1996 Acura RL Car Vibrates badly at 55 to 60 MPH

This problem started about two weeks ago. The car vibrates between 40 - 65 mph. I did notice yesterday it vibrated at idle, but that was the only time. I also notice the accelerator seem to stick. The steering wheel seem to be very hard when after just starting during initial take-off, but is fine while driving. A mechanic told me it probably the rear upper control arms. All though the control arms do need replacing I do not think it is my source of vibration, but it started all of a sudden. I did the rev test(up to 4000 rpm) and the did not vibrate/shake badly. The badly shaking vibration problem seem to happen every other time I drive the car.