Engine fan rattle/groan on startup

When I first start up my 1997 Nissan pickup, I get a rattle from the big fan at the front of the engine (I don’t know the right name for it). Sometimes I also hear a sort of groaning/grating sound from the same area while the car idles immediately after startup, but not at other times. Visual inspection shows that the fan is vibrating forwards and backwards slightly as it spins. I never hear it rattle except at startup and get no noise while driving it. Should I be worried? Thanks!

What you describe sounds like the water pump is about to give up the ghost. And if the water pump bearing fails where the radiator fan hits the radiator, that’ll have to be replaced too.