Which of the following terms describes the action of swinging back and forth in a steady rhythm?

The term that describes the action of swinging back and forth in a steady rhythm is "oscillate." This word signifies a regular, repeating movement, typically around a central point or position. Oscillation implies that there is a consistency and predictability to the movement, making it distinct from other similar actions.

For instance, oscillation is often used in physics to describe the motion of a pendulum or a swinging spring, where the object moves away from a point of equilibrium and returns back, creating a continuous cycle. This steady rhythm is integral to various scientific and engineering principles, including those in sound waves and electromagnetism.

In contrast, while "vibrate" may suggest rapid movements back and forth, it doesn’t inherently convey the rhythm or regularity associated with oscillation. "Sway" refers to a more gentle or slow moving side to side action, not necessarily that continuous or rhythmic nature. On the other hand, "waver" implies an irregularity or uncertainty in motion, often used to describe hesitation or fluctuation rather than a consistent swinging motion. Thus, "oscillate" is the most precise term for describing a steady rhythm of swinging back and forth.