Damping dilution factor for a pendulum in an interferometric gravitational waves detector

Mechanical loss in pendulums is a subject of great importance to gravitational waves detectors being built and being planned, as this determines the level of thermal noise associated with the detector suspensions. Relationships between the mechanical loss of the pendulum and the mechanical loss of the suspending fibres or wires can be derived in two apparently contradictory ways which give answers different by a factor of two. In this paper the differences are resolved and it is shown that both methods lead to the same answer.