Tune out the Package Capacitance
Look at the wikipedia page to determine how to make an inverter out of the operational amplifier:
Using equal valued resistors for Rin and Rf will create a non-amplifying inverter.
Insert the inverter into the circuit below:
Doing so will create two halves of the circuit which join together exactly out of phase, providing destructive interference to cancel the effects of the package capacitance.
(a) Skewed from Package Capacitance
(b) Symmetry after Canceling Package Capacitance
Your data around your peak should shift from the diagram (a) to diagram (b).
Tune the capacitor until the resonance peak becomes symmetric. The background noise should also drop significantly. The package capacitance is on the order of a few nano-Farads. Be careful not to change the wires connecting the circuit too much as the capacitance due to the physical components of the circuit is near the nano-Farad range and affects the tuning.
If you find that the noise levels are still high compared to the resonance peak, shield the circuit board (remember to re-tune the capacitance). Ensure your shielding does not short any circuit element.
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