This is a common problem on older Maytag washers and is caused by a worn drive belt. I bought this washer and dryer pair in fall of 1983 and had to replace the belts on the washer in the late 1990s.
The repair is very easy. Pull the machine away from the wall a few inches, tip it back and place a 2x4 block under the front of the machine. There are two belts on the machine. The lower one (smaller belt) runs the pump and the larger one runs the tub. The motor is on the left near the front and there are a pair of springs that tension the belt. Reach underneath and push the motor towards the center of the machine to relieve the belt tension. Pop the pump belt off of the motor pulley and then off of the pump pulley. The pump is near the front on the right. Do the same thing for the tub drive belt. Put the new drive belt on the tub pulley first and then work it on the motor pulley. The pump belt is next and put the belt on the pump pulley first and then on the motor pulley. Spin the motor around by hand a couple of times to make sure everything is in place and remove the block.