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Some pendulum wave videos show two hooks and strings coming up from the ball and some show only one hook and string. Why is it considered better to have two strings?

I am making these with the grandchildren during self isolation but there are so many questions and so many different ways of doing it any help appreciated.

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Thanks Jack I really appreciate the depth of your reply. I have my friendly mathematician working out the algebra for me. I did go through each pendulum and adjusted where necessary so the swings went in sequence eg 23 24 25 etc. I think the problem is that the holes I have drilled in the top board aren't even enough and also I have two strings sharing one hole. I will correct that today and hopefully it will all come right. At the end I can write an article about all of the mistakes newbies like me make and how to fix them. I want to get it finished before we get out of our level 3 Bubble to level 2. In New Zealand that is tomorrow. So I know what I will be working on today.

Using two strings constrains the path of the pendulum to an arc in a plane, and that is helpful when you want to put a whole bunch of 'em (a plurality of pendulums? a plethora of pendulums?) all side by side.

In a typical one of these "pendulum wave" (or "wave pendulum") toys,

https://www.instructables.com/howto/pendulum+wave/

all the planes containing the trajectory of each pendulum, are stacked next to each other, similar to slices of bread in a loaf of sliced bread.

With just one string holding each pendulum bob, it would be possible for the bobs to collide into each other, or into the strings of the other pendulums.

Hi Jack thanks so much for your reply. I am hoping you or somebody else can help a bit more. I have the balls swinging well. I have checked the oscillations and they number correctly through the 14 balls. I am just making the minor changes in length I had no idea it would be so complicated but maybe it is just perseverance.

I have never built one of these toys. However, I have read about them,

here:
https://sciencedemonstrations.fas.harvard.edu/pres...

and also here:

https://hippomath.blogspot.com/2011/06/making-your...

and I think I understand the premise.

The premise is that there is this sort of long period or "dance period,"
and in that amount of time, the individual pendulums all complete an integer number of oscillations. So that ideally, after one "dance period," all the pendulums arrive in the same position they were in at the beginning.

Also there is some math, relating the lenghts of the pendulums to their periods Ti and frequencies fi = 1/Ti. In general this is T = 2*pi*(l/g)^(1/2), where I have to write the square root as, "to the one half power", because my keyboard does not have a key for the square root symbol.

Curiously, the period of a pendulum does not depend on the mass of the bob. T just depends on l, the length of the string, and "little g" the local acceleration due to gravity, in your home or laboratory.

However, pendulums tend to work better if the bob is heavy, because more mass means more stored energy, which means more ability to keep swinging, without noticeable losses in amplitude. Or in other words, more initial stored energy helps to offset the effects of friction forces, slowly taking that energy away.

From a construction perspective, I guess you have to get all these pendulums tuned correctly, to the right frequencies.... and how do you do that?

Well, one way is to assume you can get it right by measuring, and adjusting the lengths of the strings precisely.

Another way is to measure the period, or frequency, of each pendulum, and I guess the way to do that is by watching it closely, and counting the number of oscillations it makes, in the period you want for the dance period.

I admit that would take a lot of time, since the test for each pendulum to make sure it has the right frequency, is done dance period, or 60 seconds, in the examples I have read about, and you might have to do the test several times, to get one pendulum adjusted perfectly.

I am guessing that most of the people who build these successfully, do so through precise measurements of the lengths of the strings holding each bob. Although, that is just a guess on my part, guessing people could more easily measure lengths of string than "lengths" of time.

I noticed NightHawkInLight authored some Youtube videos on this topic. I have not watched these all the way through, but I am pretty sure this dude knows what he is talking about.

Video IDs: "v=08ueDogNkP8" and "v=_8JMVl-_KKs"

By the way, I have no idea what sources you have utilized for the construction of your pendulum wave toy, including what videos you have already seen, because you did not mention any of your sources.

OK I have it built and the oscillations are correct but I cannot get anything perfect once the snake finishes. I also can't see what I need to adjust. I don't quite get 3 lines and I dont quite get the helix. Any help would be appreciated. I have spent hours adjusting it.

Single string: Pendulum can swing in 2 axis and can create stuff like:

Double-String: Single axis pendulum. Can only go in one direction.

Neither is better or worse than the other. They are used for different things. If you want to have 2 axis: single string. If you want to have 1 axis: double string.

On a sidenote: 3 string (in some sort of triangular fixation) would give you 0 axis