wag, swing, wave, shake, scull
搖 centers on rhythmic back-and-forth motion: wagging, swinging, waving, shaking, or sculling. All meanings share the idea of something moving repeatedly from side to side or up and down.
搖 is the traditional form of 揺. It combines 扌 (hand) with a phonetic component that historically represented a jar or container, possibly suggesting the motion of shaking or agitating something by hand.
The hand radical 扌 on the left holds a container-like shape on the right. Imagine a hand shaking a jar back and forth, making the contents swing and wave inside.
For ヨウ, picture a hand waving a yo-yo up and down: yo-yo -> ヨウ, and the hand keeps the yo-yo swinging rhythmically.