Swingin' physics

By Phil Plait | June 1, 2011 2:00 pm

There are four things most people don’t know, or simply don’t appreciate, about physics: 1) the right answer to a question is sometimes surprising; 2) it’s simpler than you think sometimes; 3) that simplicity can spawn terrible complexity; and 4) in simplicity, complexity, and the border in between lies great beauty.

For example, I bet if you went up to people on the street and asked them why different pendula (I prefer Latin plurals) swing with different times, they’d say it was the weight of the bob at the end. But it’s not that at all: it’s actually the length of the pendulum itself that is the major factor in determining the swing time (called the period) — the mass of the bob has nothing at all to do with it! A heavy bob and light bob will still have the same period if the length of the string is the same (try it yourself).

Surprising and simple, right? So what about the other two things, complexity and beauty? Well, here’s a perfect example of that:

Isn’t that lovely? Note the bobs are all the same, but the length of each pendulum is different; the shortest has the smallest period. Each one swings at its own pace, and as time goes on those different rates sometimes line up, giving you the gorgeous patterns. But then that breaks up and you get what looks like random motion. There are also slight variations in the period of a pendulum; friction, imperfection in the exact length used, and so on. Later in the video you can see that as the pendula don’t line up perfectly.

Do yourself a favor: watch the video again, but this time instead of watching the whole set-up move, just fix your attention on one of the bobs as it moves. You’ll get a startling change of reference as it looks like the other pendula are swinging around it. You can also watch as the ones on either side swing with longer or shorter periods, imparting the very odd illusion of what looks like communication between the bobs.

See what I mean? Simplicity, complexity, beauty, and my favorite, surprise. It’s that last that keeps a lot of scientists in the business. We get the same sense of awe and wonder that everyone gets when contemplating the mechanics of the Universe, and we get it all the time. Throw in that surprise every now and again, and you guarantee a life-long addiction to science.

Tip o’ the to Mike Lunenburg and Amanda Bauer of Astropixie (whose post reminded me I wanted to write about this as well).


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CATEGORIZED UNDER: Cool stuff, Science, Top Post
MORE ABOUT: pendulum

Comments (66)

  1. That.
    Was.
    Awesome.

    I REALLY liked it when they lined up again. Like going one full harmonic.

  2. Thanks, I’ll be building one of these tomorrow!

  3. Steven

    I have a minor gripe about (occasionally careless) Latin plurals. Pendulum comes from the Latin “pendulus”, and “pendulum” is the neuter form. A neuter plural in Latin is indeed made with a -a ending, so “pendula” is the correct neuter plural. In this case, you’re safe (unless you wanted to talk about a masculine pendulus or a female pendula)! However, you gotta check your etymology when creating a Latin plural… some people apply basic Latin rules to “octopus”, which seems like a masculine Latin noun. Well since “octopus” has Greek origins, the plural is “octopodes”, and not “octopi”, as the standard Latin methods would suggest. In general, when speaking/writing in English, it seems safer to make plurals in plain English following our (multiple) rules, rather than having to look up the etymology of every word before determining its plural. Saying “pendulums” would have been just fine.

  4. @Steven (#3)

    To quote an old Eddie Izzard bit:

    “RUN! He knows Latin!

    :D

  5. Andrew H

    That. Video. Is. Awesome. I really want to make that now.

  6. MT-LA

    @Dotan Cohen: Take a look at the way the pendulum lengths vary. I think they increase at a quadratic -rather than linear – rate. It could also be exponential, but I’m pretty sure its not linear. Anyways, I would be interested to know how changing the length relationship equation changes the modes. Please let us know if you build one!

  7. @MT-LA #5: drat, I knew I should have brought my physics notes home for the summer! FWIW, I looked it up and the period of oscillation is T = 2 * pi * sqrt(L/g), where L is the length, and g is the local acceleration due to gravity. This only works if the angle that it sweeps out is less than around 1 radian though. I don’t think a pendulum oscillates in modes, that would look something like the center of the string remaining stationary, the string above it moving back and forth, and the string with the pendulum attached moving back and forth in the opposite direction.

  8. Keith

    I saw something similar to this a while ago on Richard Wiseman’s blog. There was info regarding how it was done and I wrote up a short perl script to figure out each pendulum’s length. Here’s a link to the script on Google (which includes the output at the end listing the lengths) if anyone’s interested:

    http://bit.ly/jga49C

  9. MT-LA

    @Carson: I was referring to the relationship between the lengths of the pendulums in the linked video…not the relationship between length and period of a single pendulum. For example, what is the difference between length 1 and length 2, then between length 2 and length 3, and so on. I could have made that more clear.

