The periodic vibrations of a body with diminishing amplitude in the presence of a resistive force are known as damped vibrations.
When a body is forced to vibrate in a medium, the amplitude of the vibrating body gradually diminishes over time until it stops vibrating entirely.
When a slim branch of a tree is tugged and then released, it produces damped vibrations. The damped vibrations are the oscillations of a spring in the air that has a mass at its end.