When a particle or a body moves to and fro in a straight line such that the restoring force acting on it, and hence the acceleration is always directed towards a certain fixed point on its path and is proportional to its distance from that point, the particle or the body is said to execute simple harmonic motion (SHM).
Ideally, a body should vibrate with its natural frequency for an indefinite period of time with a constant amplitude.
In fact, however, the free vibrations are seen to decay gradually in amplitude with the passage of time and finally stop altogether.
The body comes to rest at its mean or equilibrium position.
The decay of the amplitude vibration is due to the resistance of the frictional forces, external or internal, such as the viscosity of the medium, and the internal friction due to the relative sliding of different layers of the vibrator in motion etc.
This phenomenon of decay of amplitude with time is called damping and such vibrations of decaying amplitude, are the resisted or damped vibrations.
The damping force is only dependent on velocity and is independent of displacement and acceleration of the vibrator.
Hence, a damping force executing SHM varies with the velocity.