  Gravitational forces that oscillate at audio-band frequencies are measured
with masses suspended as pendulums that have resonance frequencies even lower.
If the pendulum is excited by thermal energy or by seismic motion of the
environment, the measurement sensitivity is reduced. Conventionally, this
problem is mitigated by seismic isolation and linear damping, potentially
combined with cryogenic cooling. Here, we propose mechanical parametric cooling
of the pendulum motion during the gravitational field measurement. We report a
proof of principle demonstration in the seismic noise dominated regime and
achieve a damping factor of the pendulum motion of 5.7. We find a model system
for which mechanical parametric feedback cooling reaches the quantum mechanical
regime near the ground state. More feasible applications we anticipate in
gravitational-wave detectors.
