These words refer to back-and-forth motion. Vibrate is the most general of these, suggesting a rapid continuing pulsation: feeling the train begin to vibrate with the monotonous roll of wheels along the track. Oscillate , a more formal word, often used in scientific contexts, applies to any regular movement back and forth, as of pendulum, or to any uncertain change of position: common stocks that oscillate in a predictably cyclical way; attitudes that oscillated between extremes of despair and hope. Apart from technical contexts and especially where uncertainty rather than regularity is intended, oscillate may sound stiff or ambiguous.

Swing , while much more informal, relates closely to oscillate in suggesting motion like that of a pendulum or of anything stationary at one end and free at the other: swinging ape-like from vine to vine. Unlike oscillate , the word may suggest a curving movement, like that followed by a pendulum’s weight: swinging the car sharply to avoid being struck. It is used also to indicate a change of opinion away from an existing situation: The election result showed a decided swing against the government.

Undulate and sway are more specific than the foregoing words. Undulate suggests the slow, irregular alternation of swells and hollow in an elastic surface: smooth waves undulating across the bay. Unlike the other words treated here, undulate can be applied also to things completely at rest but composed of gentle swells and hollows: foothills that undulated gently beside the highway. Sway may suggest the swelling and hollowing of a surface, like undulate , but most specifically it suggests the slow back-and-forth movement of something standing upright: trees swaying in the first gusts of the storm. This contrasts with swing , which strongly suggests the movement of something attached at the top and free to move at the bottom, rather than vice versa.

Fluctuate and waver refer less to physical motion than to changes in rate or changes of mind. Fluctuate suggests an irregular up-and-down motion or an uncertain or erratic course: share prices that fluctuate for no apparent reason. Waver stresses indecisiveness or aimlessness: wavering between going to the drive-in and staying at home. Waver , in referring to observable motion, suggests a faltering, unsteady course: the ragged caravan that wavered across the last mile of desert.