Spelled “Asswaged” is now an obsolete variant of assuage. The meaning is the same, but apparently, the “leaders” of the English language preferred to change the spelling to “assuage.”
The meaning of assuage is to make (an unpleasant feeling) less intense.
Genesis 8:1
King James Version
8 And God remembered Noah, and every living thing, and all the cattle that was with him in the ark: and God made a wind to pass over the earth, and the waters assuaged;