00 Police Impala Shaking with Acceleration

I have a 2000 Police Impala with 74K miles. When I accelerated from 30 through 45 mph I get a shaking in the car. It seems to come from the left side. Note: The steering wheel is not shaking (Rotors). When I let off the gas it stops shaking. It will start again with acceleration. Seems to stop when I get to around 50 mph but picks up again at 70mph.

I have had the tires checked, rebalanced, car aligned, and the brakes checked -- all OK. Any help would be GREATLY apprecitated.

Thank you. :mad: