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I have a question about my Physics Stack Exchange post: AC Circuits with Frequencies Dependent on Initial Conditions

I don't understand why this question was put on hold. It clearly matches all the guidelines for homework-type questions.

  1. The question clearly asks about a specific physics concept

  2. I have an attempt at a solution, and the solution doesn't seem to be correct. I don't understand what kind of mistake I made. And it's clearly not a technical mistake, but rather something to do with the right way to approach this type of problem.

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    $\begingroup$ For starters, there is no question anywhere (no "?" sign). $\endgroup$ – AccidentalFourierTransform May 12 '18 at 18:03
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    $\begingroup$ Are you being serious? $\endgroup$ – Noamyoungerm May 12 '18 at 18:05
  • $\begingroup$ If you like, my question is "I don't get how this situation can exist" $\endgroup$ – Noamyoungerm May 12 '18 at 18:07
  • $\begingroup$ The comment under your question basically answers it. $\endgroup$ – Jon Custer May 12 '18 at 18:12
  • $\begingroup$ I'm pretty sure it's not common to close questions when they are answered, rather to mark them as having an accepted answer and to leave them open $\endgroup$ – Noamyoungerm May 12 '18 at 18:15
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    $\begingroup$ @Noamyoungerm no, it really is common to have answered (and accepted) questions that are closed. Note though that a comment is not an answer to a question, at least in terms of this site. $\endgroup$ – Kyle Kanos May 12 '18 at 19:00
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I don't know why the question was put on hold either; the only people who can truly answer that are those who voted for the hold. Hopefully one or more of them will contribute an answer.

However, my best guess as to why it was put on hold was that it's not clear what the post is actually asking. In other words, at least some readers had a hard time identifying the conceptual issue you want to know about. If this is what the voters thought, I can see how they would deduce that you didn't meet the part of the guidelines where it tells you to "ask about a specific physics concept" and therefore they voted to put your question on hold for that reason. But really, if this was their thought process, we have a hold reason for "unclear what you're asking" questions, and that would have been a better fit.

I'll note that, in most respects, your post is one of the better homework-like questions I've seen in a while. It quotes the problem you're working on, summarizes your progress on the problem so far, does not ask for the solution to the original problem, and it does mention a specific physics concept which confuses you. All that is great. But there are two things you didn't do, which would greatly improve the question if you did:

  1. You didn't make it entirely clear what conceptual question you actually wanted to ask. This is not part of our homework-like question policy, it's more of a general communication principle: when you want to ask a question, do it in a way that sticks the actual question in the reader's face, so to speak. Make it impossible to miss.

    For example, you might try any of the following:

    • Actually phrase your question as a question, i.e. an interrogative statement with a question mark at the end
    • Use a "question phrase" like "What I want to know is..." or "I'm confused about why..." (this one you actually did, by saying "The basic thing that doesn't make sense is...")
    • Put the question at the end of your post
    • Show the question in bold text (usually overkill)
    • Phrase your title as a question which asks the same thing that you ask in the post

    None of these changes are required, but I find that they can help your posts get better receptions.

  2. You didn't show, or at least didn't explain, your progress toward resolving your confusion about that conceptual issue. This is separate from showing your progress toward solving the original problem - and in fact, I think this is more important.

As an example, if I found myself in your situation, here is one possible way I might rephrase the part of your question after the quote block:

The basic thing that doesn't make sense is that the frequency of the current somehow depends on the initial conditions of the circuit. In particular, this system is a totally linear system totally described by linear differential equations. And clearly the solution to those equations can't depend on initial conditions.

To check my intuition on this, I wrote out the equations describing the circuit in the general case. I'd expect these equations to determine the frequency on their own, without reference to initial conditions.

I defined: $$I_{center} = I_{left} - I_{right}$$ and got $$3L (\ddot{I}_{left} - \ddot{I}_{right}) + \frac{1}{C}(I_{left} - I_{right}) = 0$$ In other words $$\ddot{I}_{center} = \frac{-1}{3LC}I_{center} = 0$$ which has a solution with frequency $\omega = 1/\sqrt{3LC}$. As I suspected, this doesn't depend on the initial conditions.

In light of this, can someone explain how the initial conditions of the circuit could affect the frequency?

I would probably also change the post title to "How can the frequency of an AC circuit depend on its initial conditions?"

Notice that I added a phrase or two to make it clear how the calculation represents your attempt to resolve the conceptual issue yourself (as opposed to being just an attempt to solve the original problem, as in your post). I also repeated the main conceptual question at the end, so that it is right at the forefront of a reader's mind as soon as they finish with the post, and I used interrogative phrasing and ended it with a question mark to make it explicitly clear that this is the thing I want to get out of the answers.

