansion for the true (large angle) period of the pendulum

{\displaystyle {\begin{alignedat}{2}T&=2\pi {\sqrt {L \over g}}\left(1+{\frac {1}{16}}\theta _{0}^{2}+{\frac {11}{3072}}\theta _{0}^{4}+\cdots \right)\qquad \qquad (1)\end{alignedat}}}

A second formula for the true period has been repeatedly added, which I have reverted

${\displaystyle T={\frac {2\pi }{M(\cos(\theta _{0}/2))}}{\sqrt {\frac {L}{g}}}\qquad \qquad (2)}$

where ${\displaystyle M(x)}$ is the arithmetic-geometric mean of 1 and ${\displaystyle x}$.

193.233.212.110 argues that the second formula is faster-converging. My feeling is that the choice should not be based on that, but on which gives the most insight for readers. The first (series) formula is the traditional starting point for large-angle analysis of the pendulum 1, p.113, eq.8 Its clear from inspection that it reduces to the formula 2π√(L/g) in the limit of small angles. The first-order perturbation correction θ^2/16 from the series is widely used both historically 2, p.10 and today 1 to correct the finite swing of pendulums to get the equivalent period of a pendulum of infinitesimal swing. In fact it is referred to in the article itself. The second formula also gives readers the misconception that the true period can be calculated in closed form with elementary functions. The arithmetic-geometric mean used in the formula must be calculated by an iterative process, but that isn't obvious from the formula. --ChetvornoTALK 15:52, 13 September 2012 (UTC)
Apart from your arguments: the nonlinear pendulum has been studied -- and published about -- for a long time. Eq. (2) is from a very recent publication, and has not been referenced (yet) in other publications, while the series in Eq. (1) (and similar series) are of widespread use. So, I would say that WP:UNDUE applies, and Eq. (2) should not be included. -- Crowsnest (talk) 22:32, 13 September 2012 (UTC)

• P. A. Tipler, G. Mosca (2008). Physics for Scientists and Engineers - with Modern Physics (6th ed.). Freeman. p. 473. ISBN 0 7167 8964 7.
• H.D. Young, R.A. Freedman. University Physics – With Modern Physics (12th ed.). Addison-Wesley. p. 437. ISBN 0-321-50130-6.

each give (Θ = angular amplitude):

${\displaystyle T=2\pi {\sqrt {\frac {L}{g}}}\left[1+\left({\frac {1}{2}}\right)^{2}\sin ^{2}{\frac {\Theta }{2}}+\left({\frac {1}{2}}\cdot {\frac {3}{4}}\right)^{2}\sin ^{4}{\frac {\Theta }{2}}+\cdots \right]}$

While this ref:

• D.W. Jordan, P. Smith (2007). Non-Linear Ordinary Differential Equations: Introduction for Scientists and Engineers (4th ed.). Oxford University Press. ISBN 978-0-19-902825-8 Check |isbn= value: checksum (help).

gives:

{\displaystyle {\begin{aligned}K(\beta )&=\int _{0}^{\pi /2}{\frac {\mathrm {d} {\phi }}{\sqrt {1-\beta \sin ^{2}\phi }}}\\&={\frac {\pi }{2}}\left[1+\left({\frac {1}{2}}\right)^{2}\beta +\left({\frac {1}{2}}\cdot {\frac {3}{4}}\right)^{2}\beta ^{2}+\cdots \right]\\\beta &=\sin ^{2}{\frac {\Theta }{2}}\end{aligned}}}

for small amplitudes (they use a = Θ):

${\displaystyle T=2\pi \left(1+{\frac {1}{16}}\Theta ^{2}+{\frac {11}{3072}}\Theta ^{4}+\cdots \right)}$

and we should use what most sources use, so the first is certainly justified. Maschen (talk) 22:52, 13 September 2012 (UTC)

It looks like this arithmetic-geometric mean formula is not entirely novel; it appears as a combination of equations 3 and 15 in this Am J Phys paper by Carvalhaes and Suppes (vol. 26, no. 12, p. 1150). At any rate, I agree with those who say that it is fine material for the corresponding mathematics article but probably shouldn't be included here. It seems like a relatively obscure formula, and surely anyone who is interested in optimal methods of numerically computing the period of a pendulum will find their way to the full mathematics article. Zueignung (talk) 06:46, 14 September 2012 (UTC)
I removed the second formula in compliance with the consensus above but 193.233.212.110 added it back again. 193.233.212.110, Let's talk about this here, and come to a consensus, before making changes. --ChetvornoTALK 12:27, 14 September 2012 (UTC)
To IP: WP:COI? WP:NPOV? No intension to be accusatory... Maschen (talk) 13:19, 14 September 2012 (UTC)

Hiding the best formula formula is hardly consistent with the principles of the wikipedia for free and wide access to human knowledge. Even the question of removing it ought not be posed. Furthermore, it's well referenced and need not necessarliy be derived here. A more general derivation would be appropriate when the topic of elliptic integrals is being discussed. — Preceding unsigned comment added by 193.233.212.18 (talk) 13:56, 14 September 2012 (UTC)

