My 94 convertable starts to vibrate around 65 mph.

Feels like it is in the back of the car. Can feel it through the gear
shift, so could it be drive shaft? Car is just at 100K.

Recently acquired the car, first vette, so no history on the car and not
sure where to start looking.

Is this a common problem, or do I just go through the check the tire
balance, rim straightness, etc. routine?

Everything feels tight. No clunking on acceleration or deceleration, so at
this point I don't suspect U-joints.

Ideas anyone?

Thanks!

Alex