Hey Suirrel.................You have a pretty good knack for figuring this tuff out.
I figure , when you took the Core out from under the bus, you changed the resonant frequency of the mounting points thus giving more audible vibration. The vibration would have been dampened by the overall surface area of the hanging piece to a frequency much lower and making it much less audible to the human ear.
Makes plety of sense to me...................LOL
This all comes together pretty quick if you have done any vibration hunting after adding audio systems to cars, and having new exhaust put on, and stuff like that........................
Glad you found what causes the noise.............now how ya gonna fix it????
Keep us posted.
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