I would challenge your claim that yours is the "best" formula, since it relies on an obscure mean, but at least we have a linked article to explain the obscurity. I would tend to agree that the unusual formula (or perhaps both versions?) should go in the mathematical version of the article. Should we just link to the other article for the more complex formulas? Dbfirs 15:58, 14 September 2012 (UTC)
I agree with Chetvorno that only one formula should be used. This artcile, unlike the artcile Pendulum (mathematics) is about the physics of the pendulum. Since physicists often disregard "small terms", the first equation is the appropriate form to use - the reader can see immediately that for small θ, the θ2 can often be ignored while the θ4 becomes vanishingly small in practice. This article rightly makes a reference to the mathematics of the pendulum, there is no need to clutter up the discussion here with equation 2 - an equation that cannot be easily programmed into an EXCEL spreadsheet. Martinvl (talk) 20:02, 14 September 2012 (UTC)
Also the article actually refers to the first equation; in Early observations in 1747 it tells how Bernoulli developed the method of using the 2nd term of the series θ02/16 to correct the period of gravimeter pendulums for the finite length of swing. --ChetvornoTALK 01:18, 15 September 2012 (UTC)
The problem with including the second, modern, equation is that it's a slippery slope; everyone who has looked at the problem of calculating the "true" period has their favorite "fast convergence" equation just as 193.233.212.18 does (as can be seen from Pendulum (mathematics)), and there will be endless edit wars about which to include. --ChetvornoTALK

Obscurity of the formula to someone hardly challenges its state of being the best! Editing wars are entirely OK as long as they do not deprive interested readers from most valuable knowledge. Efforts aimed at understanding are welcome whereas efforts aimed at concealing whatever seems obscure are certainly not. Once again, the formula is well referenced and, furthermore, the reference is freely accessible to the interested reader.

No edit warring is NOT ok since it can be potentially endless, is annoying, and disruptive. And removing the formula you provide does not "deprive" anyone's understanding of the article. Please desist reverting against consensus. Thanks. Maschen (talk) 12:44, 18 September 2012 (UTC)
I agree, there should be no edit-waring. I also agree that for the casual reader the expansion formula is the "best" on grounds that it is the simplest to understand and can easily be programmed onto a spreadsheet (I would however leave the θ8 term off - for a typical grandfather clock with an amplitude of ±0.1 radians (such as the clock I inherited recently) it accounts for 7.5 nanoseconds a day! Martinvl (talk) 16:11, 18 September 2012 (UTC)
I've started a Dispute resolution discussion on this topic. Feel free to join in, everyone. Martinvl, my grandfather clock is accurate to 5 nanoseconds, guess I'll have to use a 9th term. --ChetvornoTALK 19:40, 18 September 2012 (UTC)
User:193.233.212.18 has posted again and has been reverted. This user is from the Computing Centre of Russian Academy of Sciences, an institute that has IP addresses 193.233.208.0 - 193.233.223.255. Martinvl (talk) 12:45, 20 September 2012 (UTC)
It doesn't matter what country/academy/institute he's from, it does matter that he's so persistent. Clearly he is intent on continuing so maybe a temporary 24hr block will give the message that it's possible to prevent people from editing, for easily breaking the 3rr? Maschen (talk) 13:02, 20 September 2012 (UTC)
I reported the situation on the Edit warring noticeboard --ChetvornoTALK 15:52, 20 September 2012 (UTC)
If you don't mind I made the link you give more direct, so people can find it quicker. Maschen (talk) 16:10, 20 September 2012 (UTC)

Hi, I am interested in the formula 2, WoW very impressed by its simplicity and power. It can be conveniently computed with computer assistance. Why mention complex and inexact formula where we have a simple and exact one. The new formula has just been published. It is further interesting to put it there now. I don't think it really essential to the philosophy of Wikipedia to put in the article only one formula?!! Why? Let it be a huge article, the new formula takes only half a line ! Syrmath — Preceding unsigned comment added by Syrmath (talkcontribs) 20:44, 27 September 2012 (UTC)

I moved your comment here, please write below and after people respond so the discussion thread is continuous, instead of people randomly writing any/everywhere.
Just out of interest - are you the same person as IP 193.233.212.18 and/or 193.233.212.110? No intension to be accusatory... Just curious that there is actually ONE person so very addicted to the "exact" formula, when everyone else (except those IPs) has already stated millions of times that it is obscure and less easy to interpret, and is not "complex" at all... Maschen (talk) 21:24, 27 September 2012 (UTC)

Thank you for your correction. It was just an error on my side to write in the wrong place. I'm not the same person as the IP mentioned. I did not say that the formula 2 was complex neither ! I would like just to point out that the consensus does not seem so logical to my eyes. I also just give my opinion with arguments, in no way, intending any edit-warring. To end my intervention, by the way, I'm also curious that actually only one person is so attached to the "exact" formula!Syrmath (talk) 21:44, 27 September 2012 (UTC)

