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:
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.
- 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.
