Tall Painting and Pendula Waves

I can sit for hours watching stuff like this, and experimenting with stuff just to see what happens. I look constantly for what carlos Casteneda calls 'omens', things that the spirit does just for me and me alone, just for the sake of a memory. When I hear someone say they are bored, I can never quite comprehend. So much to do, so much to see, so little time.

Larry

Cool!  I was curious to know what the pendulums looked like from the side view:  Here is a similar pattern viewed from the side:  http://www.youtube.com/watch?v=1M8ciWSgc_k&feature=related

This led me to wonder what causes pendulums to synchronize, which is defined as Odd Sympathy:  http://en.wikipedia.org/wiki/Odd_sympathy 

The phrase odd sympathy (the actual phrase used was odd kind of sympathy) was used by Dutch mathematician and physicist Christiaan Huygens (1629–95) in a letter to the Royal Society of London pertaining to the tendency of two pendulums to synchronize, or asynchronize, when mounted together on the same beam. Huygens, the inventor of the pendulum clock, noticed the effect while lying in bed. Two pendulums, mounted together, will always end up swinging in exactly opposite directions, regardless of their respective individual motion. This was one of the first observations of the phenomenon of coupled harmonic oscillators, which have many applications in physics.

Huygens originally believed the synchronization was due to air currents shared between the two pendulums, but he dismissed the hypothesis himself after several tests. Huygens would later attribute sympathetic motion of pendulums to imperceptible movement in the beam from which both pendulums are suspended. This idea was later validated by researchers from the Georgia Institute of Technology who tested Huygens' idea.[1]

Using instruments capable of registering movement too small to have been measured in Huygens' time, the Georgia Tech researchers chronicled the nature of the forces at work on the supporting beam. They found that if the pendulums are moving in the same direction, together they tend to move the beam the opposite direction, giving rise to frictional forces that resist motion in the same direction. If however, the pendulums are moving in opposite directions, these forces cancel each other out, causing the beam to remain motionless. Thus, motion, in this example, tends to be perfectly asynchronous

Huygens observed anti-phase synchronization of pendulum clocks. Bennett and co-workers from the Georgia Institute of Technology reported also anti-phase synchronization of pendulum clocks in 2002. However, in-phase synchronization of pendulum clocks has also been observed. This was discussed by a book written by I.I. Blekhman. This was also mentioned in the book by Pikovsky and co-workers. A detailed analysis was provided by Fradkov and Andrievsky from Russia in 2007 regarding the conditions for in-phase or anti-phase synchronization of a 2-pendulum system.*

(Now, I understand my fascination with this subject... as I've always been a "odd sympathizer.") 

*Apparently, the beam is the essential ingredient in the synchronization, as demonstrated here with metronomes: http://www.youtube.com/watch?v=W1TMZASCR-I

Hi Noa-

I think the synchronizing here is just math. The shorter strings beat back and forth say 4x in a certain time period, the longer strings 3x in the same time period, others 2x and really longer strings just once. When you reach 12 times that time period they will be together again because they are all multiples of 12.

Wendy

Okay Wendy, that would make sense if it weren't for the synchronization occuring within the same length pendulum strings.  Take a look at the first link I posted above.  (Lots more examples on Youtube.)