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:
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

How about this. Let's call the position of any one 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.