Rrerku

I know that post-tonal and popular music can't always be analyzed through the same methods as the Common Practice Period, but I still like to see how people would try analyzing things.

This is a chord progression from a song that came out last year that I love ("Fragile" by Yes).

In the second chord (C/D), would that simply be analyzed as IV/pedV? I don't know if the D is a pedal tone since in the next chord it moves down to the G, and it's not really a suspension since it doesn't resolve to anything there.

Is this simply too different from tonal practice methods to be analyzed the same way classical pieces from the past would have been?

I would personally view this second measure as its own chord that embellishes the previous measure. In popular music, it's very common to have a IV chord over scale-degree 5 in the bass. Some call this a "rock dominant," and it's basically just a particular voicing of a V11 chord. (See also Is there a specific name for the use of IV chord over the V in the bass, e.g. F/G in the key of C)

Looking at this chord in context, it just adds some extra dissonance above the already tension-filled dominant chord to help lead to the succeeding tonic even more strongly.

It's a very common chord progression. The C/D works as a milder or more ambivalent substitute for D7. You could think of it as having a sus4. Other chords that work similarly are D11, Dsus4, D7sus4.

When you have a "can this be analyzed as an X chord" question, why not treat it like a hypothesis and then try to prove or disprove it? If you think the C/D chord could be seen as serving a V chord function, take existing songs that have a V chord (just about any song will do, because almost all songs have a V chord somewhere), and replace the V chords with IV/V chords. How does it change things? When does it work and when does it not work?