To Be Shaken
To Be Jolted
intransitive verb, ichidan verb
Remember 揺る which means "to shake" or "to jolt"? This is like that, but now you're not doing the shaking and jolting, making it to be shaken or to be jolted. You know this because it's really rare (れる) for you to be shaken like this.
The reading comes from 揺る.
The swings at the park swayed in the wind.