Reciprocating oscillation
Encyclopedia
Reciprocating oscillation is an action of oscillation
Oscillation
Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...

 where the oscillation vector varies its amplitude, frequency and or displacement reciprocally
Multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the...

. (Note: not to be confused with the reciprocal of the given sinusoidal function). For example, an oscillation that changes its amplitude and thereby, for example, its displacement every cycle to half that of its initial amplitude is said to be reciprocating. Note that the term reciprocating can be used loosely to describe such an action but usually is not because such an action can be defined easily as two separate oscilations. Instead it is more commonly used to describe an oscillation in which the second definable oscillation can be defined as a non-rotary cycle as its displacement.

Reciprocating oscillation is an action where an oscillating body reciprocates within the oscillation, where reciprocation is distinct from just another oscillation by only "jumping up and down" and not oscillating about an axis.
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