Ok - no worries. Maschen (talk) 21:48, 27 September 2012 (UTC)
I agree with Syrmath about the power of the formula, but is: ${\displaystyle {\frac {2\pi }{M(\cos(\theta _{0}/2))}}{\sqrt {\frac {\ell }{g}}}}$ simpler than the other "exact" formula: ${\displaystyle 4{\sqrt {\ell \over g}}Ksin(\theta _{0}/2)}$ in Pendulum (mathematics) (given that you are equally familiar with M and K)? Dbfirs 16:50, 29 September 2012 (UTC)
I agree with Dbfirs, and there are a number of other formulas for the "true" period. Who knows which is best? More importantly, this is a specialty topic. If we're going to add more math to the article, I can think of more important stuff than this. What about the differential equation of the pendulum? --ChetvornoTALK 17:17, 29 September 2012 (UTC)
This is not a speciality topis, it is a general topic. I would like my 17 and 18-year-old students to use this topic when I tutor then about pendulums in "A" Level physics. The mathematical article about pendulums is the home for details of the mathematics behind pendulum motion. I would also draw to attention that this artciel touches on, but does not describe in detail, the effects of temperature on the period of a pendulum (the pendulum expands with temperature). We could discuss the relationship Δτ/ΔT (τ = period, Τ = temperature), but this is only described in general terms. Lets try to keep the whole article at the same level and not introduce high detail in one area without high detail in other areas. Martinvl (talk) 18:04, 29 September 2012 (UTC)
That's what I was saying. I meant the formula we are discussing for the true period, (2) above, is a specialty topic that does not belong in this article. I wrote most of the present article. I was going to include the equation for temperature dependence, along with the math of the gridiron and mercury temperature-compensated pendulums, but I never got around to it. --ChetvornoTALK 22:47, 29 September 2012 (UTC)
193.233.212.18 reverted again. I reported it again on the edit-warring noticeboard if anyone would like to add their opinion. --ChetvornoTALK 18:15, 1 October 2012 (UTC)
I have again reverted the changes - this time User:Syrmath reinstated the so-called "simpler" formula. I dispute the word "simpler" - how does one program the function M(x) on a spreadsheet? If User:Syrmath can tell me, fine. if not, please do not reinstate!
Let me say again for the umteenth time, this formula is perfectly acceptable in the article Pendulum (mathematics), but as we are trying to trim this article down, it is inappropriate to include a formula that 95% of the readers will not understand (the remaining 5% will probably go tto the maths artcile anyway. Furthermore, if we wanted more of a mathematical discussion, I agree with Chetvorno that we should include the differntial equation rather than yet another solution.
BTW, if you consult WP:SIZERULE, one will see that artciles which exceed 100 kbytes shoudl almost certainloy be spilt. This article is 116 kbytes, so we do need to filter oujt unneccessary information. Martinvl (talk) 20:41, 1 October 2012 (UTC)
Syrmath, above, was a sockpuppet of 193.233.212.18 and has been blocked. --ChetvornoTALK 20:13, 4 October 2012 (UTC)
Looks like 193.233.212.18 is back in the form of a new sockpuppet. SupremeFormula (note the name!) reverted the article twice 1 to include the arithmetic-geometric mean formula. A sockpuppet investigation has been started, if anyone would like to add a comment (that includes you SupremeFormula) --ChetvornoTALK 08:37, 10 October 2012 (UTC)

SPI resolution: After I was called a sockpuppet I spent several long days and night crying my big beautifully hazel-green eyes out in my softly soothing pillow. Prior to that incident I had never fathomed that people are capable of such cruelty. I went on to tell my story to everyone I knew and was consoled every time and reassured that my faith in people shouldn't really be shaken merely because some bastards decided to name call me without having the slightest clue about me. Finding them and bringing them to justice in a court of law would be the right way to proceed but these wimpy cowards are unlikely to abide by honor rules and disclose themselves. Would they dare looking me straight in the eye and repeat their allegation? I bet they won't!

Let me honestly confess that I’m an amateur in math and I haven’t even encountered the concept of the arithmetic-geometric mean before it was referenced in the article that was first pointed out thanks to that PP using that IP. Yet I keenly studied in school and I am not as dumb a blonde as to say that the exactness of the AGM is deceiving. I am used to thinking before clarifying and I do not like babbling nonsense. I took me a few minutes to program the AGM on an excel worksheet where I observed 10 digits accuracy after 3 iterations. I do know what quadratic convergence means so I was not surprised to see the accuracy raised to 20 digits after 4 iterations. This accuracy is amazingly stable even for large angles where the standard formula is prone to substantial errors. Now, I understand what the IP meant by saying that the convergence was better. He meant that the supreme formula converged even as the period grew without bound whereas the formula given with 3 or however more terms is bounded by its value at the angle corresponding to the pendulum being placed at the highest point. Even then the supreme formula gives the value of the period as infinite whereas that truncated series would give some meaningless uncorrectable value. All that garbage about the circular error might be removed, after inserting the exact formula, from the WP articles and eventually from all CCF level textbooks. I full heartedly support his/her invitation for WP editors to come out to light from the dark ages and I think that volunteer should not had judged his/her invitation as being irrelevant. After all, only paying attention to all these details has enlightened me personally. So I do not want be among manipulated losers fighting a formula which will undoubtedly become widespread. I would independently and happily spread any formula of any WP pendulum editor once I like it. I and other WP editors can easily comply with the rule of not promoting our formulas if we have none. So this clearly stupid rule seems superfluous as far as pendulum editors are concerned, and I do want to be neither as stupid nor as bitter as to accuse anyone of promoting their own formula while being too oblivious about the formula itself.

