the modern English word is a merger of two words, both in Middle English as quashen, from two unrelated Latin verbs.
1. "to suppress, overcome" (mid-13c.); "to make void, annul, nullify, veto" (mid-14c.), from Old French quasser, quassier, casser "to annul, declare void," and directly from Medieval Latin quassare, alteration of Late Latin cassare, from cassus "null, void, empty" (from extended form of PIE root *kes- "to cut"). The meaning "subdue, put down summarily" is from c. 1600.
2. "to break, crush, beat to pieces" early 14c., from Old French quasser, casser "to break, smash, destroy; maltreat, injure, harm, weaken," from Latin quassare "to shatter, shake or toss violently," frequentative of quatere (past participle quassus) "to shake," from PIE root *kwet- "to shake" (source also of Greek passein "to sprinkle," Lithuanian kutėti "to shake up," Old Saxon skuddian "to move violently," German schütteln "to shake," Old English scudan "to hasten").
In Medieval Latin, quassare often was used for cassare, and in later French the form of both words is casser. The words in English now are somewhat, or entirely, fused. Related: Quashed; quashing.
"act of shaking, concussion," early 15c., quassacioun, from Latin quassationem (nominative quassatio) "a shaking or beating," noun of action from past-participle stem of quassare "to shatter, shake or toss violently" (see quash).
"water-tight, barrel-like vessel for containing liquids," mid-15c., from French casque "a cask; a helmet," from Spanish casco "skull; wine-vat; helmet," originally "potsherd," from cascar "to break up," from Vulgar Latin *quassicare, frequentative of Latin quassare "to shake, shatter" (see quash). The sense evolution is uncertain.
1560s, from French fricassée, noun use of fem. past participle of fricasser "mince and cook in sauce" (15c.), which is of uncertain origin. Perhaps a compound from elements related to or altered by French frire "to fry" (see fry (v.)) and casser, quasser "to break, cut up" (see quash (v.)). As a verb, from 1650s.
c. 1400, "a bruising, contusion (to the head)," from Latin concussionem (nominative concussio) "a shaking, an earthquake," noun of action from past-participle stem of concutere "shake violently," from assimilated form of com "with, together" (see con-) + quatere "to shake" (see quash).
From late 15c. as "act of shaking or agitation," especially by impact of another body; from 1540s as "brain injury caused by a fall or blow."
a generic name for Italian dough-based foods such as spaghetti, macaroni, etc., 1874, but not common in English until after World War II, from Italian pasta, from Late Latin pasta "dough, pastry cake, paste," from Greek pasta "barley porridge," probably originally "a salted mess of food," from neuter plural of pastos (adj.) "sprinkled, salted," from passein "to sprinkle," from PIE root *kwet- "to shake" (see quash).