    The equation you quoted is burned into the brain of all engineering students as a good example for numerical analysis methods. Engineers are (required to be) lazy, so an approximation is good enough! We leave exact solutions for those nerdy physicists.

    PS – the reason that pendulum equation only works if the initial release angle is small: (L) is a pretty good approximation for (L sin A) if A is small – less than a 1 radian.

  10. Dave

    I wanna know why Phil prefers latin plurals. Because it sounds cooler? Seems to me there are already far too many completely unnecessary exceptions to rules in english. If we’re gonna make changes wouldn’t simpler be the better direction? I think so (which is why I always omit exceptions to perfectly good rules and say things like indexes and stupider).

    And what’s up with plurality?: Two dogs, one dog, zero dogs. Zero is even less plural than singular, why does it get a zero? I guess that’s what happens when your language predates the concept of zero.

  11. Jason

    I do an experiment every year with my 4th graders where I pose the question, “What effects the speed of a pendulum’s swing? The length of the string or the mass on the end?” They always think it is the weight, but after they figure out how to design the experiment and run it a few times, they figure it out.

  12. Douglas Troy

    I see what you’re really trying to do Phil, you’re trying to hypnotize us all into reading your blog day-after-day.

    Well it won’t work I tell you, your evil mind control plan is going to fail. I, for one, am not going to come back here day-after-day to read your blog, I’ll just stay logged onto it all the time. So, HA!

    Oh wait.

    :P

  13. @MT-LA I see, but by looking at the equation, it appears that they vary exponentially

  14. @MT-LA: I figure that I’ll have to experiment. I might do a few just to see the differences: linear would be first, then maybe exponential. How about X-log(n) for a variable relationship between them?

    @Keith: Thanks, that could be helpful! Could you post a real link, blind links are fragile and dangerous. Thanks!

  15. My head just exploded. I love this video.

    Science. Physics. Mathematics. FOR. THE. WIN!!!

  16. mark

    I made a model of this in geogebra, it was fun to make!
    http://www.geogebra.org/en/wiki/index.php/Pendulums
    would it work on the moon? you can play with the lengths of the pendula and strength of gravity

    p.s. instructions on how to make one here (via exploratorium)
    http://www.exo.net/~donr/activities/Pendulum_Snake.pdf

  17. James

    @2:

    Of course, octopus is a Latinised Greek work, so the plural is not indisputably “octopodes” and most dictionaries would list that plural as rare. I’d go with “octopuses”.

  18. jearley

    We looked at this a few weeks ago, and one of my students has already built the frame. He intends to finish the entire apparatus this week.

  19. Anthony

    Question to ponder:

    Is the period of the pendulum still dependent solely on the length of the string if you do not neglect the mass of the string relative to the bob?

    I’m fond of saying that the real trick to physics is knowing what you can safely ignore.

  20. JohnW

    You are getting verrrry sleeeeeepppyyyyyy…..

  21. If the common support is not exceedingly rigid, the pendula do talk to each other. They come to concertaciónes. (The English plural of “consensus” is ugly.)

  22. Bill

    Cool trick o’the eye – to me, during the ‘chaotic’ bits, it almost looks like the farthest left and farthest right bobs freeze in place as if they hold stationary while the rest sort themselves out.

  23. James H.

    I want one of these! I’m going to build one this summer

  24. Mike

    For those of us with motion-hearing synesthesia, this video is even more intense. I’m glad that the person or people or put it together didn’t add a soundtrack!

    (New Scientist ran an interesting short article a few years ago about this form of synesthesia, and how it was accidentally identified. Check out http://www.newscientist.com/article/dn14459-screensaver-reveals-new-test-for-synaesthesia.html)

  25. Theramansi

    Then there are words that are the same singular or plural. Herd animals for example: both “herd of zebra” and “herd of zebras” are correct.

    A change in gravity strength would affect all the pendulums, so weaker gravity they would all be slower – stronger gravity they would all be faster. There is one factor not mentioned yet: size. Unless in a vacuum, there is air resistance.

  26. Pete Jackson

    @3,17: I think that using octopi for the plural of octopus is easier in English than octopuses.
    After all, you would then have to consider if the plural shouldn’t be octopusses, in analogy with busses.

  27. I plan to add this to my ‘Scientists in Schools’ toolbox and show it to 5 and 6-year-olds. Awe + wonder + surprise = kids who want to learn more science.

