Thumping sound at the end of spin cycle.

You can check the belt, pulley, and the motor

Sounds like you have an unbalanced load. I know this sounds too easy but lots of times this is the issue. If it doesn't help then you could have a bearing issue where the belt goes around a pully under the tub itself. If so you will have to replace the pully itself and perhaps the belt if it's gotten worn too much.

What is the model number of your unit?

Your break mechanism probably needs break shoes

Could be coin in pump hitting blades...Try pump only no spin this will discount the drum ....Check filter if you have one.

make sure the shiping rod is out it will do that if it,s not out

My guess is that one of the three counterweights have separated from their support. Probably rusted away.
36 years is quite a feat. Today's machines would be lucky to 1/3 of that life.
Sounds like its time to go shopping.
Do you have an anniversary coming up?
Ladies love washers for an anniversary gift.

my friend had this happen,apparrently a bearing was leaking then finally broke!

It doesn't look like a motor problem !!! It seems like an unbalanced tub issue. The machin has suspension dampers and suspension rods, and it's look like one of them was damaged or "run away" from its location during machin's movement. Goog luck !!

I replaced the drive block and it solved my problem. (thumping noise at the end of spin cycle) Easy repair. Videos on utube show all the steps.