forget - forgot - forgotten. Because "forgotten" is the past participle, you can use it in past perfect and present perfect (as well as other places such as passive voice and imagined past). If you're asking about choosing between the two perfect forms, there's an implied "but then I remembered" in the first example.

Oh Sergey, be very careful here! This is a mistake that even native English speakers make, and it will irritate English teachers. "Would of" and "should of" don't exist. It's "would have" and "should have." The mistake comes from their contracted forms "would've" and "should've," which, when spoken very quickly, sound like "would of" and "should of." As for what they mean... 1) "Would have" is used to express something that might have happened under certain circumstances. For instance: "I would have cooked a fish if I knew our guests loved seafood." 2) "Should have" is used to express something that might have happened if the correct choice was made. For instance. "I should have listened to my doctor's warnings about the dangers of this medicine." I hope this helps answer your question. Please let me know if it doesn't.