Not any swing but a rhythmic movement helps induce sleep including music and a lullaby. Wakefulness with all things pulling us in multiple directions disturbs the rhythms. The Universe and the movement of Time are both rhythmic in nature and hence rhythms have a healing effect as well as create restfulness.
Affectionately
Alok da
Reference:
शरीर भी भगवान को याद करेगा | TH 407
YT Link: https://youtu.be/Ujv1LksrXS4