My newly aquired (used) Ibanez RG1527 has 5 springs installed and they ring when and after a note sounds. I've read several solution for fixing this problem, but what would be the best?

My Gibson Explorer with a Tune-O-Matic bridge also have a problem with ringing, but I don't know where it's coming from. It only occurs when I dampen the low E string (and only that note). It's not a long ring, but it's loud and annoying. Destroys the purpose of dampening. I don't know how to solve this problem. Any suggestions on what could be causing it and how I go around fixing it?

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Even my Esquire does that, I think it's the strings ringing out between the nut and tuners. Never have figured out how to stop that without adversely affecting the sustain.
Epiphone Dot
DIY Esquire w/Neovin Power Rock pickup
Vox AC30VR 212
Arion MTE-1 (LED clipping diodes added)
Vox Tonelab LE
Roland SDE1000 delay

Quote by DaMarsbarPerson
By high-gain I don't mean stupid stuff. I just mean styles like Motley Crue or Iron Maiden