celtschk
Reputation
1,655
Next privilege 2,000 Rep.
Edit questions and answers
Badges
5 9
Newest
Impact
~69k people reached

• 0 helpful flags
• 127 votes cast

# 139 Actions

 Jun 14 comment How can I find the motion equations of the 2-dim harmonic oscillator? @math12: No. A specific implementation (not the most general one) would be a mass that can move on a plane (horizontally, so no gravitation, and frictionless) which is connected through a (frictionless, massless, arbitrarily bendable) fiber through a small hole in that plane to a spring which is in its rest position when the mass is exactly above the hole. Jun 14 comment How can I find the motion equations of the 2-dim harmonic oscillator? $x$ and $y$ are just two directions in which the oscillator can be displaced. They don't even need to be orthogonal. The potential energy $ax^2+bxy+cy^2$ is just the most general possible quadratic form without linear or constant term. It has that form because that's what makes the system a harmonic oscillator (you could plug another potential in here, but then you'd no longer have a harmonic oscillator — well, unless your coordinates are something else than displacements, then it may be a harmonic oscillator in different coordinates). Jun 14 comment How can I find the motion equations of the 2-dim harmonic oscillator? See the edit of my answer. Jun 14 revised How can I find the motion equations of the 2-dim harmonic oscillator? Added an explicit calculation with Lagrange formalism Jun 14 comment How can I find the motion equations of the 2-dim harmonic oscillator? The harmonic oscillator is where the force is proportional to the displacement. A physical implementation of the one-dimensional h.o. is the spring pendulum. The normal pendulum isn't a harmonic oscillator (but can be approximated as one if the amplitude is sufficiently low). Solving a spherical pendulum is much harder than solving a harmonic oscillator, so you'd not normally substitute a spherical pendulum for a harmonic oscillator (rather, the other way round). Jun 14 answered How can I find the motion equations of the 2-dim harmonic oscillator? Jun 14 comment Is the graviton hypothetical? @Anixx: In a theory where there are no gravitons, gravitational waves will certainly not be composed of them. If there could also be theories where there are gravitons but gravitational waves are not composed of them, I don't know. Jun 14 answered Is the graviton hypothetical? May 17 revised Quantum Mechanics - Observable terminology correction: average value → expectation value May 17 comment Atomic nucleus consisting of only neutrons? @ashpool: See my edit May 17 revised Atomic nucleus consisting of only neutrons? added information about higher mass number May 17 answered Atomic nucleus consisting of only neutrons? May 17 answered Quantum Mechanics - Observable May 5 comment Finding current in a sphere while given a changing current density A sphere has a constant radius $R$, therefore you don't have to integrate over that. OTOH, your integral is missing $\phi$. And BTW, your integrals get much more readable if you prefix each $d$ with a thin space which you get using \,. May 5 answered Evaluating position vector between 2 hydrogen states May 4 comment Superluminal neutrinos Actually the impossibility of FTL neutrinos is quite different from the impossibility of tunnelling through a brick wall. Tunnelling through a brick wall wouldn't actually violate any known law of physics, it's just sufficiently improbable according to those laws that if we ever observed it, we'd consider it more likely that our theories have to be amended than that we just have observed such an unlikely event. As such, it is comparable to an object spontaneously heating up in a cold environment. FTL OTOH is not just extremely improbable, but forbidden by the currently known laws of physics. May 4 comment Superluminal neutrinos Indeed, they didn't report "we found superluminal neutrinos" but "we measured data that looks like superluminal neutrinos, but after searching for quite some time still cannot find an error in the experiment, so we now decided to publish so that others can check if we have possibly a real effect; we keep searching for an error anyways." How more honest can you be? (I'm a theorist, BTW; you do not have to be an experimentalist to acknowledge that.) May 4 answered How do we know quantum entanglement exists/happens? May 1 revised Show that two families of curves are orthogonal (without using orthogonal trajectories) fixed two index mistakes May 1 comment Show that two families of curves are orthogonal (without using orthogonal trajectories) @user3321289: The mathematical field which treats such questions is called differential geometry.