1988 Oldsmobile 98 Some kind of motor killing my Battery!

I have a 1988 olds regency brougham 98, when I turn my ignition off, a motor under the hood continues to vibrate on and off. Leaving me to find a dead battery the next day. To give some perspective: If you're looking at the car head on the motor can be found almost right behind the right headlight. What is it? And if you can, what would be a rough estimate for repair?