Romney silent on climate change

crotchflame says...

Jesus! I mean Republican rallies have bothered me before but this is the first time I've seen something I'm going to be having nightmares about.

32 Metronomes Become Synchronized

crotchflame says...

>> ^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.

32 Metronomes Become Synchronized

crotchflame says...

>> ^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.

32 Metronomes Become Synchronized

crotchflame says...

>> ^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.

32 Metronomes Become Synchronized

crotchflame says...

>> ^messenger:

Up. The answer is always up. It's a law. In this case, it's the amount of energy randomly dissipated through sound, the unwinding of the springs, and other movement. Unless you're being cheeky, in which case pretend I said something witty and didn't just kill the joke by explaining it.>> ^crotchflame:
Ah phase locking: http://salt.uaa.alaska.edu/dept/metro.html
Here's one to ponder: is the entropy of the system going up or down?

I was being a little cheeky. The entropy is going up but not only because of dissipation in the metronomes themselves: even if they were perfect, the system's entropy would increase as the coupled oscillators synchronized. I like it because it's a system moving towards what seems to be a more ordered state as the entropy increases.

Another free example: the gravitational collapse that turned a disordered molecular cloud into our current, well-structured solar system generated an enormous amount of entropy.