Now that the investigation is so successfully completed and the consensus with my opinion would undoubtedly be unanimously attained I can act accordingly exposing whoever dares to revert my competent editing as a conniving conspirator and a devil complice. As for my accusers, I have no doubt that justice will be once served as they will eventually end up being caught for harassing other women. Good bless you all and I thank you for your avid support. — Preceding unsigned comment added by SupremeFormula (talkcontribs) 16:04, 15 October 2012 (UTC)

And why do you make wild and obviously false accusations? I suggest that you look under your own bridge. Dbfirs 07:53, 16 October 2012 (UTC)
SupremeFormula has been blocked as a sockpuppet, and the IP also 1. --ChetvornoTALK 07:59, 18 October 2012 (UTC)

What makes a formula better than another?Theexamined life (talk) 01:47, 28 November 2012 (UTC)

Some formulae present a mathematically perfect solution, others present a practical solution which is "fit for purpose". One also needs to take into account the readership and the amount of space that wil be devoted to the formula. In the case of this article, we have been limited by space, so the mathematically perfect (but rather complex) solution is deferred to another article and we only deal with the practical soution (which is also the solution taught in physics classes). Martinvl (talk) 06:48, 28 November 2012 (UTC)
I agree with Martinvl, but just to clarify, neither solution is "perfect" in the sense of being a closed-form solution. Both solutions are based on infinite series. The arithmetic-geometric mean M(x,y) appearing in the second formula must be calculated by an iterative process which is equivalent to an infinite series. Calculating both formulas exactly would require an infinite number of arithmetic operations; as you calculate successive terms in the series your approximate answer gets better, but eventually you must stop calculating, leaving an approximate answer. The only advantage of the second (arithmetic-geometric mean) solution is that it is faster-converging; it gives a closer approximation to the true answer for a given number of arithmetic operations. There are no closed-form solutions to the large-angle pendulum period. --ChetvornoTALK 10:51, 24 December 2013 (UTC)

## Length of article

It was pointed out in the above discussion that this article is quite large. Unusually for such a large article, almost all of the material is coherently written and well-cited. I think this argues for some material being spun off into its own article (the two sections on timekeeping, for instance). Any objections? Zueignung (talk) 16:14, 14 September 2012 (UTC)

Very true - the article byte count is 112.36 kB! Do you mean the sections: Accuracy of pendulums as timekeepers and Use for time measurement? Maschen (talk) 16:31, 14 September 2012 (UTC)
Another idea is moving the Gravity measurement section to Gravimeter or Gravimetry. It could fit well there, and we wouldn't need to create a new article. --ChetvornoTALK 00:52, 15 September 2012 (UTC)
Do both? That should trim 50.915kB (measured by copying pasting the sections in my sandbox - no damage done to the article). Then the main article will be 61.445kB... Maschen (talk) 02:24, 15 September 2012 (UTC)
Yes, I was thinking the sections Accuracy of pendulums as timekeepers and Use for time measurement could be split into an article on an article called Pedulums as used for timekeeping or something similar. Zueignung (talk) 09:39, 15 September 2012 (UTC)
Lets notify the WikiProject Time and WikiProject Physics, given that more ideas may arise and since it's such a big article... Maschen (talk) 10:36, 15 September 2012 (UTC)
I'd like to see the Use for time measurement section stay, since that was the main use for pendulums, and is still a major use in pendulum clocks, and is likely to be of most interest to mainstream readers who come to this article. I suggest moving Gravity measurement and Standard of length. Both are in essence historical. That would reduce the article to 72 kB. To reduce the article further a large part of Accuracy of pendulums as timekeepers could be moved to Pendulum (mathematics). --ChetvornoTALK 11:26, 15 September 2012 (UTC)
I'm just thinking a new Pendulums as used for timekeeping article would require duplicating a lot of the content in this article, such as "Period of oscillation" and a lot of "History". --ChetvornoTALK 11:40, 15 September 2012 (UTC)

Presumably there will be many different preferences, so for now lets summarize the potential moves (feel free to top it up) then choose one by consensus:

1. transfer section/s: Accuracy of pendulums as timekeepers + Use for time measurementnew article/s: Pedulums as used for timekeeping
2. A. keep section/s: Use for time measurement
B. transfer section/s: Gravity measurement + Standard of lengthnew article/s: ?
C. transfer section/s: Accuracy of pendulums as timekeeperscurrent article/s: Pendulum (mathematics)
3. transfer section/s: Gravity measurementcurrent article/s: Gravimeter or Gravimetry

Maschen (talk) 11:52, 15 September 2012 (UTC)

Looks good. Yeah, maybe some of the editors from Wikiproject Time will have other ideas. --ChetvornoTALK 12:58, 15 September 2012 (UTC)
An alternative would be to rewrite the artcile as an overview that provides an introduction to other artciles. One such article, already in place, is the article Pendulum (mathematics). Martinvl (talk) 13:02, 15 September 2012 (UTC)
Yes, if any material is moved to its own article there would be a link and a summary here, just as with the mathematics material. A paragraph on pendulums on clocks, a paragraph or two on materials/environment challenges, etc. The material on Q factors actually applies to more than just timekeeping; maybe it should stay in this article in a section on dissipation. Zueignung (talk) 21:30, 15 September 2012 (UTC)

