Oscillate
Etymology
From Latin "oscillare" (to swing), from "oscillum" — a little swing, and also, curiously, a small mask of Bacchus that the Romans hung in vineyards to sway in the breeze. From that swaying image the word entered science for regular back-and-forth motion, and everyday speech for wavering of mind.
verb · /OS-uh-layt/
To swing steadily back and forth, or to waver between positions or states.
What it names
Both the physics of a pendulum and the very human habit of swinging between two moods or choices.
Example
Public opinion continued to oscillate between hope and alarm as each new report landed.
Related idea
Vacillate is specifically wavering in decision or resolve; oscillate is the broader physical or figurative swinging back and forth between two points.