Talk:Pendulum/Archive 3

Not Galileo Galilei
Ibn Yunus

Prince Charming
Surely the pendulum was not discovered in 2009 by prince charming. —Preceding unsigned comment added by 71.199.104.98 (talk) 04:52, 5 January 2010 (UTC)
 * No, of course not. The silly addition was made by an anonymous editor an hour before your post here, and has since been reverted.  You are welcome to revert such vandalism yourself.    D b f i r s   07:49, 5 January 2010 (UTC)

Torture
For the other uses section the part that says about torturing people with a pendulum slowly coming down shouldn't there be a link about The Pit and the Pendulum? —Preceding unsigned comment added by 69.136.72.16 (talk) 01:06, 28 January 2010 (UTC)

pendulums for divination is a wrong link
The link for this leads to Dowsing which complete different from using a pendulum for divination. Dowsing has been pretty mush proven to be fake through apparently 6 in 500 dowsers aren't outright fakes but that might just be random. A pendulum on the other hand has the chance of being a connection to your unconscious mind thus your probably just talking to your own mind or something.

It would be as if I were to click on a link to a architectural method and I got the page that describes why you shouldn't put a 13th floor in any building.--tumaru 23:29, 25 January 2011 (UTC)


 * No, it wouldn't be like that because neither pendulums for divination nor dowsing has any scientific supporting evidence, whereas architecture has a basis in science. I would have thought that pendulum swingers are more likely to be fake, but that is just my personal bias.  The link is to a specific section of the dowsing article that mentions use of pendulums.  Personally, I would be happy to remove the whole religious paragraph, including the link, but others might think that it adds to the article.    D b f i r s   08:07, 26 January 2011 (UTC)

Q definition
This article has contradicting definitions of Q. The definition that "q = 2 pi times the number of oscillations" is the most common definition, as the ampitude of a free swinging pendulum then decays at exp(-omega t/q). But the expression q=m omega/gamma contradicts that and gives the decay as exp(-omega t/2q). If instead you say q=2m omega/gamma you'll be okay. I've not checked the article to see if other contradictory definitions of q exist. For example the relationship between the energy lost and Q will depend on which definition you settle on. Most clock people go with the first, but some mathematics books use the second.

Dsdrumh (talk) 00:06, 6 May 2011 (UTC)

Confused by the Animation
Basically, why is there an acceleration vector when the pendulum is at its lowest point? Isn't it in equilibrium, with its weight counterbalanced by the tension in the string, hence no net force, hence no acceleration?

--86.163.123.101 (talk) 11:03, 29 July 2010 (UTC)


 * The tangential component of the acceleration is zero, but there is a radial component correctly shown. The bob is not in equilibrium.  The tension in the string or rod is greater than the weight, and this imbalance causes the bob to follow a circular path rather than continue in a horizontal straight line.  See Circular motion for a more detailed explanation.    D b f i r s   12:15, 29 July 2010 (UTC)


 * Thanks for the response. So why is the tension in the string/rod greater than the weight of the bob - if the bob were just hanging stationary from the string/rod (before it is set swinging, for example), the tension would be equal to the weight, right?


 * --86.163.123.101 (talk) 13:13, 30 July 2010 (UTC)


 * That's right, the reason for the tension being greater than the weight is that the bob is accelerating upwards (so that it can follow the curve). You can actually feel this extra "apparent weight" if you swing a weight on the end of a string.  Try whirling it around in a vertical circle (carefully) so that it just completes circles and only just keeps going at the top.  You will feel the tension reduce almost to zero at the top of the circle, and it will be double the weight at the bottom.    D b f i r s   17:09, 30 July 2010 (UTC)


 * So the acceleration is the source of the extra force? I thought it was the other way around...


 * --86.163.123.101 (talk) 17:42, 30 July 2010 (UTC)


 * Yes, I think you are right that it is the other way round. The bob tries to obey Newton's first law and continue in a horizontal straight line, but the string is not elastic so tension increases, so the bob is accelerated towards the centre by the increased force.    D b f i r s   18:42, 31 July 2010 (UTC)


 * I see. Thank you very much for explaining it.


 * --86.135.250.118 (talk) 13:35, 1 August 2010 (UTC)


 * When the mass is at its lowest point (otherwise known as the equilibrium position) it is, as its name suggests, in equilibrium, there are no resultant forces, therefore the tension = the weight. The added force you are describing as the pendulum reaches the lowest position is due to the fact that when the pendulum is at it highest position (lets say we start it at 90°) then the tension will be mgcos θ in this case mgcos 90°=0; so when it gets to the equilibrium point the tension now has the weight of the mass on the end, so we feel a gain in weight. see http://www.sparknotes.com/testprep/books/sat2/physics/chapter8section5.rhtml for a more detailed explanation.


