I am familiar with linear non-homogenous differential equations, just didn't really have the wherewithal to confirm it that way; but I am extremely glad you did it and confirmed it, gives a new insight!
the attempt is visible in the image. my question is more... pedantic (?). if the initial conditions are to be taken into account, v_0=0, x_0=0 and F_0=+6, then isn't the velocity supposed to be v=+8sqrt(2)? or am I grasping at straws here.
my thought is, if the force is acting in the positive...
I am hopeful sometime in the future I will study EE; it's my favourite. And I am also hopeful that sometime soon, I will read up on that. I'd jumped headfirst into electromagnetism (Electromagnetic Fields by Wangsness, is it a good book? I find it's pretty great) back before the school year...
I think I realised by the end of the KVL/KCL that it was symmetric all around. The currents going into the center junction are the same ones going out, the horizontal currents up top and down bottom are also equal.
Rewriting the problem in LaTeX for future convenience (for other people) so...
This problem was sent to me by a good friend of mine. He said that he'd attempted it, but that he couldn't find an answer—at least, not an answer that matched the proposed answer (5/6 * R). So, I attempted it (armed with Kirchhoff's rules) and after a bit of running in circles, I got: 4/5 * R...
It's an oversimplified question, but the coil's wire itself is of neglegible resistance (or zero in this case), the coils' resistances (which you can think of as an actual device/resistor connected in series) are listed just after the question and before the drawing, suppose that R_M=R and work...
Thanks so very much, I knew my answer was correct but I needed the extra confirmation.
Yeah, the teacher ended up making me have to try to prove it to them with calculus; they still disagreed.
Glad you answered so quickly, much appreciated.