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  • $\begingroup$ This is perfectly good advice, but fundamentally you haven't changed the question at all; you just added a few words of signposting. I just feel that we 3k+ users should have good enough reading comprehension/empathy to not need that. $\endgroup$ – knzhou May 13 '18 at 9:13
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    $\begingroup$ I disagree. Sometimes that signposting makes all the difference. Also, this has nothing to do with empathy. $\endgroup$ – David Z May 13 '18 at 9:28
  • $\begingroup$ The question as it is has 3 signposts pointing the right way and 1 pointing the wrong way. With reading comprehension, you can figure out that the 3 are more important than the 1. Or, alternatively, with some empathy or teaching experience you can figure out the OP is much more likely to be confused, as a beginner, about the 3 than the 1. $\endgroup$ – knzhou May 13 '18 at 9:31
  • $\begingroup$ I get what you're saying, you're proposing the OP put in 6 signposts all pointing the right way. I have no doubt that will make the question clearer, but we really shouldn't be closing questions in the first place just because they don't restate the question literally every other sentence. We're smarter than that. $\endgroup$ – knzhou May 13 '18 at 9:31
  • $\begingroup$ @knzhou It doesn't sound like you get what I'm saying. In particular, I did not mean to say that all 6 of these "signposts" are necessary, nor did I mean to propose that the OP make all of those changes. Neither did I mean to imply that the OP should restate the question every other sentence, or that failure to do so is a reason to close a question. $\endgroup$ – David Z May 13 '18 at 21:35
  • $\begingroup$ But that's exactly what you've implied. The OP repeated themselves 3 times and still got their question closed. As a helpful example, you wrote something that repeats the same question 6 times in 8 sentences. The fact that one would even consider this reasonable is evidence that close voters are not paying as much attention as they should be. $\endgroup$ – knzhou May 13 '18 at 22:14
  • $\begingroup$ @knzhou The bit “frequency of the current” is what threw me off. I just realized the OP means the frequency of oscillation of the circuit, and I can’t believe I didn’t realize this sooner. I think the OPs argument is that the solution to the system should not depend on choosing the current in the rightmost branch to be up or down since this ought to be fixed by the sign of the appropriate solution to the linear system. $\endgroup$ – ZeroTheHero May 15 '18 at 1:18
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    $\begingroup$ @knzhou I don't see where you're getting those numbers from. But ultimately it doesn't matter. The point is, I think the OP's question could stand to be improved, and I've given a detailed example of how it could be done in a way that would make me vote to reopen. You can take this as an indicator of how I vote on other questions. $\endgroup$ – David Z May 15 '18 at 3:15
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I think this is a clear call: closing this question was a mistake, and I'm voting to reopen it.

This is an example of a common problem on Phys.SE. A lot of experienced users are going on autopilot in the close queue. The minimum judging time is three seconds. I certainly get a bit lazy, but I feel that many users are deciding in just these three seconds with cheap heuristics:

  1. Is introductory physics involved? Quantum field theory gets a free pass, but anything with an inclined plane or a circuit is probably doomed.
  2. Does the question contain equations? If so, it must be somebody asking for us to check their work, so the question must be closed. Ironically this means that questions with a conceptual core are punished when their writers put in more effort.

Many times, after a few more seconds of reading, I have decided a question has a conceptual core and is appropriate for Phys.SE. I'm usually appalled to see that question already has three or four close votes! I don't see how this can be explained without either people going on autopilot or fundamentally disagreeing on what the homework policy is.

This question is a perfect example: it contains an obvious conceptual question,

The basic thing that doesn't make sense is that the frequency of the current somehow depends on the initial conditions of the circuit. In particular, this system is a totally linear system totally described by linear differential equations. And clearly the solution to those equations can't depend on initial conditions.

The OP is very clear that they are confused about the bolded statement. They quote the problem specifically because it makes this statement. A short version of this statement is in the question title. They show their work in full because they don't see how it's compatible with this statement. There are a few distractors, such as the fact that the last sentence quoted here is wrong (it is missing the word "frequency"), but if you think that's what the question is about you haven't read it at all!

This is a useful question for students and it isn't specific to this homework problem at all. However, the question was doomed because there's a circuit diagram right above it (hitting heuristic 1) and equations right below (hitting heuristic 2). I urge other close voters to examine questions more carefully before voting to close. If you disagree and think this question should be closed I would appreciate an explanation of how that fits with current policy.

