The first sentence is more natural. My glasses are on the table in the living room. 'On' shows the location as it relates to the table, the word 'placed' is not required.

First one is more natural for speaking... The second one would be nicer when writing.

PLACED is a verb. It basically means PUT when used this way. So don't use it to say where the glasses are. Only use it if you want to say how they got there. If so, it would likely be in the past tense: My glasses were placed on the table.

The first one sounds better