When we say the door swung open, does it mean that the doors keeps moving back and forth after it was pushed open?


No, it would normally be taken to mean that it stayed open, or at the very most it closed afterwards. It wouldn't normally suggest any repeated back and forth motion.

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Is there another word for swung open that doesn't imply the door closed after ward? Also, is there a word for when two door panes open and form a V and stays that way? Like think of a door with two panes and you need to push them both to comfortably get through it.

The door swung open only refers to the door opening. It doesn't imply anything about what it did after that. It could stay open, or the person who opened it might close it after going entering the room, or it might be a door that swings shut when the person who opened it lets go of it. What I meant by my earlier comment was that there is nothing whatsoever in the door swung open that would make you think that it swung to and fro after it first swung open.

Consider also flung open.

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