>> ^messenger:

So would two pendulums of the same length hung from the same string (like on the Wikipedia page) be considered in phase, even though they have opposite patterns? What about the Wilberforce pendulum? Is it considered to be in phase?>> ^crotchflame:
You're right: a double pendulum is a coupled oscillator and is a good example. It's a coupled oscillator with multiple normal modes that can give it a complex motion even for small oscillations where it isn't chaotic - some would argue that at larger amplitudes it's no longer a simple oscillator so a lot of the terminology in use here doesn't apply. The point is that it doesn't settle into one coupled mode that is stable against perturbations the way phase locked oscillators would.



The two pendula on a string can be put into motion where they are in phase but they aren't phase locked because they don't have to stay that way. Like the example being shown on the wikipedia entry, they are mode coupling where one oscillates but loses amplitude as the other begins to move - this is the motion it will be in if you start one of them but not the other. If you set them both swinging at the same time from the same height they would be in phase but if you then perturbed them they would go into a more complex modal behavior so you couldn't say they are phase locked.

The Wilberforce is the same - if you just twist the spring, it will be twist back and forth for a while until it loses energy to the pendulum motion; it will eventually stop as the pendulum takes over and then it will start coupling back the other way. You can put the system in phase where the rotations and the swings are aligned in phase but the strong coupling allows them to share energy more rapidly and to take on more complex modal interactions.

So would two pendulums of the same length hung from the same string (like on the Wikipedia page) be considered in phase, even though they have opposite patterns? What about the Wilberforce pendulum? Is it considered to be in phase?>> ^crotchflame:

You're right: a double pendulum is a coupled oscillator and is a good example. It's a coupled oscillator with multiple normal modes that can give it a complex motion even for small oscillations where it isn't chaotic - some would argue that at larger amplitudes it's no longer a simple oscillator so a lot of the terminology in use here doesn't apply. The point is that it doesn't settle into one coupled mode that is stable against perturbations the way phase locked oscillators would.

>> ^messenger:

I'd imagine very few of them phase lock, no? Most of them result in chaos, I'd think, assuming a double pendulum counts as coupled oscillation.>> ^crotchflame:
>> ^draak13:
Actually, the answer is known as coupled oscillation
http://en.wikipedia.org/wiki/Oscillation#Coupled_oscillations

Oscillators have to be coupled to phase lock but not every coupled oscillator phase locks.




You're right: a double pendulum is a coupled oscillator and is a good example. It's a coupled oscillator with multiple normal modes that can give it a complex motion even for small oscillations where it isn't chaotic - some would argue that at larger amplitudes it's no longer a simple oscillator so a lot of the terminology in use here doesn't apply. The point is that it doesn't settle into one coupled mode that is stable against perturbations the way phase locked oscillators would.

I'd imagine very few of them phase lock, no? Most of them result in chaos, I'd think, assuming a double pendulum counts as coupled oscillation.>> ^crotchflame:

>> ^draak13:
Actually, the answer is known as coupled oscillation
http://en.wikipedia.org/wiki/Oscillation#Coupled_oscillations

Oscillators have to be coupled to phase lock but not every coupled oscillator phase locks.

my favorite was by the still-probie @DrivelsAdvocate in this video:

http://videosift.com/video/The-double-pendulum-gives-an-example-of-chaotic-motion

the comment was:
"That reminds me, I need to wear tighter fitting pants the next time I go jogging."

**ahem** (in Jon Stewart voice) Nailed it!

It's amazing to me how hard it is for people to understand the difference between random and chaotic.

On the one hand, it's incredible because the movement of the double pendulum appears so chaotic.

On the other hand, it seems like a pretty straightforward system so it's not entirely surprising that it's possible to monitor, calculate and manipulate it.

But that doesn't keep it from being mesmerizing to watch.

Stabilizing a swing up on a double pendulum is fracking amazing.

Congratulations! Your comment has just received enough votes from the community to earn you 1 Power Point. Thank you for your quality contribution to VideoSift.

>> ^HaricotVert:
Attach an LED to the end, turn off the lights, and then take a long exposure picture until the motion gets boring.
Do this as many times as you want with different colored LEDs. Post all results onto DeviantArt. Profit.


http://en.wikipedia.org/wiki/File:DPLE.jpg

>> ^syncron:
I'm sure it's not hard to write a formula to calculate the moment and potential of a double-pendulum system given initial conditions and duration.


It is hard actually, because the second pendulum rotates around a moving axis, which fucks up your equations royally.

It's not really that big, especially at this time of the year with the cold weather.


In reply to this comment by residue:
oh man that's awesome

In reply to this comment by DrivelsAdvocate:
That reminds me, I need to wear tighter fitting pants the next time I go jogging.

I'm sure it's not hard to write a formula to calculate the moment and potential of a double-pendulum system given initial conditions and duration.

oh man that's awesome

In reply to this comment by DrivelsAdvocate:
That reminds me, I need to wear tighter fitting pants the next time I go jogging.

>> ^poolcleaner:
If you drop it from the precise point it was dropped from in this video and observe again, will it be random? What other conditions would factor into its perceived random movement? (These aren't rhetorical questions. I'm curious.)


It is indeed chaotic motion -- if you attempt to recreate the exact same conditions of movement you will get different results. The reason is that there are many "balance points" where the motion could go either one way or the other, and there is no way to predict which way it will move. Sort of like balancing a ball exactly at the top of a curve -- you know it will fall one way or the other, but you can't predict which.