  28. Phil,

    “There are four things most people don’t know, or simply don’t appreciate, about physics: 1) the right answer to a question is sometimes surprising, 2) it’s simpler than you think sometimes; 3) that simplicity can spawn terrible complexity; and 4) in simplicity, complexity, and the border in between lies great beauty. ”

    Concerning your quote above:

    A one day old posting with 25 and counting postings? pretty good I would say. I’m now going to dissect your quotations/ statements above (1 through 4) one at a time :) I hope you don’t mind.

    “There are four things most people don’t know, or simply don’t appreciate, about physics:

    1) the right answer to a question is sometimes surprising.

    This statement is understated. It is ” often” that answers and observations differ from mainstream theory.

    But by using the work “sometimes” your statement is certainly correct.

    2) (the answer is) simpler than you think sometimes.

    by using the word “sometimes” you cannot be wrong.

    The answer is always simple, in my opinion, it just depends upon present understandings, knowledge, and theory.

    3) that simplicity can spawn terrible complexity

    Since you used the word “can” then the statement could be considered valid, but I consider it to be generally false. Reality is only complex to those who do not understand it, in my opinion. To all others (if any) it is simple.

    4) In simplicity, complexity, and the border in between lies great beauty.

    This statement as a whole is generally false. Beauty is only in the eyes of the beholder. What is beautiful to some, lacks beauty to others.

    Your articles and material as a whole are interesting and logical, otherwise I wouldn’t be here :) Thanks again for presenting all of your interesting material and perspectives to us over the years.

    best regards, Forrest

  29. Peter Ozzie Jones

    I hesitate to enter the fray.
    But Peter Atkins in his book “Galileo’s Finger: The Ten Great Ideas of Science” on pages 205, and 223 (in the paperback edition) mentions that the amplitude of the pendulum swing is quantized and is not continuous . . . steps of only 10^-30cm for a 1m pendulum at the Earth’s surface!

  30. TDL

    @Jason (#11)… Hopefully you really ask them what “affects” the speed of the swing and then let them experiment to see the real “effects” ;)

    I think it’s great you teach kids by letting them try it out for themselves. It will definitely leave a more lasting impression.

  31. Goldie

    @forrest noble, As you pointed out while dissecting statement number 3, ‘Reality is only complex to those who do not understand it’, which is somewhat like saying ‘complexity is in the eye of the beholder’. Therefore statement 4 ‘In simplicity, complexity, and the border in between lies great beauty’ is in fact correct, as all of these elements are determined by the understanding and beliefs of the observer.

  32. That was so beautiful!

  33. Hmm…

    No one mentioned how the characteristics of the ‘string’ affect things.

    For example compare the use of cotton, string, rope, and fine steel wire…

    Note, it is more than just considerations of mass and stiffness!

  34. James

    @26:

    But “octopi” is definitely incorrect, since that suggests that octopus is a second declension Latin noun, which is certainly isn’t.

  35. Nigel Depledge

    Dave (10) said:

    I wanna know why Phil prefers latin plurals. Because it sounds cooler?

    I was under the impression that some words in English always took Latin plurals. After all, have you ever heard anyone speak of “datums”??

    One pendulum, two pendula. I had never previously heard of “pendulums” as an accepted plural of “pendulum”.

    Seems to me there are already far too many completely unnecessary exceptions to rules in english.

    All words in English follow the rules of the language from which they were derived. Except for the ones that don’t, obviously.

    If we’re gonna make changes wouldn’t simpler be the better direction? I think so (which is why I always omit exceptions to perfectly good rules and say things like indexes and stupider).

    “Indexes” is the plural of “index”. It has the variant spelling “indices” because that is closer to the way it is pronounced.

    “Stupider” – or, rather, the form “more stupid” – is not an exception. Only adjectives of one syllable take the “-er” ending when they are turned into comparatives (and “-est” when turned into superlatives). Thus, we have “hard / harder / hardest” but “difficult / more difficult / most difficult”.

    What makes the rules of English appear to be so illogical and inconsistent is the fact that they are very often bent, ignored or downright abused.

    And what’s up with plurality?: Two dogs, one dog, zero dogs. Zero is even less plural than singular, why does it get a zero? I guess that’s what happens when your language predates the concept of zero.

    Old English predates the knowledge (in the west) of zero, but it had irregular plurals, of which very few remain in the language. “Mice” and “lice” are the only two examples that come to mind readily. IIUC, the format of plurals ending in “-s” or “-es” post-dates the knowledge of zero. But then, until relatively recently, the form used would have been “none”, “no” or “nought”.

  36. Nigel Depledge

    Jason (11) said:

    What effects the speed of a pendulum’s swing?

