21 Jun 2011

Making your own pendulum wave machine

This post is a continuation of a three part post started here.

To make your own pendulum wave machine, you can see from the video that you just need to place 15 pendula or so beside each other at equal separations. What is hard to see however, is how long the length of string should be. Below we'll derive a function for you to calculate the lengths of each pendulum on your machine (or just scroll to the bottom to see some precalculated lengths).

In the small angle approximation, the period of a pendulum is $T=2\pi\sqrt{\frac{l}{g}}\implies \omega=\frac{2\pi}{T}=\sqrt{\frac{g}{l}}$ where $g$ is 9.8 m/s and $l$ is the length of the pendulum.

Since length of the pendulum depends on its location on the apparatus, we have $l(n)$ instead of a constant $l$ (where $n$ is the pendulum number). Putting it all together, $\omega(x)=\sqrt{\frac{g}{l(x)}}.$

But we also know from the previous post that $\omega(x)=\frac{2\pi}{T}=\frac{2\pi \left(N+\frac{x}{d}\right)}{\Gamma}=\frac{2\pi \left(N+n\right)}{\Gamma}.$
Isolating for $l(n)$, we have $l(n)=g\left(\frac{\Gamma}{2\pi\left(N+n\right)}\right)^2$ where $\Gamma$ is the duration for the entire dance (60s in the video), $N$ is the number of oscillations the longest pendulum performs in the cycle (51 in the video - I always mistake this for the number of pendula for some reason), $n$ is the pendulum index (starting from 0).

As an example, we can calculate the lengths of the pendula in the video of the previous post.
 Pendulum Index 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Length (m) 0.343 0.33 0.318 0.306 0.295 0.285 0.275 0.265 0.256 0.248 0.24 0.232 0.225 0.218 0.211

You can calculate your own pendulum lengths on the online spreadsheet file I've posted here.

UPDATE: I've newer much better simulations and calculators. You can find them at http://www.cs.ubc.ca/~inutard/webapps/pendulumcalc.html, http://www.cs.ubc.ca/~inutard/webapps/pendulum.html

All that left to do is decide on the dimensions of your pendulum wave machine. For example, if I wanted to make the machine above, I'd place each pendulum above 5 cm apart, making the entire machine at least 70 cm long and 34.3 cm tall. However, one thing to note is that these pendulum wave demonstrations are made perfect by careful timing of the periods on each pendulum, not by careful measurement of the pendulum lengths. As such, make the individual pendulums on your machine adjustable! The very first design of this demonstration used 15 adjustable screws to which each pendulum tied on to. By carefully adjusting each screw and timing each pendulum, the correct number of oscillations can be tuned for each individual pendulum.

That's all there is to it, I'll leave the nitty-gritty details of the design to all you talented folks out there. They make for great gifts! I made my girlfriend one for her birthday and she loved it! OK, that was a lie. But it did get her parents to like me.

1. Hey, thank you very much for this post and especially the excel pendulum length calculator. I just got through making my own pendulum wave apparatus for a class demo and your post was very helpful. I made it out of various scraps in the machine shop, with rubber stoppers for bobs. Thanks again!

2. i love your stuff u just saved my life in science class thank you sooooooooo muuuuuuuuccccccchhhhhhh
cuddle bear

3. thank you so much for these posts! i'm making one for a physics summative, and i'm so grateful to have this post to guide me. i was wondering if you had any suggestions as to what kind of materials to use (ie for the apparatus, type of string, pendulum bob, etc). and also (if you posted this above, i've missed it, sorry!), how to attach the pendulums to the apparatus. thank you~

4. @Anonymous
For my pendulum wave machine, I got some cheap plywood boards from Rona and cut it up to make the basic frame. Since I had a limited budget, I got a bag of bouncy balls to function as the bobs and a bag of hooks with a sharp end to stick into the balls as well as a curved end to hook onto the string. The string I used was some leftover yarn that my friend found in his kitchen. Screws were drilled onto the top of the wooden frame so that we could attach the strings to them and adjust the length of each pendulum by screwing/unscrewing the screws.