 * BravoNovemberGolf (talk) 12:14, 25 March 2011 (UTC)


 * Acctually upon giving it some more thought I see how the acceleration is not perpendicular to the pendulum, although it is very confusing. As the pendulum gains momentum the centripetal force needed to keep the mass on the end of the wire increases, this is shown by the formula F=(m*v*v)/r. and so the tension would be (mgcos θ+(m*v*v)/r) and the acceleration is the sum of (tension+weight)/mass the mass cancels out leaving the acceleration = (gcos θ+v*v/r+''g')
 * BravoNovemberGolf (talk) 19:28, 26 March 2011 (UTC)

Why do we have an initial theta_0 insread of 1-cos(theta) for height?
Like so:
 * $$h = l\left(1-\cos\theta\right)$$

This eliminates the need for the initial condition. This is also the way I've seen it in every Mechanics book I've ever encountered.


 * I've seen it both ways both in Mechanics books and on examination papers. As you suggest, it all depends on where you start.    D b f i r s   17:15, 30 July 2010 (UTC)

Centrifugal force factor
The pendulum is a unique instrument in that it is the only device that has to deal with a congruent direction of operation of the gravity and the centrifugal force vectors. Is the centrifugal force factor taken into consideration in the mathematical calculations related to the functioning of the pendulum?WFPM (talk) 03:48, 9 March 2012 (UTC)
 * The centrifugal force doesn't play a role in calculating the period, because it is directed along the line of the pendulum rod through the pivot, always perpendicular to the velocity vector.  So it doesn't affect the velocity of the pendulum, and isn't part of the "restoring force" that returns the pendulum toward the center.  However, it would play a part in calculating the tension in the pendulum rod, of course. -- Chetvorno TALK 06:02, 9 March 2012 (UTC)
 * Centrifugal force exists only in the frame of reference of the pendulum (as for an insect clinging to the swinging bob). Almost all treatments are from the point of view of the frame of reference of the "fixed" pivot, where only centripetal force is real.    D b f i r s   09:49, 9 March 2012 (UTC)


 * What I am getting at is that the oscillating motion of the pendulum is initiated by an integrated amount of gravitational force to a certain velocity past a centerpoint, and then slowed back down to a stop by a reversal of direction of that gravitational force. This could only happen if the mass of the pendulum remained a constant. And if the mass of the pendulum increased due to its velocity, then the velocity of the pendulum would be slowed down at the center position and the oscillatory motion would be damped by a factor. And I,m surprised that somebody hasn't used this logic to argue that a moving object doesn't acquire additional mass due to translational motion.WFPM (talk) 19:46, 9 March 2012 (UTC)


 * Mass does, of course, increase with velocity in one interpretation of special relativity (though experts don't look at it that way). Even if the effect were more dramatic (and real) then I don't see why the motion would be "damped" by this effect, provided that the energy could be regained as the pendulum bob slowed down again.  The period would be longer because of the lower velocity.  I'm unclear about what logic you are using.    D b f i r s   23:27, 9 March 2012 (UTC)


 * I certainly appreciate your trying! But if the oscillating pendulum slowed down at the centerpoint, then it would no longer have the velocity and energy to regain its original height against the slowing gravitational force vector and the second kinetic to potential energy conversion process would be affected. I noted in the other article that a circular orbit looks better because the circular path velocity remains constant and just changes direction, which simplifies the situation. So, to my amazement we have an argument against the increase of mass with velocity! I was originally fascinated by the action of the oscillating pendulum's being able to line up the gravitational force vector and the centrifugal force vector in the same direction. Generally, they work at right angles to each other. And I believe in the existence of a measurable centrifugal force as you note in your article about vertical rotation.WFPM (talk) 01:26, 10 March 2012 (UTC) And note that if you had the pendulum in a box on an instantaneous weighing scale the recorded weight of the apparatus would be a sine wave of the average weight of the apparatus plus or minus the centrifugal force value.WFPM (talk) 02:11, 10 March 2012 (UTC)


 * This formula is a model based on an idealized situation. By definition, there is error. Any effects of special relativity may be disregarded because of the low speeds involved. The change in acceleration due to gravity across the pendulum's path would introduce a greater error. MSWurmstein (talk) 04:59, 12 April 2012 (UTC)


