  We precisely measured the binding energy of a molecular state near the
Feshbach resonance in a $^{85}$Rb Bose-Einstein condensate (BEC). Rapid
magnetic field pulses induced coherent atom-molecule oscillations in the BEC.
We measured the oscillation frequency as a function of B-field and fit the data
to a coupled-channels model. Our analysis constrained the Feshbach resonance
position [155.041(18) G], width [10.71(2) G], and background scattering length
[-443(3) a$_0$] and yielded new values for $v_{DS}$, $v_{DT}$, and $C_6$. These
results improved our estimate for the stability condition of an attractive BEC.
We also found evidence for a mean-field shift to the binding energy.