As you can see, my materials weren't the best. But fortunately, they worked and I was able to make a decent machine.

Here are some important things I learned while making the machine though:

- The string lengths I provided are approximations. You must attach the strings in a way that makes it very easy to adjust their length.
- Cheap wood tends to crack (but still works).
- It's better to overestimate the amount of string you'll need for each pendulum, since point 1 (above) ensures that you should be able to adjust the string length relatively easily.

All in all, my machine took my friend and I one Sunday afternoon to make (approx. 5 hours). Good luck!

5. This description is great. I am looking forward to making a pendulum wave demonstrator for my students' (and my) enjoyment. I am planning on using 1 inch ball bearings as bobs. I hope to solder narrow brass tubes to the balls to pass fish line through to suspend the balls. Based on your recommendation for adjustability, I will incorporate something like a guitar tuning peg. I'll try to let you know how it works out!

6. @David the Chemist
That would sounds awesome! Thanks for keeping me updated!

7. @Paul Liu
thank you so much for the tips! they will come in very handy when i go scouting for materials

8. Hi, Do you think using a christmas deco ball would wokr as well??

9. @Anonymous
They may work. However, they are rather large and light, so air drag may play a large role. Something small and dense would work best.

10. Are the length's related linearly? Could you just adjust the balls to be lined up?

11. @William
Unfortunately the lengths of the pendula are not related linearly. However, you could have the balls line up by changing the bar from which the pendula are hung from (as done here.)

12. hello @Paul Liu
can we take double the length . would it work properly.

13. @Anonymous
Doubling the length is just fine, but the period will be roughly 1.4 times longer :).

14. so would i still see the patterns which are in the video if i double it

15. thanks a lot

16. Are the lengths you posted the lengths of the string, or are they the lengths of the string and the weight combined?

17. @Anonymous
The lengths are the lengths of the string after you have tied the weights on (i.e. don't forget to leave a little extra string for the knot you'll use to tie the weight on).

18. Hi! :) What is the best weight to be used in this experiment that could be bought within the nearest supermarket/bookstore? Since Christmas balls are too light to be used, what could be the best alternative for them? Thanks and hoping for a quick response. :))

Something with the same mass and size as a marble would be good.

20. Paul, Thanks so much for all this great infomation! When measuring the lengths where are the measuring points? Would they be the pivot point at the top and the center of the ball? Thanks

21. @Anonymous
They would be from the pivot to the centre of the ball, just as you said. Thanks for the compliments!

22. hey i am planning to make this machine and i was wondering if its possible to cut the lengths half the size of what you have provided would that result in a 30sec period? the same patern? doubled amount of cycles?
btw i thought your explanation of the device was very thorough.

23. @Anonymous

I think reducing the length by 1/2 reduces the period by 1/sqrt(2) (since the period is proportional to the square root of the length). However, reducing the length has the effect of causing some of the patterns in the dance to flash by very fast. I think reducing the lengths by 1/2 should be OK, but I haven't tried it myself.

24. Hi Paul, this is a nice post - I have made a reference to it from my site, see
http://www.engineers-excel.com/Tools/Pendulums/Description.htm

and

http://www.engineers-excel.com/Tools/Pendulums/How%20it%20works.htm

Best wishes
Nitin

25. @Nitin Mehta

Thank you for the reference! And nice website!

1. Thanks Paul! :)

26. Hello Paul,
We are looking to make a 15 foot high Pendulum. What you recommend the Gamma and N to be.
Thanks
Steve

27. @Anonymous
Holy cow! 15 feet high! I am no engineer, so I can only give you an approximate recommendation. I suggest at least 120 seconds for gamma. This gives roughly 27 for N. May I ask for more details on this project? I could do more appropriate (and precise) calculations given more information.