## Hello, from a DR/N volunteer

No consensus reached. DR/N volunteer recommends RFC as next logical step.--Amadscientist (talk) 14:16, 29 September 2012 (UTC)
Hi, I'm the editor that filed the DRN case. I feel the dispute has been resolved; there is consensus on the disputed point (see Which formula for the true period should be used? above) and the article reflects that consensus, and there haven't been any complaints for a while. As I stated on the DRN page, I feel this was really a case of editwarring by one editor and it was inappropriate of me to make it a DRN case. That editor, 193.233.212.18, has desisted editwarring, following a partial page protection, although I believe he still disagrees with the consensus. So I'm not sure how much of a dispute there is, although of course I'd have no objection to a RfC. Comments? --ChetvornoTALK 16:34, 29 September 2012 (UTC)

I'll take your word for it. If you feel this was resolved I will change the status on the DR/N. RFC is only needed if the content dispute arises again. Sorry if I missunderstood your comment.--Amadscientist (talk) 23:31, 29 September 2012 (UTC)

User:193.233.212.18 has again started adding the material that he believes shoudl be in the article - I have requested that the article be semi-protected again. Martinvl (talk) 14:48, 2 October 2012 (UTC)

## Quantity of maths in article

Quantity of maths in article

Concern has been expressed about the length of this article, so we need to reduce the amount of text. I believe that the following equations represent a set of candidate equations for in respect of the simple pendulum in this article (together with supporting text).

${\displaystyle {d^{2}\theta \over dt^{2}}+{g \over \ell }\sin \theta =0\qquad \qquad (1)\,}$
${\displaystyle \theta \ll 1\ \qquad \qquad (2)\,}$,
${\displaystyle \sin \theta \approx \theta \ \qquad \qquad (3)\,}$,
${\displaystyle {d^{2}\theta \over dt^{2}}+{g \over \ell }\theta =0.\qquad \qquad (4)\,}$
${\displaystyle T\approx 2\pi {\sqrt {\frac {L}{g}}}\qquad \qquad (5)\,}$
{\displaystyle {\begin{alignedat}{2}T&=2\pi {\sqrt {L \over g}}\left(1+{\frac {1}{16}}\theta _{0}^{2}+{\frac {11}{3072}}\theta _{0}^{4}+\cdots \right)\qquad \qquad (6)\end{alignedat}}}
${\displaystyle T={\frac {2\pi }{M(\cos(\theta _{0}/2))}}{\sqrt {\frac {L}{g}}}\qquad \qquad (7)}$
${\displaystyle \theta (t)=\theta _{0}\cos(2\pi t/T)\,.\qquad \qquad (8)\,}$

Given the on-going discussion, I think that it is appropriate for editors to list these equation in order of importance to the article as a whole. If I have left any significant equations out (in respect fo the simple pendulum), please add them.

In my view, the following equations should be in the article (in ascending order of number of equations):

• Minimal selection - 2 Equations: Include equations 5 and 8
• Intermediate selection (1) - 3 Equations: Include Equations 4, 5 and 8
• Intermediate selection (2) - 5 Equations: Include equations 2, 3, 5, 6 and 8
• Intermediate selection (3) - 6 Equations: Include equations 1, 2, 3, 4, 5 and 8
• Intermediate selection (4) - 7 Equations: Include equations 1, 2, 3, 4, 5, 6 and 8
• Maximal selection - 8 Equations - all equations.

We currently have intermediate selection (2). I would have no objection if the consensus was that we should restructure the article to use Intermediate selection (1) or Intermediate selection (3). I would not be happy if consensus veered towards intermediate selection (4), particularly since we have the article Pendulum (mathematics) where this material can be added. I would be even less happy if consensus pointed to the maximal selection as that woudl make the article just too bloated. Martinvl (talk) 14:12, 2 October 2012 (UTC)

Good idea to discuss this. Your equations 2, 3, and 8 are not parsing in my browser, though. --ChetvornoTALK 14:20, 2 October 2012 (UTC)
That's better. I'm pretty close to your view. I think my top choice would be equations (2), (4), (5), (6), and (8) (Equation (2) has to be included with (4) or (5)). Leave linearizing the diff. eq. to Pendulum (mathematics), except for a note in the text. I think eq. (6) should be included because of its historical importance, even though it will forever attract alternatives like eq. (7). But I could live with selections 1, 2, or 3. --ChetvornoTALK 15:41, 2 October 2012 (UTC)
Since we have detailed equations in the linked article, I'd prefer something nearer the minimum (even just 5 and 8), but I'll be happy with whatever you decide as long as it isn't maximal (in which case I would add others!) Dbfirs 15:52, 2 October 2012 (UTC)

## Question

Who among us believe the simple explanation of the pendulum? Do we have to factor in centripetal force and the universal effect of orbiting on an axes? Is the most objective explanation best tested in space, without the 9.8? Theexamined life (talk) 17:11, 2 November 2012 (UTC)

