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PM 2Ring
PM 2Ring
19:00
Yeah, I just need to write a few more answers. But that entails finding decent questions that I can answer. ;)
enumaris
enumaris
lol they put my salutation as my title
so my name is displayed XXXXX XXXX Dr.
rather than Dr. XXXXX XXXX
hmmm
Anonymous
@rob Yeah. I was mainly talking about 3k-ers active in chat though.
enumaris
enumaris
oh they don't have Dr. as salutation, only as title, so I guess that's just the way things are formatted...
rob
rob
@Blue Yes, that population is much smaller.
Emilio Pisanty
Emilio Pisanty
19:21
damn
Nasa confirms Mars rover Opportunity is dead
Thanks for bringing us along.
Loong
Loong
We all remember those famous first words spoken by an astronaut on the surface of Mars: "That's one small step fo- HOLY SHIT LOOK OUT IT'S GOT SOME KIND OF DRILL! Get back to the ... [unintelligible] ... [signal lost]"
DanielSank
DanielSank
I'm trying to write up a pedagogical note on coupled oscillations.
Given two coupled oscillators with frequencies $\omega_1$ and $\omega_2$, we can arrive at the following equation:
enumaris
enumaris
which iphone should I get for my company phone
o.O
is the 8 plus the newest line
rob
rob
@EmilioPisanty What a shame that Opportunity only survived for fifteen years out of its planned ninety-day mission. A great loss and an astounding success. Still too soon.
DanielSank
DanielSank
$$\left( \begin{array}{c} x_1 \\ x_2 \end{array} \right) = \left( \begin{array}{cc} -(1+\epsilon_1)/\omega_1^2 & \epsilon_1/\omega_1^2 \\ \epsilon_2/\omega_2^2 & -(1 + \epsilon_2)/\omega_2^2 \end{array} \right) \left( \begin{array}{c} \ddot{x}_2 \\ \ddot{x}_2 \end{array} \right)$$
OH SNAP FIRST TRY I AM A MASTER OF MATHJAX
2
Here $\epsilon_1$ and $\epsilon_2$ are both much less than 1.
Given eigenvalues $\lambda_1$ and $\lambda_2$ of that matrix, the normal mode frequencies are $\sqrt{-1 / \lambda}$.
Emilio Pisanty
Emilio Pisanty
19:31
@rob Sol 5352 sounds even better
@DanielSank ahem
you were saying?
DanielSank
DanielSank
@EmilioPisanty >.>
PM 2Ring
PM 2Ring
Mary had a little lambda
DanielSank
DanielSank
Ok so now the question is this: can we come up with a nice expression for $\lambda$?
I can get half-decent expressions by using the $\epsilon \ll 1$ approximation liberally.
I don't suppose anyone else would like to have a go?
Emilio Pisanty
Emilio Pisanty
@DanielSank wait, why is that not hermitian?
shouldn't it be?
DanielSank
DanielSank
@EmilioPisanty No.
@EmilioPisanty Because the two oscillators aren't identical.
Emilio Pisanty
Emilio Pisanty
19:33
huh
still though
there should be some sense of hermiticity there, right?
DanielSank
DanielSank
But this is a very good question. I think the problem may simplify considerably if we rescale the variables to make it Hermitian.
Emilio Pisanty
Emilio Pisanty
$\uparrow$
DanielSank
DanielSank
@EmilioPisanty I think it is {Hermitian up to rescaling of stuff}, and actually that's exactly where I would like some help.
Are there new variables we should use to achieve hermitian-ness?
Emilio Pisanty
Emilio Pisanty
@DanielSank would love to dig into it, but I'm rushing to send off a paper asap
DanielSank
DanielSank
@EmilioPisanty Ok. Good luck.
Emilio Pisanty
Emilio Pisanty
19:35
@DanielSank indeed
Glossy Number One has said that they're not keen enough on our stuff
they've referred us down to Glossy Number Two
DanielSank
DanielSank
Who is GNO?
Ah, the magazine.
Bah, publish in a journal. Forget the magazines.
Emilio Pisanty
Emilio Pisanty
@DanielSank it is a journal
it just has a glossy cover
DanielSank
DanielSank
I see.
 
2 hours later…
PM 2Ring
PM 2Ring
22:00
This perpetual motion Q just got bumped. physics.stackexchange.com/questions/106742/…
Anonymous
Unrelated: commenting on meta seems to be a trap. Replying to comments is just so tempting. Gotta self-control! :P
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