It happens. The vibrato springs have a resonant point to them and will vibrate in sympathy with certain notes/chords. What some guys do is get some 1/4" surgical tubing, and slide it inside the springs. It has a deadening effect, so the ringing sound goes away. It works well, because it expands/contracts with the springs as you use the vibrato. Also, because it's silicone, it lasts a very long time.