28. OMG PAUL you are SO cool <3

1. Thanks! Nothin' better than complements from a stranger!

29. Hello Paul,
We are working on a Burning Man Art project that was inspired by your post. It will be a 12 or 15 foot high Pendulum. Here is the YouTube video submitted to BM: http://www.youtube.com/watch?v=0spySCNqfoM
Also you can go to www.burningman.com to learn more about Burning Man. Can you please give us the steps on how to tune a pendulum.
Can you also give us a definition of Gamma and N.
You can email me directly if you prefer at SteveEatHome@Hotmail.com.
I can also send you more information if you like.
Thanks Steve

1. Hi Steve,
Sorry for the relatively late reply. Gamma is the length of the entire pendulum dance (about 90 seconds in the video), and N is the number of oscillations the pendulum with the longest length performs in Gamma seconds.

Keep me updated on your project! It seems really ambitious and cool.

30. This comment has been removed by the author.

1. Hi Ris2214, even though you removed your comment, I'll still answer it :)
If you use only 12 bulbs, 51 oscillations for the entire dance will still work.

31. Just wondering does the distance of the balls have any effect on the illusion
or does the distance not matter at all?

1. The distance should not play a large effect on the illusion. However, if the distance between the balls is too large, one might not be able to see some of the more subtle wave patterns.

32. Paul,
Thanks for the definition of Gamma and N. I now understand them.

Here is more info on the BM project. We are planing to use hollow frosted spheres and light each sphere with 50 LED RGB computer controled lights. See www.coolneon.com or go to http://youtu.be/b70aCvmCJYA This lighting will allow us to make any sphere any color with many patterns.

Can you please give us the steps on how to tune a pendulum?

We will keep you updated on the project.
Steve

1. Hi Steve,

Unfortunately, there isn't a precise science to tuning the pendulums. For my own pendulums, I attached each pendulum to a set of adjustable screws which allowed me to vary the length of individual pendulums. I suggest that when measuring out the lengths for each pendulum, cut out more than you need, and then slowly vary the lengths to the theoretical lengths calculated with the formula. From this point, you'll have to use your own sense of judgement to adjust pendulums which swing too fast or too slow.

Good luck!

- Paul

33. Hello Paul,
Thanks for the info. Lets see if I have this right. For your pendulum with a Gamma of 60 and N of 51. It should be tuned so that the longest pendulum (0) swings back and forth 51 times in 60 seconds and the shortest pendulum (14) swings back and forth 65 times in 60 seconds. Is that correct?
Thanks Steve

1. That is absolutely correct! Good luck!

-Paul

34. how do yu figure out the oscillation of the logest string

35. Thanks for all information. Is it possible that the different mass 50g and 100g of bob can affect frequency of pendulum for the same length of string?
Thanks, Sylvain

36. Hi Paul, thanks for the great informative site.
I've been building a wave pendulum and have reached the point to decide on the N value. It seems that this number affects the number of different patterns achieved, correct? (Compare N=16 @ http://www.arborsci.com/cool/pendulum-wave-seems-like-magic-but-its-physics, N=25 & N=22 @ http://en.demo.phy.tw/experiments/mechanics/pendulum-wave/, N=51 @ http://engineers-excel.com/Tools/Pendulums/Description.htm)

It seems that the higher the N value, the longer it takes to cycle through the patterns. In addition, does it change the number of alias points? Eg. some will reach a point in time where it forms 2 rows, 3 rows and sometimes 4 rows. Not sure if I've seen one with 5 rows being formed - is that to do with the N value?

Regards,
Grant D (New Zealand)

1. Hi Grant,

As you said, N does affect the number of different patterns achieved. However, it is the combination gamma, N, and the number of pendulums that decides the number of alias points as well as the time it takes to cycle through the patterns. However, increasing N does not increase the time to cycle through the patterns. The time to cycle through the patterns is much more dependent on gamma, the length of the entire pendulum dance.

