One of the water sprays seems to be catching on the top of the drum when it is spinning causing a loud knocking when using the machine

Does the drum wobble quite a bit or does it look normal? If it's wobbling it could be the drum casing knocking the internal structure. Might need a new drum spring if this is the case

Could be a loose basket nut, or on the bottom tub support there are a few springs that help locate the tub. One of the springs could have come off or broke.

Possible that the grinding noise comes from the drum, irregular movement or broken paddles.
You can try and attempt only if equipped with a fundamental understanding of the working .
I shall give you some tips to this click 1..: Washing Machine


2. Replacing bearings

more than likely the rear bearing has gone bad and when a load is applied the difference in weight distribution causes the knocking.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/jason_4570d45317834dd3

Hi if its very noisy on spin its likly yo be the drum bearings this can be a costly repair

Hello

Loud knocking sound while spinning is usually caused due to the bearings going bad and the inner tub should also be checked. The repair is not easy and requires some time to do the replacement. Please get back to me if you have any other questions.

Kevin

replace the balance springs from the bottom of the tub to the frame there weak and letting the tub rock

This assumes that you have a basic Kenmore / Whirlpool top load, direct drive, neutral drain (it doesn't spin until the pump removes most of the water) machine.

First, see the Sears parts site for your washer:
http://www.searspartsdirect.com/partsdirect/index.action

Enter your model number and you'll see a list of major sub-components with diagrams and parts.

There is also an excellent PDF document from Whirlpool describing how Direct Drive washers work.

https://secured.whirlpool.com/Service/SrvTechAdm.nsf/2cd44500d572193285256a45004fd9d6/f7e2147fa98b28cf85257122007475cb/$FILE/L-55.pdf

We has the same basic problem with a Kenmore direct drive washer. At the end of the spin cycle we heard a loud noise as the brake stopped the drum from spinning.

Sometimes, what can happen is that the brake will grab the brake drum, like a brake on a car suddenly locking a wheel.

The brake is supposed to slow down and stop the drum without locking.

We were able to spray a small amount of silicone spray inside the brake drum, which allowed the shoes to more gently grab the drum.

See GURU JSROCK516 Description of how to remove cabinet and access the transmission. http://www.fixya.com/support/r699497-replacing_gearcase

Remove the cabinet and look at the drum directly above the silver colored clutch assembly.

Using an spray can of silicone spray, and a directional tube, spray a very small amount into the brake drum.

sometimes the agitator gets loose, causing the drum to sway to far all over the place.make sure its tight , remove the softener dispenser (manual nut), then tighten the metal nut that holds the agitator down

Usually this is an out-of-balance condition caused by too much weight on one side of the tub, move the clothes around and try again.