Could you explain which part of the article you find difficult to believe? The centripetal force is just the tension in the rod. A pendulum will not work in the absence of gravity, though I suppose that the effect could be simulated in deep space by supplying some equivalent force, or using a rotating spaceship to simulate gravity. Dbfirs 21:12, 2 November 2012 (UTC)

## Vector diagram

The captions in the animated diagram state "The acceleration vector a is related to the gravitational vector {{{1}}}. This relationship is not explained in the article or by the rest of the caption. I suggest that it be removed as it adds nothing to the article and might be confusing for some readers. I would even question the usefulness of the animated diagram as vectors are not dealt with in the article. The vector discussion, if written up fully, does have a place in the article Pendulum (mathematics). — Preceding unsigned comment added by Martinvl (talkcontribs) 18:57, 5 November 2012‎ (UTC)

I support removal of the entire diagram. It doesn't really illustrate anything described in this article's text. In Pendulum (mathematics), the vector treatment is actually already described in the Force derivation box. — HHHIPPO 19:18, 5 November 2012 (UTC)
= = = Copied from Maurice Carbonaro's Talk page by Martinvl = = =
Hi Maurice,
Thank you for your edits to the artcile Pendulum. They certainly explain the vectors associated with the diagram. However this information might not be understood by many of our reader, for this reason we have a sister article Pendulum (mathematics) where it might be more appropriate to make these additions in that article, for example a new section called "Vector representation of the pendulum solution".
Martinvl (talk) 15:56, 5 November 2012 (UTC)
Hallo there Martinvl (talk),

thanks for taking time in reviewing my edits and reading the changes I have recently done the Pendulum article.
Honestly I forgot there was a "Sister" article called Pendulum (mathematics):
but even after trying to read it and understand it I noticed that Partial differential equations were treated which are not exactly "simple equations".

So I am puzzled about your interesting suggestion about moving these additions in that article. Even with a new section called "Vector representation of the pendulum solution". Maybe we could add it to the "simple" Pendulum article?

Please let's think a couple of days about it before both of us making any change at all at the two articles i.e.

1. "Pendulum" and
2. "Pendulum (mathematics)".
Tot straks!
Maurice Carbonaro (talk) 07:20, 6 November 2012 (UTC)
= = = End of copied text = = =

Hi Maurice,
When we have two artciles of this nature, we need to consider the reader (who after all is the customer). Firstlym there is a consensus that this artcile is too long and that it needs some pruning down, though no-one has yet come up with a proposal on how to do it. This means of course that we should be careful about adding anything to the article. If you look up this page you will see that I listed a number of equations that could be included in teh artcile and the consensus was not to steer clear of differential equations. I think that the same will apply to the use of vector notation. The article, as it stands, is easily understood by students who are about to enter university - I do not think we shoudl pitch it any higher, especially as we already have a forum for more advanced maths. For that reason, I disagree with the vector notation being shown at all in this article, but support it being discussed in the article Pendulum (mathematics).
Martinvl (talk)

## Temperature Compensation

The maths seems to be incorrect in the sentence:

"A pendulum with a steel rod will expand by about 11.3 parts per million (ppm) with each degree Celsius increase (6.3 ppm/°F), causing it to lose about 0.27 seconds per day, or 16 seconds per day for a 33 °C (60 °F) change."

(unless my brain is more confused than normal). Which figures are the correct ones? Roly (talk) 11:46, 4 January 2013 (UTC)

Same here in the Invar paragraph:

"This has a CTE of around 0.5 µin/(in·°F), resulting in pendulum temperature errors over 71 °F of only 1.3 seconds per day"

Is my maths ability really that much up the spout? Roly (talk) 14:03, 4 January 2013 (UTC)

The maths is incorrect - somebody got confused between degrees Celsius and degrees Fahrenheit when they bolted on the second half. I have reworded it. Martinvl (talk) 15:17, 4 January 2013 (UTC)

The reference [83] to Matthys concerning the supposed tendency of the gridiron pendulum to move in jumps should be removed along with the statement itself until a definitive reference can be identified. Matthys merely repeats the assertion with no evidence or authoritative reference. Thomas Reid in his 'Treatise on Watch and Clockmaking - Theoretical and Practical' writing in 1848 when gridiron pendulums were state-of-the-art does not mention such a tendency. Rees' Cyclopedia also makes no mention of this motion being in jumps.Peter R Hastings (talk) 21:54, 2 March 2017 (UTC)

Matthys is a fairly authoritative source. There are many other statements in this article whose supporting sources give "no evidence or authoritative reference". The temporary rate deviations due to the friction induced jumps is only significant in precision astronomical regulators used for high accuracy scientific work, so it might not be mentioned in a general encyclopedia or a clock treatise such as Reid. Alternatively, it may not have been recognized until the end of the 19th century, when a lot of research on clock accuracy was done, which would have been after the Reid and Rees sources were published. --ChetvornoTALK 22:41, 2 March 2017 (UTC)

## Sumerian culture

An editor recently added a reference to the Sumerian culture having developed a one-second pendulum some 5000 years ago. Is this a "Fringe Theory", a hoax, a coincidence or a forgotten art? It is certainly not mainstream thought? Does anybody else know anything about this statement, and if so, should it be prefixed with "Certain archeologists are of the opinion that ...". Martinvl (talk) 20:48, 26 September 2013 (UTC)