 * The instantaneous weighing machine would not record either the "centrifugal force" or the (more real) centripetal force. It would record only the vertical component (which would indeed vary periodically).  Why select only one component?  Perhaps you could have a "weighing machine" that independently records horizontal "weights" (i.e real forces)?   D b f i r s   15:38, 14 September 2012 (UTC)

Correction for physical pendulum formula
Would it be relevant to include the infinite summation correction for the formula of a physical pendulum? It is discussed for a simple pendulum, but not a physical pendulum. MSWurmstein (talk) 04:48, 12 April 2012 (UTC)
 * My feeling is that people can figure out from the "Period of oscillation" section that the infinite summation formula also applies to compound pendulums.  The subject is already treated in Pendulum (mathematics) and the "Period of oscillation" section  directs readers there.  This article is already huge, and I think that as much of the mathematics as possible, outside the basic stuff, should be offloaded to that article. -- Chetvorno TALK 17:18, 11 September 2012 (UTC)

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
 * $$\begin{alignat}{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{alignat}$$ A second formula for the true period has been repeatedly added, which I have reverted
 * $$T = \frac{2\pi}{M(\cos(\theta_0/2))} \sqrt\frac{L}{g} \qquad\qquad (2)  $$

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

I think only one formula for the true period should appear in the article. This article is already huge and bloated. We have Pendulum (mathematics) which is the proper place for additional formulas. So which true period formula should appear in this article? -- Chetvorno TALK 15:52, 13 September 2012 (UTC)
 * 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. -- Chetvorno TALK 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)

Agreed, in addition these refs each give (Θ = angular amplitude):
 * $$ T = 2\pi \sqrt{\frac{L}{g}}\left[ 1 + \left(\frac{1}{2}\right)^2\sin^2\frac{\Theta}{2} + \left(\frac{1}{2}\cdot\frac{3}{4}\right)^2\sin^4\frac{\Theta}{2} + \cdots\right]$$

While this ref: gives:


 * $$ \begin{align}

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{align}$$

for small amplitudes (they use a = Θ):


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

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.   -- Chetvorno TALK 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?    D b f i r s   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. -- Chetvorno TALK 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. -- Chetvorno TALK

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.  -- Chetvorno TALK 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 -- Chetvorno <i style="color:purple; font-size:smaller;">TALK</i> 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 (talk • contribs) 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: $$\frac{2\pi}{M(\cos(\theta_0/2))} \sqrt\frac{\ell}{g}$$ simpler than the other "exact" formula: $$4\sqrt{\ell\over g}K sin(\theta_0/2)$$ in Pendulum (mathematics) (given that you are equally familiar with M and K)?   D b f i r s   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?  -- Chetvorno <i style="color:purple; font-size:smaller;">TALK</i> 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. -- Chetvorno <i style="color:purple; font-size:smaller;">TALK</i> 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. -- Chetvorno <i style="color:purple; font-size:smaller;">TALK</i> 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. -- Chetvorno <i style="color:purple; font-size:smaller;">TALK</i> 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) -- Chetvorno <i style="color:purple; font-size:smaller;">TALK</i> 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!

