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Jun 29, 2022 at 10:10 history bumped CommunityBot This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.
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May 16, 2021 at 3:47 answer added ZeroTheHero timeline score: 1
May 15, 2021 at 21:23 comment added Voulkos Related : Lagrangian for two coupled second order linear differential equations.
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Mar 18, 2019 at 16:21 answer added Elio Fabri timeline score: 0
Mar 16, 2019 at 23:06 comment added knzhou I suppose you could write the matrix in general as $a_0 I + \vec{a} \cdot \vec{\sigma}$ and then apply a rotation (by conjugating with $e^{- i \theta \hat{n} \cdot \vec{\sigma}}$) to align $\vec{a}$ with $\hat{x}$. However, doing this explicitly might be more complicated than doing it the normal way.
Mar 16, 2019 at 19:55 answer added InertialObserver timeline score: 0
Mar 16, 2019 at 19:17 comment added DanielSank @InertialObserver Yes I know about matrix diagonalization, and yes this is a question about coupled oscillators. The equation ($\star$) are the equations of two coupled electrical harmonic oscillators. The question is how to diagonalize the matrix (i.e. decouple the equations of motion) in a systematic way when the oscillators are not identical.
Mar 16, 2019 at 19:00 comment added InertialObserver I don’t understand.. this isn’t a problem about coupled oscillators then.. do you know about matrix diagonalization?
Mar 16, 2019 at 18:59 comment added DanielSank @InertialObserver Finding that basis in a systematic way is exactly the point of this question.
Mar 16, 2019 at 18:56 comment added InertialObserver Have you tried working in a basis where the matrix is diagonal?
Mar 16, 2019 at 18:01 history edited DanielSank CC BY-SA 4.0
Add footnote about frequencies
Mar 16, 2019 at 18:00 history tweeted twitter.com/StackPhysics/status/1106978555894861825
Mar 16, 2019 at 8:07 history edited DanielSank
Remove dimensional analysis tag
Mar 16, 2019 at 7:58 history edited Qmechanic
edited tags; edited tags
Mar 16, 2019 at 7:16 history asked DanielSank CC BY-SA 4.0