  Through simultaneous but unequal electromechanical amplification and cooling
processes, we create a method for nearly noiseless pulsed measurement of
mechanical motion. We use transient electromechanical amplification (TEA) to
monitor a single motional quadrature with a total added noise $-8.5\pm2.0$ dB
relative to the zero-point motion of the oscillator, or equivalently the
quantum limit for simultaneous measurement of both mechanical quadratures. We
demonstrate that TEA can be used to resolve fine structure in the phase-space
of a mechanical oscillator by tomographically reconstructing the density matrix
of a squeezed state of motion. Without any inference or subtraction of noise,
we directly observe a squeezed variance $2.8\pm 0.3$ dB below the oscillator's
zero-point motion.
