tailpiece hum??

[bluegrasscat]

here is my question!- how much vibration should the strings have below, and between the bridge and the tailpice have when the strings are played???(example..--play a open A string and then mute it! then checking lower sting for vibration at tailpiece!) mine seems to go for along time, and it actually vibrates the tailpiece to the point of hearing the tailpiece hum at a high vibration rate.( but its not a buzz! or a rattle. more of a hum!! the tailpiece will still be vibrating/humming long after muting the A string, i can mute all strings and still the tailpiece is still hummn.! even if i touch lower strings it still goes!! and when i touch the tailpiece the hum stops!! kind of like how a tuning fork will vibrate for along time!! is this normal or bad / good / or should all the strings do this equally? or not at all?? and is it a string slot issue?? i was just a wondering if anyone else has seen this..