Nevertheless, in spite that I was so badly and unfairly hurt I decided to carry on my own investigation of the case of that mysterious IP. Firstly, I could not understand why would that IP so insistently and repeatedly intervene only to suddenly disappear. That Computing Center is known to be as a quite large extension of the Steklov Mathematical Institute encompassing specialists in various fields of Pure and Applied Mathematics, Mechanical and Electrical Engineering, Physics and Computer Science. The Steklov Institute itself is one of the epicenters of top mathematical research on our planet employing many of the most prominent and internationally acclaimed mathematicians. Most prominent mathematicians residing elsewhere frequent or regularly visit the Steklov Institute. The scientist at the Computing Center are unlikely to differ form other serious scientists worldwide in their attitude towards WP as a source of junk science the way McDonald's food chains are regarded as a source of junk food. So I realized that whoever used that IP so openly is actually likely to have been a temporary visitor, given a great number of international exchange programs and an endless chain of international conferences, who might then surface far elsewhere easily fooling naïve WP administrators. I further realized that the whole edit warring was, in fact, a theatrical conspiracy aiming at bringing an attention to a formula by repeatedly inserting and removing it, while imitating a battle, with some participants may have become unwittingly involved. Then I read the article and realized that the author who, by the way, did point out that the formula is not known thus far to exist in any textbook, wouldn’t probably want see a vulgarized version of his work in a WP article, so I emailed him for a confirmation and asked him to respond if and only if he thought otherwise. Now, I confirm that he, as expected, did not respond, and I feel that he is not among those who would involve himself in a debate with some average people like me or many WP administrators or editors. The formula so mysteriously promoted is certainly supreme and it would be an honor for WP to include it before all other formulas. All other here means nothing more than the customary Taylor series expansion which is no match whatsoever. It’s not exact, it’s cumbersome, it converges linearly for small angles and it fails to converge for angles close to a straight angle. The truncated form given in the article would not, of course, fail to converge, but it would simply become unusable, with an error indicated in the article depending on the magnitude of the angle, unlike the suggested supreme formula which never fails! Even on historical grounds that supreme formula is far more important as was nicely explained in that AMS article so I won’t have to reiterate. With little additional effort after replacing the outdated formula with the supreme formula the article might be substantially shortened so as to satisfy lovers of brevity to whom I belong. Of course, the quality of WP articles would go up if its administrators become as competent as to abide by their own rules, rather than taking someone's word about "resolving" issues they are clueless about and siding with whomever addresses them first, the way EdJohnston did. That administrator did not even apologize to any of the accounts he wrongly identified as a sockpuppets and then proceeded with too little hesitation, highly questionable justification and without any consultation to chaotically block accounts clearly led by independent users capable of making their own personal contributions. The true sockpuppets, as you’ll next see, were of course happy to support that administrator so as to further divert his attention. The consensus of a herd incapable of understanding its own actions is undoubtedly incomparably less valuable than a single well justified opinion no matter to whom it belongs and no matter how strongly does the herd feel or disagrees and no matter what an administrator have decided to further do or say. Having contemplated all that, a major breakthrough in sockpuppet investigation has immediately and clearly emerged before my, now dry and tearless, eyes. So, secondly, it dawned to me that the mysterious IP does, in fact, have surprisingly many sockpuppets, some obvious ones are A13ean, Dbfirs, Martinvl, Maschen, Velella and more. Clearly their best option to conceal themselves is to attack me or assign someone to attack as if I was the sock not all them. Maschen even shamefully alleged that someone else admitted sockpuppetry which I carefully checked to confirm that he is bluntly resorting to open lies. I am unlike any of them neither a sock nor a puppet. No deep analysis was required for me to determine that these sockpuppets live on the same farm although I don’t quite know whether it’s small or large. They haven't been too careful in hiding that they attended the same local college which is quite likely to be named The Cornell Of The Corn Fields (CCF) although, admittedly, I’m uncertain about its exact name. Undoubtedly, all of them experienced severe difficulty with the concept of the arithmetic-geometric mean claiming it converged obviously quickly yet insisted that it was not exact. They argued that only numbers such the square root of 2 are. Yet A13ean told them that the exactness of the square root of 2 was deceiving since it relied on some vague limiting process which he read about in some WP article. He could not recall whether or not that process was iterative. However, they reached a consensus on that the arithmetic-geometric mean is not programmable on an excel worksheet. They further thought that since they cannot do it then it was unlikely that another a bit less average person can. They also agreed with each other that the Taylor series was important for historical reasons while all other concepts not given in their physics CCF textbooks are unimportant. Some of them could not even distinguish the notation for the arithmetic-geometric mean M from the notation for the complete elliptic integrals K and thus became even more confident that any alternatives to their favorite Taylor series terminating with 3 dots would bloat their WP article with obscurity since, after all, the letter M is not simpler than the letter K as they once noted. Luckily, that “busted” IP claims he/she won't be editing WP again but if he/she does then blocking US and Chinese accounts is the only option to teach him/her a lesson on how he/she ought to behave discussing issues with people having little clues about articles they're editing. With this becoming the only mean available EdJohnston administration must then be permanently relocated to Kenya while his contacts would then be made restricted to Obama's relatives who would further consult him on his subsequent steps to combat that IP's snobby attitude thereby preserving WP mediocracy unelevated. A careful follower of the debate may notice that I have not enlisted Chetvorno among the sockpuppets but I have no doubt that he was merely manipulated into such an active participation being an ideal victim incapable of sustaining a debate and craving frequent approvals of a WP administrator. While he successfully raised multiple cases around the formula in the pendulum article he hasn't noticed a sneaky Phancy Physicist (note the name which I meant to parody) who created a separate section for the formula in the related pendulum (mathematics) article. This article is currently referenced from the period section of the pendulum as “the main article”. That PP kept a low profile after uncarefully disclosing too much personal knowledge of the author while imitating uncertainty and a need of further consideration. Thirdly and finally, the last straw for me was realizing that PP was the only editor who mentioned author’s full name twice in a single contribution to a talk page. He/she is undoubtedly trying to popularize the name. He/she might have been an exchange student directly or indirectly supervised by the author. There are other subtleties which I’ve noted but are bordering on a breach of confidentiality concerning lists of exchange students between academic institutions, so I’ll spare you and summarize that PP is highly likely to be the one who temporarily used that IP bringing the issue to a boiling attention.

