Pendulum Waves

COSteve · Post by **COSteve** » Fri Oct 28, 2011 3:48 pm

You may recall from a Mechanics course that the period of a pendulum is proportional to the square root of the length of the line suspending the weight - i.e., the longer the pendulum, the slower it swings. Harvard students built a device with a series of 15 pendulums in a row, each one slightly longer than its neighbor, then set them in motion and filmed the result. The resulting patterns in this short video are quite fascinating to watch. Read the article below before starting to watch the video.

What it shows: Fifteen uncoupled simple pendulums of monotonically increasing lengths dance together to produce visual traveling waves, standing waves, beating, and random motion. One might call this kinetic art and the choreography of the dance of the pendulums is stunning! Aliasing and quantum revival can also be shown.

How it works: 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. When all 15 pendulums are started together, they quickly fall out of sync—their relative phases continuously change because of their different periods of oscillation. However, after 60 seconds they will all have executed an integral number of oscillations and be back in sync again at that instant, ready to repeat the dance.

One instance of interest to note is at 30 seconds (halfway through the cycle), when half of the pendulums are at one amplitude maximum and the other half are at the opposite amplitude maximum.

Pendulum Waves

Blaine · Post by **Blaine** » Fri Oct 28, 2011 3:58 pm

Dang engineers....

66GTO · Post by **66GTO** » Fri Oct 28, 2011 4:28 pm

When I see things like that, things that are so simple, yet so complex, I can only think it proves the existence of God. Their are too many designs in nature that are in perfect harmony, like music and mathematics, that show the hand of God in the creation of the universe. Man had no hand in the creation, yet in his vanity he thinks he is the ruler of his domain.

crs · Post by **crs** » Fri Oct 28, 2011 4:33 pm

Steve,
I hope the snow melts soon there, because you need to get out of the house!

damienph · Post by **damienph** » Fri Oct 28, 2011 4:49 pm

crs wrote:Steve,
I hope the snow melts soon there, because you need to get out of the house!

+1+!!

Rusty · Post by **Rusty** » Fri Oct 28, 2011 4:57 pm

When I was in school I remember going on a field trip to Washington D.C. I think it was at the Natl' Bureau of Standards where they had a huge pendulum. It had a ball that was about the size of a volleyball on the lower end with a pointer on the bottom. It was swinging from a cable that was probably 50' long. As the pendulum would swing back and forth it would rotate to different points in the circle around it. At exactly the top of the hour it would knock over a little marker on the floor. There should be a web cam for that thing somewhere.

Pitchy · Post by **Pitchy** » Fri Oct 28, 2011 5:15 pm

Very cool, and Rusty i seen that one your referring to on TV once.

COSteve · Post by **COSteve** » Fri Oct 28, 2011 6:10 pm

damienph wrote:
crs wrote:Steve,
I hope the snow melts soon there, because you need to get out of the house!
+1+!!

Tell me about it! Today I processed another 2,300 pieces of NATO LC brass for my ARs and my boy's Savage bolt 'grab your hip' type shooter. Decaped, resized, trimmed, and swaged the primer pockets on every one of those suckers. Those were some of the brass I got from the Denver SWAT practice at our range when they were practicing for the 2008 DNC here. That makes 3,500 pieces of AR brass I processed just this week and I also reloaded 1,200 rds the other day! Add in the 700 pieces of 30-06 I process and then handloaded and I'm getting sick of looking at brass!! Actually, I'm getting my stock back up for fall shooting with my son and so it's really a 'labor of love' because the time we spend together is very precious. He told me he's working on a deal with a friend who's parents live up by Wyoming so we might have a line on some p-dog hunting soon. I'm getting the cases ready just in case.

BTW, I did take a break and went outside today but that was just to start cleaning up the millions of leaves that are all over the place. I decided that they need to dry out a bit before I gather them so I'm good until Sunday as the snow in the front yard is almost gone.

2571 · Post by **2571** » Fri Oct 28, 2011 7:44 pm

Interesting demonstration of how fliers act in target shooting.

Post by **Hobie** » Fri Oct 28, 2011 8:52 pm

Neat!

gak · Post by **gak** » Fri Oct 28, 2011 9:14 pm

Very cool!

kimwcook · Post by **kimwcook** » Fri Oct 28, 2011 9:18 pm

That's really cool.

Tycer · Post by **Tycer** » Fri Oct 28, 2011 9:26 pm

T T T T T too much time on my hands.........

geeks. Gotta love em. I saw "intelligent design" too.

jeepnik · Post by **jeepnik** » Sat Oct 29, 2011 7:55 am

Rusty wrote:When I was in school I remember going on a field trip to Washington D.C. I think it was at the Natl' Bureau of Standards where they had a huge pendulum. It had a ball that was about the size of a volleyball on the lower end with a pointer on the bottom. It was swinging from a cable that was probably 50' long. As the pendulum would swing back and forth it would rotate to different points in the circle around it. At exactly the top of the hour it would knock over a little marker on the floor. There should be a web cam for that thing somewhere.

A local observatory has (or maybe had, they remodeld it a bit ago) the same sort of thing. It was designed to show how the earth rotates around a fixed point or something like that. Think I'll go up there Monday and see if it's still there.

Mokwaw · Post by **Mokwaw** » Sat Oct 29, 2011 8:22 am

Amazing..............

66GTO.........you nailed it.

Rusty.....there is a replica of that pendulum hanging in the cave at Mermac Caverns in Missouri, does the same thing.

2571 · Post by **2571** » Sat Oct 29, 2011 10:15 am

Foucault pendulum was at the Smithsonian for a long time. Really old folks still ask about it. :>)

Space now used for Old Glory. New flag exhibit is really great.

Post by **Hobie** » Sat Oct 29, 2011 10:27 am

http://www.youtube.com/watch?v=aMxLVDuf4VY
and
http://www.youtube.com/watch?v=b14l3-A8 ... re=related

Rusty · Post by **Rusty** » Sat Oct 29, 2011 5:24 pm

Thanks Hobie, I found this one too. Knocking over the little pins at
a given time http://www.youtube.com/watch?v=XJc1dnbV ... re=related

And thank you Steve for tickling the old creases of the of my gray mater.

Edited... get this, I showed this to my wife and she's watching it and she says, OK so that proves the pendulum is staying in the same place and the floor is moving. DUH!!!! I never looked at it like that.

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