The word excited in
The project excited us
is not a past participle, but past tense. You can tell here because project is the subject and excited is project's verb.
Some irregular verbs have distinct forms for past participle as opposed to past tense.
Take the half eaten food and throw it away
I don't care what you do with the broken things, just throw them out.
Anyway, a past participle is part of a verb phrase or used as a modifier.
I have been known to go there from time to time.
The excited dog jumped all over our guests.
It was laid on the floor.
The interested parties should convene tomorrow.
It can get complicated when phrases are involved instead of words.
The common known thing between them did not affect their relationship.
Her misspoken words struck me like a sledgehammer.
But really, unless the past participle does not follow a form of to have or to be, you can pretty much just treat it like an adjective.