NEMS Multimode Mass Sensing: Locating a Single Landed Particle

Nanoelectromechanical (NEMS) resonant mass sensors detect an adsorbed particle from the tiny downward shift it causes in a vibrating nanobeam's resonant frequency — but a single mode alone can't tell you where on the beam the particle landed, and position matters because the same mass produces a different frequency shift depending on whether it lands near a vibrational node or an antinode. This simulator renders a doubly-clamped, tension-dominated nanobeam vibrating in its first two flexural modes, drops a single nanoparticle at a random, initially unknown position, and applies the real perturbation-theory frequency shift for each mode. It then inverts the two measured shifts using the exact mode-shape-ratio formula that real multimode NEMS "inertial imaging" instruments use, recovering both the particle's mass and its landing position from vibration data alone, and reports the estimate directly against the true hidden values.