Sounds highly dubious to me. --Roly (talk) 21:18, 26 September 2013 (UTC)
This is amateur numerology. I found one book online which contains the theory: Christopher Knight, Alan Butler (2004) Civilization One: The World Is Not as You Thought It Was. I would not call it a RS, it is in the category of Graham Hancock-style fringe archaeology, advancing the theory, based on numerical coincidences, that megalithic civilizations were super-advanced technologically. Neither in this source nor the Roland Boucher paper is there any reference to this stuff being published in a peer-reviewed journal. I think the sentence has to go. --ChetvornoTALK 01:22, 27 September 2013 (UTC)
I will remove it. Martinvl (talk) 03:06, 27 September 2013 (UTC)

## Change to sentence in introduction

I am concerned about a recent change to a sentence in the introduction, from:

"A pendulum swings with a specific period which depends (mainly) on its length."

to

"If the amplitude of the oscillation is small, a pendulum swings with a specific period which depends on its length."

The new sentence is attempting to take account of the fact that at large amplitudes the period is dependent on the amplitude as well as the length. However I feel this can be misleading for the general readers who will be reading the introduction. The new sentence gives the erroneous implication that at large amplitudes the period is not dependent on length. The fact is that the length of the pendulum is the main determinant of its period at all amplitudes; the amplitude only has a small effect over most of the range. We already have an extensive explanation of the effect of amplitude in the next section. I feel the original sentence was clearer. --ChetvornoTALK 00:13, 18 December 2013 (UTC)

Does the latest change work for you? DOwenWilliams (talk) 04:22, 18 December 2013 (UTC)
Thanks for asking. I really feel that the amplitude dependence is an unimportant, confusing technical detail which does not belong in the introduction. If we are going to add to the introduction, there are many more notable facts about pendulums which could be added. The previous statement - that the pendulum's period depends mainly on its length - was a good generalization for introductory readers. However your changes do remove the misleading implications I mentioned, and I can live with the current text. --ChetvornoTALK 20:36, 18 December 2013 (UTC)
I think the introductuon sould include a mention of the fact that the oscillation period is usually determined by the length of the pendulum, and not by the amplitude, since this is the basis of the use of the pendulum in clocks, but that there is a caveat that the amplitude must be small. Pendulums that swing 60 degrees, say, from the vertical are no good in clocks. (I have witnessed kids trying pendulums with wide swings, and their puzzlement when they didn't keep good time.) The problem is how to summarize this in a sentence or two in the lead of the article. DOwenWilliams (talk) 03:48, 19 December 2013 (UTC)

## Pendula were never guillotines

The last paragraph of the article needs to be removed. No responsible historian actually thinks that pendula were ever used as torture devices outside of Edgar Allen Poe novels. The "main article" that is linked says as much (between the lines). British Protestant propaganda about the Spanish inquisition is not to be trusted in such matters. It is unworthy of wikipedia to repeat such ancient canards. Dlw20070716 (talk) 10:49, 17 August 2015 (UTC)

Also, the picture of the "pendulum" in the Metropolitan Cathedral, Mexico City ought also to be removed as it's actually a plumb bob, not a pendulum. (It's purpose is not to swing, but rather to point out the tilt of the Cathedral.) Dlw20070716 (talk) 11:11, 17 August 2015 (UTC)

## Semi-protected edit request on 7 June 2016

In Section "1673: Huygens' Horologium Oscillatorium", 1st para., last sentence: Change "solved the issue" to "solved the problem". Reason: Replace Microsoft euphemism "issue" with what it really means.

Not done a search for "issue" in the article gives no matches - and it hasn't been removed recently either - Arjayay (talk) 07:39, 8 June 2016 (UTC)

## The arithmetic-geometric formula again

The "Period of oscillation" section gives the series expansion for the true (large angle) period of the pendulum

{\displaystyle {\begin{alignedat}{2}T&=2\pi {\sqrt {L \over g}}\left(1+{\frac {1}{16}}\theta _{0}^{2}+{\frac {11}{3072}}\theta _{0}^{4}+\cdots \right)\qquad \qquad (1)\end{alignedat}}}

A second formula for the true period has recently been added by User:J20160628

${\displaystyle T={\frac {2\pi }{M(\cos(\theta _{0}/2))}}{\sqrt {\frac {L}{g}}}\qquad \qquad \qquad (2)}$

where ${\displaystyle M(x)}$ is the arithmetic-geometric mean of 1 and ${\displaystyle x}$.

The addition of this formula to the article has already been thoroughly discussed on this Talk page; see Which formula for the true period should be used? above. The consensus of at least 5 editors (Zueignung, Maschen, Crowsnest , Martinvl and myself) was that it should not be added, for these reasons:

• The inclusion of the series formula (1), the traditional formula for the large angle period, is important for historical reasons; it shows where the small-angle formula ${\displaystyle T=2\pi {\sqrt {L/g}}}$ comes from, and it is referred to in the text, while the new formula is not.
• The description of the second formula (2) as "exact" and "error-free" is wrong; the arithmetic-geometric_mean M(x) needed to calculate it must itself be calculated iteratively from an infinite series. At some point this calculation must be terminated, leaving an error. There are no "exact" (closed form) formulas for the large angle period of a pendulum. The only advantage of the second formula is that it is faster converging.

