Pendulum Waves with Philip Glass

We need a 1 hour loop of this!

This is awesome. They start moving in a line at 0:27. They finish moving in a line at 1:27. That's a 60 second cycle. Halfway through cycle, at 0:57, it looks like two lines opposing. 1/6 from the middle, at 0:47 and 1:07, it looks like three lines opposing. 1/4 from the middle, at 0:42 and 1:12, it looks like four lines opposing. At 1/12 from the ends, 0:34 and 1:20, it looks like a spiral. Groovy, man.

To calculate the lengths of the pendula, start with the longest time period, T. Decide how many cycles of that pendulum you would want before all the pendula are back in phase, usually 12 to 20 cycles.  Let us use 16 cycles.   This means that the time period (Ta) of the next pendulum needs to be such that it takes 17 cycles to get back in phase with the first, the next will take 18 cycles, the next 19, etc... This leads to the relationships:  16T = 17 Ta,  16T = 18 Tb,  and 16T = 19 Tc, etc. To calculate the lengths, form the ratio of time periods as a function of lengths, then solve for the ratio of lengths as a function of time periods.  When you are finished this exercise for the student, the result shows that the length you are looking for is the length of the longest pendulum multiplied by the square of the ratio of the time periods squared. For example:  La = L (16/17)2,   Lb = L (16/18) 2,  Lc = L (16/19) 2,  etc....  where L is the length of the length of the longest pendulum. When you decide how long you want the longest pendulum to be, the lengths of the others can be calculated easily. (Spreadsheets are great for this!). To build the stand, calculate the difference in lengths for adjacent pendula.  Take the difference between adjacent pendula, this will form the steps on the stand so the swinging bobs are at the same level. The method of attachment is up to the builder, but the string supporting each pendulum needs to be pinched to make a definite length. The bob support string is bifilar, or two stringed, one on each side of the bob. The top ends need to be separated by enough distance to assure stability. The ability to make fine adjustments to the length is necessary so the device can come back to line after two or even three cycles. One design for a 20 cm longest pendulum is to cut 5.0 cm long blocks of 1 by 2 pine and sand the sides so they will glue together firmly.  I then screw on a 1 cm wide strip of hard board across the bottom so that the edge of the strip lines up with the bottom of the block.  The strings to the bobs goes under the strip and is held in place by the screw.  Using the difference in length between the adjacent pendulums as the offset, glue the blocks together.

Physics really is as beautiful as it gets.

I love how in sync the beat of the song is with the movement of the penudlem.

The power of the Spiral is everywhere!...

wow! I mean just WOW! three times exquisite the reason some cannot appreciate Glass is because they are unquiet in themselves, and could not sit with the waves and tides and feel a greater part of life within themselves for it. What a demonstration. WOW!

Wonderful. Beautiful.

Amazing! It't like a ballet of the spheres! Truly physics is something like art!

The amount of different patterns is incredible!

so simple and yet so cool !

It's just a bunch of pendulums, so, what are you doing, my brain?

this is quite hypnotizing when you have been playing nonstop video games for 48 hours...

Why do I find this so mesmerizing

So mind boggoling and yet so simple.  I didn't know you could get some of those patterns from that.

Beautifully done!

this is absolutely brilliant. thank you

was and still is my favorite composer.

you can test it out by focusing on just one ball the entire video and making sure it doesn't "hang" or slow down in any one position, and then do that over and over for each ball. The way these pendulums seem to interact is similar to how different auditorial pitches (notes) seem to interact

The music with it was perfection!