I just replaced the fluorescent lights in my kitchen - two of the 40w
type, about 47" long - when the old ones would no longer activate.
After putting in the new ones, I find that after about 30 secs from
being turned on, the lights begin this rapid shimmering or pulsing.
Hard on the eyes and annoying.

The old ones were fine before they died, didn't exhibit this behavior.
Does this sound like some problem with the lights themselves or some
problem with the light fixture that perhaps didn't show up with old
lights?

Thanks.