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 (talk • contribs) 16:04, 15 October 2012 (UTC)
 * Why do you feel so strongly about this particular formula and this article? -- Chetvorno <i style="color:purple; font-size:smaller;">TALK</i> 18:55, 15 October 2012 (UTC)
 * And why do you make wild and obviously false accusations? I suggest that you look under your own bridge.    D b f i r s   07:53, 16 October 2012 (UTC)
 * SupremeFormula has been blocked as a sockpuppet, and the IP also 1. -- Chetvorno <i style="color:purple; font-size:smaller;">TALK</i> 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. -- Chetvorno <i style="color:purple; font-size:smaller;">TALK</i> 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. -- Chetvorno <i style="color:purple; font-size:smaller;">TALK</i> 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). -- Chetvorno <i style="color:purple; font-size:smaller;">TALK</i> 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". -- Chetvorno <i style="color:purple; font-size:smaller;">TALK</i> 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: <ol> <li>transfer section/s: Accuracy of pendulums as timekeepers + Use for time measurement → new article/s: Pedulums as used for timekeeping </li> <li>
 * A. keep section/s: Use for time measurement
 * B. transfer section/s: Gravity measurement + Standard of length → new article/s: ?
 * C. transfer section/s: Accuracy of pendulums as timekeepers → current article/s: Pendulum (mathematics)

</li> <li> transfer section/s: Gravity measurement → current article/s: Gravimeter or Gravimetry </li> </ol> Maschen (talk) 11:52, 15 September 2012 (UTC)


 * Looks good. Yeah, maybe some of the editors from Wikiproject Time will have other ideas. -- Chetvorno <i style="color:purple; font-size:smaller;">TALK</i> 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
This is a friendly reminder to involved parties that there is a current Dispute Resolution Noticeboard case still awaiting comments and replies. If the dispute is still ongoing, please add your input. Amadscientist (talk) 07:26, 29 September 2012 (UTC)
 * 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? -- Chetvorno <i style="color:purple; font-size:smaller;">TALK</i> 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).


 * $${d^2\theta\over dt^2}+{g\over \ell} \sin\theta=0 \qquad \qquad (1)\,$$


 * $$\theta \ll 1\ \qquad \qquad (2)\,$$,


 * $$\sin\theta\approx\theta\ \qquad \qquad (3)\,$$,


 * $${d^2\theta\over dt^2}+{g\over \ell}\theta=0. \qquad \qquad (4)\,$$


 * $$T \approx 2\pi \sqrt\frac{L}{g} \qquad \qquad (5)\,$$


 * $$\begin{alignat}{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{alignat}$$


 * $$T = \frac{2\pi}{M(\cos(\theta_0/2))} \sqrt\frac{L}{g} \qquad \qquad (7)  $$


 * $$\theta (t) = \theta_0 \cos( 2 \pi t/T)\, .\qquad \qquad (8)\,$$

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. -- Chetvorno <i style="color:purple; font-size:smaller;">TALK</i> 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. -- Chetvorno <i style="color:purple; font-size:smaller;">TALK</i> 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!)   D b f i r s   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.    D b f i r s   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 . 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  (talk • contribs)  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. &mdash;&thinsp; H HHIPPO  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)
 * [[File:De template.svg|frameless|left|300px|Treating directly pendulum movements associating them with partial differential equations could scare...
 * ... the rookie-wikireaders!]]
 * 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.
 * "Pendulum" and
 * "Pendulum (mathematics)".
 *  Tot straks! 
 * Maurice Carbonaro (talk) 07:20, 6 November 2012 (UTC)
 * = = = End of copied text = = = 
 * Hi Maurice,
 * Thank you for your reply and for the greeting in Dutch.
 * 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)
 * 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)