The sound from the guitar string will become softer and eventually stop. We can hear when this has happened. The final part of the story is that the time it takes for a system to return to equilibrium can give us useful information. In the case of the hydrogen nuclei, there are a number of factors that affect the relaxation time including the fluid molecules bumping into each other and into solids. For NMR in the oil industry it is the molecules bumping into the solid walls of the pores in rocks that is of greatest interest, because the relaxation time is related to the size of the pores.
Larger pores mean more permeability and increased oil flow.
How long it takes the kid to come to rest depends on how much friction there is with the air and in the joints where the swing attaches to its supporting structure. If he drags his foot, he will slow down more quickly. If it's less, something caused the difference, maybe touching the string. The best known use of NMR is in medical diagnosis where it allows for a noninvasive examination of the human body. In the medical field NMR is usually referred to as MRI - Magnetic Resonance Imaging.