Yeah, I just need to write a few more answers. But that entails finding decent questions that I can answer. ;)

lol they put my salutation as my title

so my name is displayed XXXXX XXXX Dr.

rather than Dr. XXXXX XXXX

hmmm

oh they don't have Dr. as salutation, only as title, so I guess that's just the way things are formatted...

@Blue Yes, that population is much smaller.

damn

Nasa confirms Mars rover Opportunity is dead

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:

which iphone should I get for my company phone

o.O

is the 8 plus the newest line

@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.

$$\left( \begin{array}{c} x_1 \\ x_2 \end{array} \right) = \left( \begin{array}{cc} -(1+\epsilon_1)/\omega_1^2 & \epsilon_1/\omega_1^2 \\ \epsilon_2/\omega_2^2 & -(1 + \epsilon_2)/\omega_2^2 \end{array} \right) \left( \begin{array}{c} \ddot{x}_2 \\ \ddot{x}_2 \end{array} \right)$$

OH SNAP FIRST TRY I AM A MASTER OF MATHJAX

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 $\sqrt{-1 / \lambda}$.

@rob Sol 5352 sounds even better

@DanielSank ahem

you were saying?

@EmilioPisanty >.>

Mary had a little lambda

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?

@DanielSank wait, why is that not hermitian?

shouldn't it be?

@EmilioPisanty No.

@EmilioPisanty Because the two oscillators aren't identical.

huh

still though

there should be some sense of hermiticity there, right?

But this is a very good question. I think the problem may simplify considerably if we rescale the variables to make it Hermitian.

$\uparrow$

@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?

@DanielSank would love to dig into it, but I'm rushing to send off a paper asap

@EmilioPisanty Ok. Good luck.

@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

Who is GNO?

Ah, the magazine.

Bah, publish in a journal. Forget the magazines.

@DanielSank it is a journal

it just has a glossy cover

I see.

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