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    $\begingroup$ I am probably missing something, but if the question is "how can the solution of a linear system of ODE's depend on the initial conditions?", then the answer is quite obviously "the solution of a differential equation always depends on the initial conditions". How is this a physics question? And what meaningful answer is there beyond "that's how differential equations work"? $\endgroup$ – AccidentalFourierTransform May 12 '18 at 22:48
  • $\begingroup$ @AccidentalFourierTransform The OP is confused because the behavior of this physical system is in conflict with their physical intuition, because, e.g. a pendulum swings with the same frequency no matter how you start it. I can think of many physical systems which demonstrate that this intuition is false. This opens the door to a nice discussion of normal modes. $\endgroup$ – knzhou May 12 '18 at 22:58
  • $\begingroup$ 1) If that is the question, then I mostly agree it should be open. But that's definitely not how I read the question initially, and I'm still unsure that's what OP was trying to transmit. If your interpretation is indeed correct, and OP were to edit the post to make it clear that that is the question, I will be happy to vote to reopen. 2) I didn't mean to say that "obvious answer = must be closed". What I meant is that there is no physics (and, arguably, no maths) in the question (at least in my interpretation of the question, which may wrong anyway). $\endgroup$ – AccidentalFourierTransform May 12 '18 at 23:03
  • $\begingroup$ Sure, it’s true that the answer is “obvious” once you know the full, proper mathematical setup. But that’s true for almost any question. For particle physics? “That’s just how representations work.” For formal QFT? “That’s just how C* algebras work.” Every piece of physics is “just” math, that doesn’t make physics questions math questions. $\endgroup$ – knzhou May 12 '18 at 23:05
  • $\begingroup$ It is important to be able to step back and imagine a time when you didn’t know something already. Sure, the question sounds to you like, “I got 1+1=3, but apparently this is wrong, why?”, but with less math background and a beginning student’s undeveloped physical intuition it is a perfectly reasonable thing to ask. For a beginner, the question asked is definitely a more puzzling thing than just “the solution depends on the ICs”, even though it is obvious to us it is just a special case of that statement. $\endgroup$ – knzhou May 12 '18 at 23:08
  • $\begingroup$ Again, what you say is true if your interpretation of the question is correct. But not according to how I understood the question. For one thing, OP says "And clearly the solution to those equations can't depend on initial conditions.". In other words, for some reason OP thinks that the solution to a linear equation doesn't depend on the initial conditions (which is a purely mathematical statement, and a false one). So, to me, the question is not about a physically counter-intuitive situation, but a wrong mathematical preconception. (1/2) $\endgroup$ – AccidentalFourierTransform May 12 '18 at 23:10
  • $\begingroup$ (2/2) The question is not that OP doesn't understand the physics of the problem, but that the solution to the ODE's didn't match their expectations about what a linear system does. $\endgroup$ – AccidentalFourierTransform May 12 '18 at 23:12
  • $\begingroup$ See the first sentence I quoted. The OP probably slipped up in the third sentence (that you quoted). From the rest of their work, it is clear that they aren’t so naive as to think initial conditions never matter; with that kind of misunderstanding they wouldn’t be in this course in the first place. They mean it’s confusing that initial conditions affect the frequency, a phenomenon they have not seen before. $\endgroup$ – knzhou May 12 '18 at 23:14
  • $\begingroup$ Beginners will often make missteps describing their reasoning, they’ll use words wrong, because they are beginners. The job of a teacher is to figure out what they are actually confused about, not hone in on the most inaccurate statement they said in their confusion. One misplaced word (i.e. not saying “frequency” in the third sentence) should not flip their question from on-topic to off-topic. $\endgroup$ – knzhou May 12 '18 at 23:16
  • $\begingroup$ We agree that "The basic thing that doesn't make sense is that the frequency of the current somehow depends on the initial conditions of the circuit." is the key sentence. OP is confused as to why the frequency depends on the initial conditions. So far so good. But you read this as OP not understanding the physics, while I read it as OP not understanding the mathematics of ODE's. I would say both interpretations are correct, and it's up to OP to make the question clear. If they were to edit it, I will be happy to reopen it. As of now, it's still unclear to me. $\endgroup$ – AccidentalFourierTransform May 12 '18 at 23:20
  • $\begingroup$ @AccidentalFourierTransform Where do you draw the line here? Would you close half of all QM questions as ‘not understanding (infinite-dimensional) vector spaces and distributions’? How about most basic GR questions as ‘not understanding Riemannian geometry’? $\endgroup$ – knzhou May 12 '18 at 23:26
  • $\begingroup$ The better you know introductory physics, the more it looks like “just” differential equations. But it doesn’t look like that at all for someone just learning it! There is a stark difference between the physics and the math for beginners, they don’t have them properly linked together yet. Anyone who wishes to retain the ability to communicate with beginners must remember this. $\endgroup$ – knzhou May 12 '18 at 23:26
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    $\begingroup$ Well, if the question contains "clearly $A^2=A$ for any operator" or "obviously the metric is always its own inverse" or a blatantly false statement like those, then yes: I will vote to close. If the confusion is based on a very basic mathematical misunderstanding, I don't think the question is on-topic. The answer is just "you got the maths wrong", which is not useful to anyone but OP (and one could argue that it lacks research effort, and that the question is unclear, etc.). $\endgroup$ – AccidentalFourierTransform May 12 '18 at 23:30
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    $\begingroup$ I simply do not understand the question. Never mind the “And clearly the solution to those equations can't depend on initial conditions.” part. Instead I’m trying to reconcile “The basic thing that doesn't make sense is that the frequency of the current somehow depends on the initial conditions of the circuit” but the OP finds $\omega=1/\sqrt{3LC}$ that does NOT depend on the initial conditions. Maybe it’s old age or I’m getting tired... $\endgroup$ – ZeroTheHero May 13 '18 at 2:22
  • $\begingroup$ @ZeroTheHero It seems completely clear to me. The problem statement says "X", where X is something we agree is true. The OP says "but I thought not-X". Then they OP shows their work, which also concludes "not-X". Then they ask what is going on. $\endgroup$ – knzhou May 13 '18 at 9:10

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