Old English swingan "beat, strike; scourge, flog; to rush, fling oneself" (strong verb, past tense swang, past participle swungen), from Proto-Germanic *swengwanan (source also of Old Saxon, Old High German swingan, Old Frisian swinga, German schwingen "to swing, swingle, oscillate"), which is of uncertain origin and might be Germanic only.
The meaning "move freely back and forth" is first recorded 1540s. Transitive sense "cause to oscillate" is from 1550s. Sense of "bring about, make happen" is from 1934. Sense of "engage in promiscuous sex" is from 1964; earlier, more generally, "enjoy oneself unconventionally" (1957). Related: Swung; swinging. Swing-voter "independent who often determines the outcome of an election" is from 1966.
Old English swinge "stroke, blow; chastisement," from swing (v.). Meaning "suspended seat on ropes" is from 1680s. Meaning "shift of public opinion" is from 1899. The meaning "variety of big dance-band music with a swinging rhythm" is first recorded 1933, though the sense has been traced back to 1888; its heyday was from mid-30s to mid-40s. Phrase in full swing "in total effect or operation" (1560s) perhaps is from bell-ringing. The backyard or playground swing-set is from 1951.