I haven't seen anyone else say that the easiest way in practice is simply to jiggle the track. In a correct duplo track every piece will be loose and easily move a few millimeters when jiggled. If any pieces are snug then the track is under tension. No need to remove a piece.
I suppose if the track is big enough then you would be able to insert a "wrong" piece without necessarily using up all the slack, so the pieces would still be somewhat loose. But in that case there would be no mechanical concern to worry about.
Actually I suspect that it suffices to check one piece. If any piece is in tension then they all will be, assuming friction with the floor is not too large. Unless you have intersections in the track, then you have to check each loop separately, or maybe you could just check the switch pieces. Might be an interesting math problem there to minimize the number of pieces to check in complex tracks.
The original asker of the question actually proposed that already.
> I know I could just take one piece out, and put it back in to feel it myself, but I am looking for a more logical way
Since that's the "puzzling" stack exchange, I think they were looking at this more as a logic problem than a real practical problem they needed to solve.
Right, that's why I'm not posting this as an answer to the stack exchange question. Though I'm pointing out that it's not necessary to remove any pieces, and also suggesting that there may be an interesting math problem still there in this case.
I guess the obvious question is "given x amount of slack per piece, after how many pieces can I fit in on piece the wrong way without tension", but that feels more like an engineering problem than a math puzzle.
In this case not-so-brute force of fitting actual pieces, since it won't take that many. And otherwise estimates based on highly simplified approximations.
I suppose if the track is big enough then you would be able to insert a "wrong" piece without necessarily using up all the slack, so the pieces would still be somewhat loose. But in that case there would be no mechanical concern to worry about.
Actually I suspect that it suffices to check one piece. If any piece is in tension then they all will be, assuming friction with the floor is not too large. Unless you have intersections in the track, then you have to check each loop separately, or maybe you could just check the switch pieces. Might be an interesting math problem there to minimize the number of pieces to check in complex tracks.
I'll also point out that bending Lego pieces isn't always bad: https://youtube.com/@BrickBending