Systems and methods for tuning resonators for enhanced sensitivity

A system comprising:

• a mechanical resonator having a flexible beam coupled to a body;
• an electrical resonator coupled through a patch to the mechanical resonator, the electrical resonator shunting the mechanical resonator and having an inductor and a resistor that form an LR circuit in series;
• and
• the electrical resonator controls frequency detuning near an exceptional point (EP) of the mechanical resonator by controlling the LR circuit according to a model using a signal, and the EP represents an intersection of eigen parameters associated with values of the inductor and the resistor.

A sensor comprising:

• a mechanical resonator having a flexible beam coupled to a body;
• an electrical resonator coupled through a piezoelectric device to the mechanical resonator, the electrical resonator shunting the mechanical resonator through an inductor and a resistor that form an LR circuit in series;
• and
• the electrical resonator is configured to measure, associated with a shock of the body, frequency detuning near an exceptional point (EP) of the mechanical resonator by controlling the LR circuit according to a non-linear model and a signal, and the EP represents an intersection of eigen parameters associated with values of the inductor and the resistor.