摆动 (bǎi dòng) means 'to sway, swing, or oscillate' — it emphasizes a regular back-and-forth motion along a fixed point, like a pendulum or a flag in the wind. It is more specific than 摆 (bǎi), which can also mean 'to arrange' or simply 'to wave'. 摇摆 (yáo bǎi) is very similar but often suggests a less steady wobbling or a metaphorical wavering.