Mass and force sensing of an adsorbate on a string resonator

The shift of resonant frequency is the sensing mechanism for a mechanical resonator. The adsorbate mass, position and induced force are the three dominant things responsible for the resonant frequency shifts of a string resonator. In the application of a resonator sensor, the (shifts of) resonant frequencies are the measured quantities and therefore, an inverse problem arises naturally: How to determine the adsorbate mass, position and induced force by the resonant frequencies? An inverse problem solving method on the string resonator with one adsorbate is presented and its accuracy is demonstrated. How the method can be used in a real string sensor application scenario is also discussed.