1996 Jaguar Vanden Plas. Problem: having trouble with vibration and noise on speeds between 30 and 35 mph. no vibration on lower or higher speeds. Any suggestions would be helpful.

Balancing the tires is the typical solution but your case sounds like it might be a bent wheel. Take your car to a tire shop to have them check for balance. While on the balancing machine, they can inspect the rim for a warped rim. Make sure you let them know prior to the wheel getting mounted on the balancing machine. Jags are known for that to happen. I hope it is just a tire balancing but if it is a bent wheel, the cost is more. Good luck.