In general, increasing gamma and the number of pendulums (while keeping N constant) will increase the number of alias points and make for a better illusion. However, there will be a point of diminishing returns. On my simulations (which I can send you if you happened to have Mathematica), I can even see 8 rows being formed when increasing the total number of pendulums to 50. However, these patterns are much more fleeting (lasting for less than one or two seconds even when gamma is already at 120 seconds). Hence, there is really a point of diminishing returns when you have to put in many more pendulums to get only a few more patterns. So if you want to stay on the safe side, I suggest using values around around what they used in the video. However, if you wish to see more patterns, increase gamma and the number of pendulums while keeping N the same.

2. Hi Paul,
Thanks for the reply. I plotted on excel the displacement of the pendula as a function of time and found that as you increase N, you get an increasing number of periods at each pattern.

For a given maximum height (in my case 0.15metres for the longest pendulum) the period of the longest pendulum is fixed. Increasing N makes it take longer to cycle through all of the patterns. I used N=59 arbitrarily (gamma = 45.84sec). If I used N=80, gamma = 62.15sec.

Higher N values also mean that the string lengths are more similar. If length of first pendulum L0=1, the shortest pendulum L14=0.6532 for N=59, compared with L14=0.4649 for N=30.

I must add, it was very difficult to tune even though I had each string-end terminated to a grub screw (to adjust height and length). A fun project none-the-less.

Happy pendulum-ing, Grant D

37. Will this machine work, if I use only 12 pendulas? I think it will but just for sure...

1. No worries, it will.

2. Thank you so much man... :-) You saved my life. :D

38. Paul,
Do you have the measurements in inches for us old farts out here?
Hans

1. Hi Hans,

To go from metres to inches, simply multiply my measurements by 39.37.

Cheers,
Paul

39. Hi Paul

Really grateful for your work!!

May I know how to make the system adjustable? I don't really get the screw part..

Thanks!!

1. Hi David,

In our design, we simply strung each pendulum to an adjustable screw. By turning the screw, the string of the pendulum wraps around the screw, thus shortening the pendulum length if needed.

Hope this helps!
Paul

40. Hey paul i wish you are fine . I would like to know what is the exact difference of lenghth between the pendulums

1. Hi Anon,

In the post above, I gave a table of pendulum lengths. Just take the difference between those lengths. If you want the exact (symbolic) difference, I also gave a formula for l(n). Take l(n+1) - l(n) to get what you need.

41. Hi Paul, I made a m/c similar to yours and inspired by you for use at Woolsthorpe science centre (Newtons birthplace). I used golf balls for my pendulums. They are adjusted by using a 4mm rod as a tuning mechanism similar to a guitar/piano tuning screw. I take my device to Woolsthorpe every Thursday pm where I am a volunteer. (it's a National Trust property). To tune it I used a stopwatch and counting method for the first 3 longest pendulums, then I swung 4 pendulums and after 30s adjusted the 4th pendula so it gave me 2 rows of ball. Then swung 5 balls ajdusted so that after 30s I got two rows and so onbringing in an extra pendula each time. Hope this helps any future pendulum wave maker.
Who was the original maker of this demo. I believe it was a Russian physicist.

1. Hi! Thanks for the update!

As for the origin of this demo: I believe this demo was first published in the states by Richard E. Berg, whose friend first saw this demo at Moscow State University. Curiously enough, one of the demonstrators at Moscow Sate claimed at the time that they had also seen this demo somewhere in the US. It's certainly a mystery where the true origin of this demo lies, as no one (as far as I'm aware) has yet claimed to be its inventor.

42. Hi Paul,

By changing the values of Gamma and N wil it have a knock on affect on the pattern observed, therefore does the difference between Gamma and N always have to be nine and does the value for Gamma need to be greater then N etc..
I'm planning on using 40 for the Gamma and 31 for N, which I assume would be okay.

I also noticed on your example spreadsheet that you used 14 pendulums, say if I knocked off two of the shortest or longest pendula, would it have an affect on the wave pattern at all.

