Impressive harmonic motion demonstration

[Q_Goest]

The YouTube video here will get you to think a bit. Basically, 15 separate pendulums that create various patterns:

The period of one complete cycle of the dance is 60 seconds. The length of the longest pendulum has been adjusted so that it executes 51 oscillations in this 60 second period. The length of each successive shorter pendulum is carefully adjusted so that it executes one additional oscillation in this period. Thus, the 15th pendulum (shortest) undergoes 65 oscillations.

I wonder though if you could say how many given patterns are created. Not sure how to describe that... what do you think?

 

[Borek]

I guess we should start with defining "pattern".

In the past I was playing with some strange curves plotted on the screen, varying their phase differences and so on. Effects can be mesmerizing.

 

[Q_Goest]

I guess we should start with defining "pattern".

How about this. Let's call the position of anyone of the balls a maximum when it is at a maximum potential energy (highest upward motion) and a minimum when it is at a lowest potential energy (hanging straight down). Given these two locations, a pattern might be defined as a state at which all the balls are either at a maximum or minimum and not somewhere in between.

Any other ideas for defining a pattern? And once the pattern is defined, I wonder how many there could be in the course of 60 seconds... my brain is refusing to even consider the math right now.

Edit: Watching the movie again, I don't think that definition of a pattern is going to work! hmmm...

 

[sophiecentaur]

As the article says, it is an example of aliasing or beating, rather than SHM or a 'wave'. The position of each of the balls is observed relative to a 'timebase', set by the front one.
It is fun to watch but very easy to misinterpret, I think.
The rule for the pattern depends on the decrement in the pendulum lengths. They have done a lot of trial and error, I think, to get such a lovely demo.