Conjugated word + んだ vs nonconjugated word + conjugated んだ?

Question

Suppose I have a verb/adjective/noun, let's say 無理, and I add (な)んだ to it as an explanatory sentence-ending particle. What would be the difference in nuance between the following two conjugated constructions? 1. それは無理だったんだ。 2. それは無理なんだった。 More generally, what is the difference in meaning between conjugating a word before adding んだ (to any tense, such as past negative) and doing it the other way around? Please also provide examples where one would be more appropriate than the other for each of the two cases, and consider what would happen if ん were replaced by の.

Answer 1

規則違法ですから、それは無理だったんです。Well, you see, because it's against the rules it was impossible. (normal explanation)

んだった expresses regret or strong feeling:

日本語能力試験を合格しなたら、それは無理なんだった。(I'm convinced that) had I not no passed the JLPT, this would have been impossible.

仕事に役に立つと知るなら、日本語能力試験をとるのだった。If I knew it would have been useful for my job, I would have taken the JLPT.

Conjugating be for the NDA is just using that phrase as an explanation. Change the DA part (DATTA, JANAI, etc.) will usually add more flavor like seek for information or assert an opinion.

NO basically just would make the sentence formal or more typical of written Japanese.