1. Hi Anon,

The difference between Gamma and N does not always have to be nine. I just used it because these were the parameters chosen for the video I linked to. 40 for Gamma and 31 for N seems fine, however the dance will be shorter (it will complete in 40s instead of 60).

Using 12 pendulums instead of 14 will not have a significant effect on the pattern, but the more pendulums you knock off, the less of a pattern you will see.

Cheers,
Paul

43. Very well described and an inspiration. I am going to attempt to build one with 16 pendulums.
Is the length measured to the centre of gravity of the weight (bob) ?
I intend to use quite large discs so this will make a difference.
Will also be using two strings to each bob. Is the length the vertical distance or the length of the strings ? If that makes sense

Thanks again

1. Hi isykic,

The length is measured to the centre of gravity, and the length is the vertical distance from the bob to where its strings are attached on the top of the pendulum wave machine.

Cheers,
Paul

44. hey paul
is keeping them at EQUAl separations important if yes pls recommend some length and can u tell me how ur attaching the pendulums to the frame i dint understand that part

1. Hi Anon,

Yes, equal separation is important for the waves to appear properly. The length that I used to separate each pendulum was about 5cm. I attached the pendulums to the frame by tying them to screws that were drilled in.

45. -.- dosent work

46. Thanks for your efforts and information! I am about to finalize my own wave machine but wanted to share the "tinkering" phase. I used a old meter stick (I have tons) laying around. I used golf balls, 3/4" eye screws, and 12lb test fishing line, athletic tape and paper clips to get my lengths just right. I have some wood I am going to cut to make the final frame. I drilled a hole every 7cm in the meter stick to get the spacing right, which only resulted in 13 balls. In the final version I will have 20 balls using your spreadsheet. Here is the tinkering pics:

http://db.tt/TyPR6PY6

http://db.tt/CCjz2peM

As soon as I have the finished product I will post it to Youtube!

1. Wow! Thanks Mr. Y! That looks great!

47. could this concept be used to produce tan(f) cot(f) sec(f) csc(f) illusions?

1. Good question!

Unfortunately, I can't see a way of producing such illusions at the moment. The entire reason we get a sin/cos illusion is because the shape of our wave obeys the travelling wave equation. It might be possible to produce tan/cot/sec/csc shaped wave pulses physically (e.g. by decomposing them to sine and cos waves - this is called a Fourier expansion), but we probably won't be able to exploit the simple setup of using only pendulums of varying lengths.

Cheers,
Paul

48. Hi Im in 7th grade and doing a science project on pendulum waves. Im having someone make the frame for me out of acrylic. Im going to use kevlar thread and 14mm onyx beads for the bobs. The frame is not finished so I havent got to experiment with it yet. I am wondering what would a good question be to investige that can be tested with out a bunch of math to explain?

1. Hi there!

For a school science fair, I think an interesting thing to test would be to see if the pendulum waves are really caused by aliasing. Aliasing basically means that the pattern you see in the pendulum wave is just part of a much larger pattern. For example, you might want to try and see if the pendulum waves (when seen from above), matches to one of these patterns here.

There is a mathematical explanation of this effect, so if you're curious, ask an adult to teach you more about the math I wrote in this blog.

Good luck on your science fair!

-Paul

49. Hi thanks for your reply. I did get the frame and strung the bobs. The frame he made had holes going through blocks of plexiglass to the top. The holes were 5mm large. The kevlar thread is very thin so I was getting a rocking inside the holes. So I made the holes smaller by glueing a bead cap (half of a bead thing)on the end. I am having a problem fine tuning. It goes great for the first 45 secs? then you can tell it is out of sync. Do you think it is because the hole is still allowing movement inside or it is still not tuned. I dont want to glue the string to the pivot point until I know for sure. He made me two of them so maybe I will string heavy steel bobs in the other and see which one works best.

1. Hi again,

From your description, it seems like the machine is still slightly untuned. However, you should try to set it up so that you can avoid gluing the string to the pivot point. This way, it is easier to fine-tune whenever you need to.

