【Swing】 ,  【sway】 ,  【oscillate】 ,  【vibrate】 ,  【fluctuate】 ,  【pendulate】 ,  【waver】 ,  【undulate】  mean to move to and fro, back and forth, or up and down.

【Swing】  (see also  【SWING】 1 ) implies movement in an arc of something attached only at one side or at one end (as by being suspended, hinged, or pivoted); apart from the context the term conveys no definite implication of whether the movement is induced or is automatic, whether it is occasional or constant, or whether it is rhythmical and regular or intermittent and irregular.

【Sway】 implies a slow swinging motion, especially in a flexible or unsteady object that yields to lack of support or to pressure from one side or another.

【Oscillate】 implies a swinging motion of or as if of something suspended so that it moves through a regular arc; the term usually implies a movement from one side or place or from one condition, attitude, or position to another, with more or less regularity.

【Vibrate】  is sometimes used in the sense of  【oscillate】 , but it more typically implies rapid periodic oscillations usually over an arc of small amplitude and may suggest the rapid pulsations of the string of a musical instrument (as the piano or violin) when touched by a hammer or bow or the rapid beating of some wings (as of a hawkmoth or hummingbird).

In a more extended sense  【vibrate】 may imply a trembling, a quavering, or a throbbing suggestive of the movements of musical strings when an instrument is being played.

【Fluctuate】 occasionally implies a tossing up and down restlessly like the waves of the sea or like something floating on such waves, but is chiefly used in an extended sense implying constant irregular alternations suggestive of the movement of waves.

【Pendulate】  , a somewhat uncommon word, is a near synonym of  【oscillate】  in implying a swinging between two extremes, but it often comes close to  【fluctuate】 in its strong suggestion of constant change.

【Waver】  (see also HESITATE ) carries a stronger implication of unsteadiness or of uncertainty in swinging than does  【sway】  or  【oscillate】 .

【Undulate】  is more often used than  【fluctuate】 when a wavelike motion is implied; especially in its extended use it seldom suggests violent changes, but rather the continuous rolling or rippling that is associated with the steady flow of waves.