(Top) The AURIGA gravity wave detector consists of a 3 m long one-metric-ton aluminum bar that is in thermal contact with a liquid helium reservoir. Distant energetic events such as orbiting binary stars produce gravitational waves that cause the bar to expand and contract longitudinally; these displacements are measured by a low-noise detector. Vinante et al. used feedback cooling to reduce the temperature of the longitudinal mode to less than 1 mK. (Bottom) The resonator is represented schematically as an effective mass m on a spring (a harmonic oscillator with angular frequency ω) modeling a single mode of a mechanical resonator. This vibrational mode is coupled to a heat reservoir at temperature T1 and to the input of a mass position detector (amplifier), where the amplifier back action behaves as a heat bath with some effective noise temperature TA and damping rate γA. If the output of the amplifier is phase-shifted and added back into the amplifier input, a much lower resonator temperature is possible.