Here's how it works:

* Natural Frequency: Every object, like a swing, has a natural frequency at which it vibrates most easily. This is determined by the object's mass, shape, and the forces acting on it.

* Pumping: When a child pumps their legs in sync with the swing's natural frequency, they are providing a periodic force that matches the swing's natural tendency to oscillate.

* Energy Transfer: This synchronized force efficiently transfers energy to the swing, increasing its amplitude (height) with each pump.

* Resonance: This phenomenon of increasing amplitude by matching a periodic force with an object's natural frequency is known as resonance.

In simpler terms: The child is essentially "helping" the swing move at its preferred speed and rhythm. By matching their pumping with the swing's natural rhythm, they maximize the energy transfer and make the swing go higher.