LP Gear (on-line) Shows that they sell a replacment belt for your model T.T.
Of course they don't say the size up front. You can have the correct length belt with a different width causing them to slip/grab differently.
The link to LP Gear is: http://www.lpgear.com/product/CECBA300.html
The fact that you said it started vibration about One Minute after starting to play a record might be significant.
I repaired a Fisher T.T. with a similar vibration. Once it warmed up enough to start the vibration, taking off the belt and "carefully spinning" the T.T.
by hand, with the Stylus on the Record, the Vibration showed up. This took the Motor and the Belt out of the equation. Just a T/S thought...Gary