Cheers,
Paul

50. Hi Paul, I'm hoping to make some of these with my physics students, so cool! A quick question though - are the lengths given the length of the string, the length of the string+ball? Or would it not make any difference as long as we stick with one or the other?

thanks!

1. oops sorry I just read through all the comments and saw someone else asked the same question :) please ignore me!

51. Hi Paul,
How does the weight of each ball affect the operation- or does it? I don't see a place for mass of the pendulum in the calculations. It's funny the pendulum equation includes the acceleration of gravity but not the mass of the pendulum.

It seems to me that the higher the mass, the greater the momentum of the ball. Does this affect the time it takes pendulum to run down?

I can get metal balls in a variety of materials and diameters which give a good range of weights.

Richard

1. Hi Richard,

It is true that greater mass means greater momentum, but this doesn't affect the motion of the balls unless they are in a collision. A marble and a boulder drops at the same speed regardless of mass (when ignoring air drag).

Cheers,
Paul

52. Hi Paul,
I want to make my own for a school project, so I was wondering what should be the distance between each pendulum for a machine with a frame of 50 centimeters? and, the length of each pendulum should be the same of your chart?(I know that maybe there would be only like 10-12 pendulums)

Greetins from México,
Eduardo

1. Hi Eduardo,

The length between the pendulums do not affect the height. They can be anything you want (e.g. 50/12). Just make sure the pendulums do not collide with each other.

Cheers,
Paul

53. Hello Paul! I just want to thank you so much for all the information you provided on how to make this project. I've searched many websites and videos and no one else provided the information you have! By the way, did you make a base for your pendulum wave?

Thanks again!

1. Hi Rachel and Tim,

Thanks for the compliments. Yes, I did have a base, but it was quite simple. Just a piece of planed plywood that my friend and I drilled everything else onto.

Cheers,
Paul

54. Hi Paul,

I am making a pendulum wave machine for a high school science fair and I'm supposed to do it all by myself.I have a lot of time to make it really nice and neat,but I don't know anything about woodwork and for some reason my school wood shop is permanently closed. Do you have any suggestions on what to use for the materials?(or just any suggestions at all...) Thanks so much!

I've spent hours reading stuff online about how to make a pendulum wave machine,and you have the best explanations!!You rock!!

And this is going to sound totally random,but just out of curiosity,do you plan to go to graduate school?(if you are 19 you should be an undergraduate..)It's just something that I keep asking every smart undergrad I know..

Thanks again!

Josh

1. Hi Josh,

My friend and I used a large piece of plywood for the base, and basically three more pieces of wood stuck together in a U-shape for the rest of the frame. However, I think even a design as simple as the one here would work well if you have little woodworking experience.

As for your other questions: I am an undergraduate, and I do plan on going to graduate school.

Feel free to ask more questions if you've got any!

Cheers,
Paul

55. may i ask one question. when making a pendulum wave, what do you use for the balls??

1. Hi there,

Sorry for the late response!

I simply used a pack of bouncy balls I got from the dollar store. The material of the ball doesn't really matter as long as its reasonably solid (so air drag is not a concern).

Cheers,
Paul

56. This is great! I just have a few questions, would I get the same effect if I only used 12 pendulums? Secondly, how come the difference between the lengths are non linear? And lastly is the lengths given from the top to the centre of the ball or for each string? Thanks for your time!

1. Hi there,

Thanks for the comment! As for your questions:
1. The same effect would be present with only 12 pendulums (though it would be slightly reduced).

2. The lengths are expected to be non-linear due to the fact that the period of a pendulum depends on the square root of the length, and not any other power.

3. The lengths are given from the top to the centre of the ball. They are only a rough approximation of the lengths needed. Make sure you leave a couple extra centimetres for manually calibrating the machine.

Cheers,
Paul

57. Hi Paul,

Love your site! Hopefully I'm sending more than a few visitors your way :)

I thought it was pretty cool to see from the comments that someone did this at The Burning Man. I bet that was quite a sight!

