A nanoscale mass sensor consists of a carbon nanotube cantilever of effective spring constant kkk. When a biological cell of mass MMM binds to the tip of the cantilever, the system oscillates in simple harmonic motion with a fundamental frequency fff.
Assuming the mass of the cantilever itself is negligible, which of the following represents the correct proportional relationship between the resonant frequency fff and the mass MMM of the cell?
f∝M12f \propto M^{\frac{1}{2}}f∝M21
f∝M−12f \propto M^{-\frac{1}{2}}f∝M−21
f∝M2f \propto M^2f∝M2
f∝M−2f \propto M^{-2}f∝M−2
