Etymology
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vacillation (n.)

c. 1400, "hesitation, uncertainty," from Latin vacillationem (nominative vacillatio) "a reeling, wavering," noun of action from past-participle stem of vacillare "sway to and fro, waver, hesitate, be untrustworthy," of uncertain origin. Originally in reference to opinion or conduct; literal sense is recorded from 1630s.

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vacillate (v.)
1590s, "to sway unsteadily," from Latin vacillatus, past participle of vacillare "sway to and fro; hesitate" (see vacillation). Meaning "to waver between two opinions or courses" is recorded from 1620s. Related: Vacillated; vacillates; vacillating.
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flexibility (n.)
1610s, of physical things, from French flexibilité (in Old French, "weakness, vacillation") or directly from Late Latin flexibilitatem (nominative flexibilitas), from Latin flexibilis "pliant, yielding" (see flexible). Of immaterial things from 1783.
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fluctuation (n.)

mid-15c., from Old French fluctuacion (12c.) or directly from Latin fluctuationem (nominative fluctuatio) "a wavering, vacillation," noun of action from past-participle stem of fluctuare "to undulate, to move in waves," from fluctus "a wave, billow, surge, a flowing," from past participle of fluere "to flow" (see fluent).

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fistula (n.)

"long, narrow ulcer," late 14c., from Latin fistula "a pipe; ulcer," which is of uncertain origin. Related: Fistular; fistulous (Latin fistulosus "full of holes; tubular").

No certain etymology. The best comparison seems to be with festuca "stalk, straw" and maybe ferula "giant fennel" (if from *fesula): the forms of a "pipe" and a "stalk" are similar. The vacillation between fest- and fist- occurs within festuca itself, and might be dialectal, or allophonic within Latin. [de Vaan]
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