We need more science blogs out there like yours. I just want to thank you for sharing your interests with the world.

1. Thanks Chris,

I appreciate it!

58. Sorry Paul but can you tell me the distance between each ball???

1. The distance between each ball does not matter. Just make them spaced out enough so that the balls do not collide with each other.

Cheers,
Paul

2. Thank you.but two more questions.first what are the materials i should use?second:are the ballballs at. The same level but they have different length of strings.?thank you again for your time.

3. Hi there,

The materials do not really matter either. I used a package of bouncy balls I bought at a dollar store, but others have used solid wood balls. The pendulums can be hung from the same height (so that the balls are not at the same level), or you can hang each pendulum from a different height so the balls are at the same level. Both of these approaches work.

Cheers,
Paul

4. Thank you very much.but one more question.can i use christmas balls insread bounce balls.i mean would it work normally?

Julia khoury

5. Yes, if the christmas balls are heavy enough. If the christmas balls were extremely light, it might not work since there would be too much air drag on the balls.

59. Hi I'm an 18 year old undergrad double majoring in physics and mechanical engineering. I am planning to design a pendulum with an angled spine. If I have 18 1.5" ball bearings as the pendulums, will this affect the T at all? Can I stick with the L(n) equation for finding L? Also, I read on another website that the pendulums must be spaced 1/2f apart, is this true and if so what is the frequency of this wave?

1. Just kidding about the frequency thing, I misread the information. Since they are spaced less then 1/2f apart the aliasing occurs, as you probably know.

2. You can stick with the L(n) equation. It should work just fine.

Good luck on your pendulum wave machine!

Cheers,
Paul

3. How is T always 60 seconds?

4. It doesn't have to be. T is a free parameter. Since the original harvard demonstration made it 60s, I made it 60s as well. You could just as easily change it to 30s or 90s, to make the dance shorter or longer.

Cheers,
Paul

5. Ok thank you so much for all your help!

60. Hi there, I built my won pendulum wave machine,but the problem is that I am not getting the pattern you have in the video. It starts right, but after ten seconds it gets messy and stops before 60 seconds. could you please tell me what you think?

1. Hi Sandy,

Do the lengths of your pendulum machine follow the ones I gave on the blog? They need to be very very close for it to work. You also need to make the pendulum lengths adjustable, because a lot of tweaking is needed afterwards to make things appear exactly right. It takes a lot of work for the pattern to last (even in the video it isn't perfect).

Good luck!
Paul

2. yes I spnet a lot time to get it as accurate as I can, but how do you make it adjustable?
What if a pendulum stops before the others, what does that mean? Do i need to make it longer or shorter and vice verse? I measured the length from the top of the ball to the beginning of the upper wood, is that right? I really need to get this machine work.

3. Hi Sandy,

You should be measuring the length from the centre of the ball to the beginning of the upper wood.

Cheers,
Paul

61. ooooooooooh, then that is my mistake, thank you a lot, I will change everthing.

62. what size were the ball bearings that were used in the one in the video?

1. I do not know. I did not make the video. However, the size of the ball bearings do not matter (as long as they are sufficiently heavy).

Cheers,
Paul

63. Hello Paul! I am a band director and I am looking at making a machine of 8 individual pendulums about 8ft tall. What would you suggest for gamma and N? The pattern will be viewed from stands in a gym so I'm worried that because of the size and limited number of pendulums that the pattern will not be clear.

64. A little more info. we are currently in the process of trying to figure out what materials to use. We are looking at making "A" frames out of wood (they need to be individually mobile) and possibly using bowling balls (however this may be outside of our budget). This whole thing is part of a show and at the end we bring the individual pieces together to form the wave pattern. Should be pretty cool if we can figure out how to build the darn thing!! I would love any input or advice you have to offer. Thanks!!