    The answer is gravity.

    I think the question you meant to pose was “What affects the speed of a pendulum’s swing?”.

    This is a common problem with the many homophones in English.

    To effect is to cause to occur. To affect is to influence.

  37. Nigel Depledge

    James (17) said:
    Of course, octopus is a Latinised Greek work, so the plural is not indisputably “octopodes” and most dictionaries would list that plural as rare. I’d go with “octopuses”.

    Yeah I just looked this up. The only dictionary I have handy here is Longmans from 1992, and it includes “octopi” as a plural for “octopus”. It makes no mention of “octopodes” nor of “octopods” (which is another vaguely greek form I have heard expounded). I was always taught that “octopi” is wrong. So, it’s probably best to stick with “octopuses”, which is a safe enough Anglicised plural.

  38. Nigel Depledge

    Pete Jackson (26) said:

    @3,17: I think that using octopi for the plural of octopus is easier in English than octopuses.

    It may be easier, but its use is likely to:
    1. Cause the heads of any classicists who hear you to explode; and
    2. Betray an ignorance of the etymology of the word.

    After all, you would then have to consider if the plural shouldn’t be octopusses, in analogy with busses.

    Not really. I think “octopuses” is widely recognised and accepted. I have not ever seen “octopusses” (with the double “s”). Until I read your comment.

  39. Nigel Depledge

    @ Forrest Noble (28) –

    Wow, and I thought I was pedantic!

    BTW, you missed out the initial capitals in your name.

  40. Nigel Depledge

    Oh, and the reason I haven’t commented on the video is that I cannot view it from work.

    Still, it’s fun to try to pick apart how English works.

  41. Niall

    So cool, loved how it cycled through so many different patterns

  42. Pete Jackson

    @33 James, @37 Nigel – We are speaking English here, not Greek or Latin, so one consults an English dictionary as a reference. Looking at m-w.com (and this is an American blog, so forget about Oxford), we see that plurals of octopus are listed as octopi and octopuses.

    Incidentally, both buses and busses are acceptable plurals of bus.

  43. tphtwpe

    @36 et. al.

    Miriam-Webster online has a neat on-line video series called “ask an editor” which takes on such topics as the pluralization of Octopus, and here is the link:

    http://www.merriam-webster.com/video/0015-octopus.htm?&t=1307014604

    Apparently all 3 are “technically correct”, which as we know is the best type of correctness.

  44. Nigel Depledge

    Pete Jackson (41) said:

    and this is an American blog, so forget about Oxford

    Yes, but the language is called English, so you ignore England at your peril!

    However good a job Mirriam Webster does, the OED is still the only definitive dictionary. Having said that, I would not be surprised to find it lists “octopi” as a plural for octopus, along with some comment to the effect that many scholars consider it to be wrong, but that doesn’t stop anyone from using it anyway.

    Having said that, I will still refrain from using “octopi” because (a) in my formative years, I was taught it was wrong, and (b) despite its latin “feel”, it is the less scholarly form.

    At the end of the day, the language is what it is, and no organisation can control it. However, your argument about the language being English (and therefore “octopi” being acceptable) does not wash. If you want to speak English (and be seen to be speaking English), use “octopuses”, which is an Anglicised plural form of octopus. If you want to sound like you’re speaking Latin (or speaking English with a nod to the Latin derivation of many words), use “octopi”. If you want instead to sound like a pedantic classicist (sorry, James), feel free to use “octopodes” despite what the dictionaries say.

  45. Pete Jackson

    @21 Uncle Al, I was reaching the same conclusion, that the pendula do ‘talk’ to each other. In the video, we see periods for the 15 pendula ranging from about 0.896 second for the shortest to about 1.176 seconds for the longest. From the formula in (7 – Carson), we calculate string lengths of 19.93 cm and 34.33 cm respectively.

    Consider a pendulum in the middle with period 1.036 seconds and string length 27.13 cm, and its neighbor with period 1.056 seconds and string length 28.16 cm. We see them maintaining coherence to within at least 0.1 period after about 60 periods, or about one part in 600. If they did not ‘talk’ to each other, the precision of the string lengths would have to be 1.03/600 cm or about 17 microns! I’m sure Allen constructed this experiment very carefully, but I doubt he could be that precise.

  46. No such thing as a definitive dictionary for a living language.
    Dictionaries record the use of language.
    The users define it.

  47. DennyMo

    At a couple points in the video, I saw the flea from the Centipede video game come dropping down the screen. The 0:59 mark is one of those places.

