A system containing a micro-mechanical or nano-mechanical device and a method of operating the same is provided. The device includes a resonator and a piezoresistive element connected to the resonator. The method includes AC biasing the piezoresistive element at a first frequency, driving the resonator at a second frequency different from the first frequency, and detecting a mechanical response of the resonator at one or both of a difference frequency and a sum frequency of the first and second frequencies.