65. Thanks for very clear description of the pendulum wave. You mentioned a spreadsheet but there is no link on this page. Please help

1. Hi Anon,

The link was hidden in the "here" written above. The stylesheet of this blog made it somewhat impossible to see! I've written the link below:

Cheers,
Paul

66. Hi Paul,

I don't know how to use your online spreadsheet. I want to change your values and make it last a little longer and I want to know how. I want to find the new lenghts of my pendulums. I have a school project and I really need to get it finished till Monday. I hope you'll see my post soon.

Best regards,

You have to save a copy of the spreadsheet before you can use it.

Alternatively, you can use the one at http://deadpanduck.com/webapps/pendulumcalc.html

Set initial angle to 30 degrees, number of swings to 51, and period to 60 to get numbers similar to what I posted on this blog.

Cheers,
Paul

67. Hi Paul
I have done the same wave machine that you have. Unfortunately, I am having hard time with this machine. I got the right lengths, but It did not work. One thing I do not understand is the initial angle. What do you mean by the initial angle? Please I wanna solve this problem.

1. Hi Sandy,

The initial angle is the angle at which you lift up the pendulums. If you start by lifting the pendulums too high, then the calculations will be off. Usually anything < 30 degrees is OK.

Cheers,
Paul

68. Hi Paul,
Thank you very much. Now, the angle is between the string and Y-axis. Is that right?

1. Hi Sandy,

That's exactly right.

Cheers,
Paul

69. Hi paul, we just built a replica with 12 pendulum and add a link to this blog, here the preliminary test. http://youtu.be/MtCZG9sd7mk,

1. Congratulations, That looks great!

Thank you for sharing!
Paul

70. man this shit be crazy... you all be smart as shit to do all this mother fucking machines shit like 2+2=6 thats how i learned all that crazy mathy shit like i graduated from harvard and shit but still what the fuck

71. god damn you are smart as shit.

72. test post - hi

73. where did you get the (N+x/d) thing? thanks

74. Dear Paul Liu, thank you very much for your post. I am a teacher and I built a pendulum wave machine with my students for a school physics project. We used a 2m wooden stick, golf balls as bobs and nylon string. We hung the bobs by two tie-rods in order they could not rotate. We made a 1mm hole in each ball and put a screw-eye inside and we used it for fine tuning: turning the screw in and out we set the length of the string. Tuning has been an hard work! It took us hours! The machine at the end worked very well and it has been a success! Thanks a lot again!

Laura, Italy

75. im making it with heavy nuts.so if i use your string lengths ,what is the vertical distance ? i mean from top of the nut to the top of string??

76. Thanks for putting up the formula. I used the math provided and made a 3d computer simulation to produce a pendulum wave. Hope you like it ;^)

77. i can send the project report if anyone wants.Just reply with your email.

78. please send to us the project report at this email:jamalsafa123@gmail.com

79. I just wanted to chime in here with my thanks to you for not only posting this to share but also for answering everyone's questions so kindly and diligently. I've had this page open (as a means to keep it in mind) for almost six months now and am finally ready to give it a try. My plan is to build a moderately sized one and set it by the sidewalk in our front yard for passersby to play with and experience.

My question for you is if you've come across any easy to understand and effective release mechanism. If not it'll add to the fun and challenge for me - which is great. But maybe you've seen something that will be a good start point for me.

1. Hi Kelly,

Thanks so much for your kind words. As for the release mechanism, most videos I've seen simply uses a large wooden board to release all the pendulums at once.

By the way, I've made new simulations and pendulum wave calculators. It might be useful to you: http://www.cs.ubc.ca/~inutard/webapps/pendulumcalc.html, http://www.cs.ubc.ca/~inutard/webapps/pendulum.html

Cheers,
Paul

80. Hi Paul! I am creating this pendulum for a final physics project. In your calculations, you mentioned a previous post and we were wondering where that was. We are quite confused on how you completed this step: 2πT=2π(N+xd)Γ=2π(N+n)Γ. What does d represent?
Thanks,
Evie

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