  We demonstrate sensitive and fast electrical measurements of a carbon
nanotube mechanical resonator. The nanotube is configured as a single-electron
transistor, whose conductance is a sensitive transducer for its own
displacement. Using an impedance-matching circuit followed by a cryogenic
amplifier, the vibrations can be monitored in real time. The sensitivity of
this continuous displacement measurement approaches within a factor 470 of the
standard quantum limit.
