Friction shaft damper includes springy projections pressing against inside surface of a portion of rotor such as drive shaft with spring force. Central mass may be positioned inside surface of drive shaft by projections extending outwardly from central mass and slideably engaging inside surface of drive shaft. Enlarged section or chamber of shaft may surround and axially trap damper. Axially spaced apart sets of springy fingers may position mass inside shaft and radially inner ends of fingers may be secured to mass and radially outer ends of fingers may be positioned and free to slide along inside surface of shaft. Two axially spaced apart annular deflection limiters may be placed around mass with small clearances C between deflection limiters and inside surface of shaft. Damper may be a multi-lobed wave spring having multi-lobed rim attached to mass by struts. Damper may be multi-lobed wave spring with crests.