For these reasons I think the second formula should be removed. --ChetvornoTALK 19:18, 3 July 2016 (UTC)

I fully agree. As mentioned by Chetvorno, the matter has already been discussed before, with the consensus to remove it. -- Crowsnest (talk) 20:35, 4 July 2016 (UTC)
I think that the first formula must be removed as outdated, only linearly convergent and error correction requiring for large oscillations. The second formula is quadratically convergent. Chetverno is entirely wrong in thinking that the second is equivalent to the first since he keeps expanding the second into power series which MUST BE AVOIDED. In fact, Gauss then in 1799 discovered a novel and an absolutely superb way of calculating complete elliptic integrals. The time has come for the masses to understand that. Here is an understandable reference for non mathematicians http://www.cse.unsw.edu.au/~en1811/12s2/assigns/assign2/ass2_pend.html. — Preceding unsigned comment added by 114.147.68.146 (talk) 08:21, 5 July 2016 (UTC)
This is not an article on mathematical methods for solving the pendulum. We have that, it's called Pendulum (mathematics), and it already discusses the formula (2). This is a general article on the pendulum, and the formula you are pushing is nowhere near WP:NOTABLE enough to be included. This has already been thoroughly discussed here. Wikipedia is not a WP:SOAPBOX for you to push your favorite math formulas on the "masses"; please read WP:Righting Great Wrongs. --ChetvornoTALK 07:11, 6 July 2016 (UTC)

I applaud the brilliant idea of 114.147.68.146. Certainly, outdated material must be removed from this blunted article to archives or elsewhere. I have researched the exact and fast period formula and found primary, secondary and tertiary material to support it, so whoever keeps arguing against it better keep their views to themselves. I can find many interesting views already presented on this talk page, which was apparently ignored by pseudoscientists who Chetvorno has led instead of refuting them as he claims to do on his talk page. So, I hope he converts his efforts to humbly serve the truth.Highness 11:00, 7 July 2016 (UTC) — Preceding unsigned comment added by J20160628 (talkcontribs)

The method is indeed useful, but it is an iterative method, not a formula in the strict sense. Thus it belongs in the mathematical article, not here in the general article. This has been discussed at length in the past, and I see no reason to change the agreed policy. Why should I keep my views to myself? Dbfirs 12:01, 7 July 2016 (UTC)
Indeed, the question is not whether the AGM method is useful to compute the elliptic integral appearing in the "exact" pendulum period. Although (because of the foregoing) not of any relevance anymore for this article, the Adlaj references are not often cited by others and of undue weight for Wikipedia purposes – an earlier and better reference for the nonlinear pendulum period and the use of the AGM to compute the elliptic integrals would be pages 1–15 of Borwein & Borwein (1987) Pi and the AGM, Wiley. -- Crowsnest (talk) 18:38, 7 July 2016 (UTC)
Excuse me, , are you the same person as 114.147.68.146? It is fairly suspicious that 114.147.68.146 is a new account that has made only 2 edits, one on this Talk page. The only other person who has pushed this formula, during the previous discussion, was a single disruptive editor who used the sockpuppets Syrmath, SupremeFormula, and 193.233.212.18, and was permanently blocked. Are you also the same person that used these usernames? If so, I don't have to tell you that an editor using multiple usernames to disguise his identity, called sockpuppeting, is prohibited on Wikipedia and can get you blocked. --ChetvornoTALK 19:48, 7 July 2016 (UTC)

(Personal attack removed) Blocking the most competent editors is a shame. It explains why 114.147.68.146 is the only one who's left. (Personal attack removed) Ignoring, deleting and denying seem to be the only tools available to them. Reasoning seems to anger them. What a pity. Highness 15:30, 9 July 2016 (UTC) — Preceding unsigned comment added by J20160628 (talkcontribs)

User:J20160628 has been blocked as a sockpuppet. --ChetvornoTALK 13:33, 29 December 2016 (UTC)

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## wiki animation

Movement is inherently distracting to the eye. All Wikipedia animations should be optional. They are great to have and it's fine to run them by default, but there must be a simple way to disable them.Propanscience (talk) 16:42, 12 July 2016 (UTC)

## mention Fedchenko prrecision pendulum clock?

Along with Shortt and Riefler precision pendulum clcoks, perhaps the Fedchenko clock deserves mentioning?

Although the article is long, something about the fundamental limit to timekeeping with a pendulum, i.e. tidal variations in gravity, would be nice. — Preceding unsigned comment added by 87.100.175.140 (talk) 11:25, 1 January 2017 (UTC)

The article seems to imply that atmospheric variations are more significant than tidal effects. Do you have a reference that compares these. We don't even have an article on Feodsii Michailovich Fedchenko (yet). Dbfirs 17:38, 1 January 2017 (UTC)

## Semi-protected edit request on 25 January 2017

203.202.240.50 (talk) 06:49, 25 January 2017 (UTC)


yuo7899i

Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format. DRAGON BOOSTER 06:50, 25 January 2017 (UTC)