I got an email the other day with a question about what to do when the Floyd Rose Tremolo "sings". When I got my first guitar with Floyd Rose I had the same problem, and it was extremely disturbing. Especially when you play with no effects and you have the need for sudden "stop" in the music, where the point is to be completely silent. A "singing" tremolo totally crashes the party.
Singing tremolos are a fairly common problem and occurs on almost every tremolo systems around, even Strats, but in particular different types of Floyd Roses.
The reason, for most of the cases, is that the springs behind the back of the guitar vibrates so much that it is taken up by the pickups. It's very annoying that they can not fix things on the factory. Even on the more "expensive" guitars costing up to like 3000 dollars this problem occurs, and it seems to be accepted in the quality chain before delivery to customer. I think its more than strange actually.
The simple way to solve this is to try to suppress the tremolo from the inside.
On the right, an Ibanez Jem7VWH the operation completed, I had apparently chosen a piece of old curtain.
//The Guitar Zombie