Why do some playstation games have a jumpy television picture while others do not. The tv is fine.?

My son gave me an older used playstation for my grandkids when they come over and many, but not all of the games have a shaking to the tv picture. They play alright. My son said it didn't do that when he played it but he hasn't played in quite some time. The tv is fine. On the opening screen of the games, the Sony trademark screen, the shaking is not there. It is stable until it gets to the game screens. Anyone have the same problem.