Timely and interesting thread.
I bought my fjr used, about 3500 miles on the odo.
Didn't like the vibes at 4k.
Read here where someone said riding the bike in the 4k range often, a lot, over and over and over, might help.
where ever I went for the next 2k miles, kept it in a gear that had me at 4k rpm.
That, and a throttle body sync (at dealership) really did seem to help. I could actually be riding and many times not even realize I was at 4k rpm, the buzz had about disappeared.
But here's my theory: I think the "buzz" comes from engine harmonics / vibrations. And I think the "harmonic" vibrations can be lessened if you break the bike in differently, as opposed to babying the snot out of it.
I really believe that. It's the babying the snot out of it that's causing the engine to break-in in such a way that causes these odd harmonics.
I have a Kawa Versys now. I broke it in. I rode it like I stole it for the first 20 miles, then changed the oil ("moto man" break in). Now the rings are set, now all the other bearings etc are set. Now with 4500k on the odo, virtually no engine harmonics / vibrations at all. Okay, every once in a while a slight buzz at 5k rpm. Hey it's a 2 banger! but you can barely notice the buzz.
I know this isn't scientific evidence, obviously. But between the feej and now the versys, I really believe it's the babying crap we do that causes this... the parts just aren't getting worn in as they should, so now when you get to certain rpm's, it's telling you "we're not broken in as we should have been".
I'd suggest reading carefully what MotoMan has to say, and look carefully at this part: once you've gotten past a certain early mileage (something like 20 miles)... it's done, break in is over. If you've babied it, you have glazed over piston walls and un seated rings, and the one and only way you can reverse that is to tear down the engine and re do the rings and piston walls.
No science here, just my opinion. Keep in mind, those old "baby it" procedures were written decades ago, when bearing and ring etc tolerances were no where near what they are with modern technology. The newer tighter tolerances don't require the old break in "baby it" stuff, that's my experience anyway.