A vehicle steering system includes a steering wheel and a steering shaft coupled between the steering wheel and wheels of the vehicle. The shaft is operable for rotating when the steering wheel is turned to thereby turn the vehicle wheels. A vibration damping system for absorbing vibrations in the steering wheel and shaft includes a rotor coupled to the steering shaft to rotate with the shaft and a case surrounding the rotor and a clutch surface proximate the rotor. A magnetic circuit generates a magnetic flux in the rotor. The rotor is operable to engage the clutch surface and thereby vibrationally couple the steering shaft to the case to absorb vibrations in the shaft, and when a magnetic flux is generated therein, to disengage the clutch surface so that the steering shaft may more freely rotate.