In the first Harry Potter book, Molly Weasley recommends running into the barrier if you're nervous. That's never made sense to me-- reaching towards the wall carefully and slowly to test whether your hand can go through it seems less nerve-wracking than running right at it and risking smacking into a hard surface at high speed. (Or at least walking at a reasonable pace, if you can't just stick a hand through it. Based on some of the other things Molly said, actually trying to step through it may be necessary, and that would make sense as a precaution against Muggles leaning against the barrier to rest and accidentally falling through.)

But I think I've figured out how that makes sense, now. To some extent magic is influenced by belief and confidence, as shown at flying lessons. However, in dangerous or emotion-high situations, especially if you're young, accidental magic can happen regardless of belief. So if you're slowly trying to reach through just to try, you're not confident that the magic will kick in and that might keep it from activating properly. But if you're running at it, even if you're just as skeptical, your own accidental magic will see you though fine.

Second year when Harry and Ron can't get through, they have both gone through before and therefore aren't actively afraid of crashing until it happens. And they've spent the last year training their magic to flow through their wands intentionally rather than with their emotions accidentally. Not only that, there's Dobby's magic in direct opposition to any accidental magic that may carry them though the barrier, rather different than the previously implied possibility of the magic simply not activating if you're too nervous or skeptical.

This all sound reasonable?