    Oddly enough, this whole “octipi/octipodes” argument demonstrates all 4 of Phil’s physics “appreciations”…

  48. Very cool.

    And yet, IIRC, we can’t write a closed-form solution for pendulum motion. We can only write an approximation.

  49. Daniel J. Andrews

    It strikes me that this is a good metaphor regarding “Argument from design”. E.g. that motion must be coordinated…the chances of them all lining up and making snake-like patterns is infinitesimal (takes out calculator to calculate the odds of one bob being at one location at one point in time and multiplying by 15 bobs, etc–yep, the odds of them forming the wave is slightly better than the odds of those Shakespearean producing monkeys.

    Just an off the top of my head thought this early a.m.

  50. Nigel Depledge

    @ Daniel J Andrews (49) –
    Erm … there’s an infinite number of monkeys outside who want to talk to you about this script for Hamlet they’ve worked out.

  51. PayasYouStargaze

    I could watch it all day. It’s very cool.

  52. This is a beautiful depiction of aliasing of a high (spatial) frequency signal with a finite sampling interval.

    I think what you want to get this lovely effect is for the oscillation parameter, t/T, to vary linearly at any given point in time t. If t is constant, then T, the pendulum period, should go like 1/(j + C) for the j’th pendulum, where C is a constant. T goes like the square root of the length, so the lengths should be proportional to 1/(j + C)^2. Reciprocal quadratic.

    I think.

  53. …That is, of course, using the small-angle approximation.

  54. Daniel

    Someone made one of these for the Maker Faire this year. Instead of weights they used people. They called it the Harmony Swing, there are a few pics around the internet if you search for Harmony Swing Maker faire but no video that I could find.

  55. Robin Byron

    Just watching the strings is interesting as well. Clear patterns and a neat 3D effect.

  56. Pat

    That would look really weird if they put it in front of a green screen and removed the strings, and didn’t say what you were watching. Synchronized UFOs!

  57. I LOVED IT. IT WAS MUCH BETTER THAN “CATS.” I’M GOING TO SEE IT AGAIN AND AGAIN.

  58. Sion

    But Phil, if complex order can spontaneously form from no more than simple objects following simple physical laws then that would imply that…… Oh. My. God! Ray Comfort IS a moron! ;)

  59. fj

    The video is great, thanks!

    As a non-native speaker I’m quite fascinated by this whole Latin/Greek plural discussion, and by what is and what is not discussed:

    Why only plural and not cases? (Yes, that would be weird: “I looked it up in the indice.” or “a property of all matricum”) Why only Latin and Greek, not e.g. French or German. (I’ve never seen anyone arguing for the “correct” plural “kindergärten” or “rucksäcke”. Andy don’t get me started on “to abseil”…)

    I don’t want to suggest that the word forms in my examples should be used in English. I’m just interested why certain foreign-language forms are considered “correct English”, others are contentious, but most are (rightfully) ignored.

    @Nigel #35: “After all, have you ever heard anyone speak of “datums”??” Maybe geodesists or surveyors? ;-)

  60. DennyMo

    49. Daniel J. Andrews Says:
    It strikes me that this is a good metaphor regarding “Argument from design”.

    It strikes me that you need to keep looking for a better metaphor. This system was built by something intelligent and set in motion by something intelligent, the laws of physics merely dictated how it progressed from there. That’s not too terribly different from the model ID tries to promote.

    35. Nigel Depledge Says:
    After all, have you ever heard anyone speak of “datums”??

    Yes, it’s a very common term in mechanical engineering design. When you have more than one “standard position or level that measurements are taken from”, you have several datums. To call that collection “data” would confuse it with our more typical use of that word.

  61. Nigel Depledge

    FJ (60) said:

    Why only plural and not cases?

    Old English was (is?) a fully-inflected language.

    After the Norman invasion, the conquerors tried to stamp out use of it, but it merely adapted by absorbing quite a lot of their mediaevel French and becoming Middle English. As Middle English evolved, fewer and fewer inflections survived. I don’t know why.

    By the time of Shakespeare (end of the 16th century), Middle English had pretty much become recogniseably modern English.

    Some inflections kind-of survive (as in “to whom” rather than “to who” and the subjunctive case in “if I were you”) but they seem to be becoming less popular.

  62. Nigel Depledge

    @ 60 & 61 re “datums” –

    Curses, I realised soon after I had posted that some smartypants was likely to bring up the use of this word in engineering.

  63. @Nigel Depledge, #39

    I use lower case letters to start my names so that I will not be accused of being pedantic, but it seems that I cannot always thwart assertions concerning failings of a humble demeanor :)

  64. Nigel Depledge
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