Qusetion: The micro cantilever of Problem is used to sense the mass of a particle mp that attaches to its free end. Calculate mp knowing that the lumped-parameter viscous damping coefficient is c = 4.27 # 10-9 N-s/m, the maximum voltage readout is DV0 = 4.5 nV, while all other parameters are the ones specified in Problem.
Problem: A micro cantilever is placed on a shaker that provides a variable-frequency input displacement motion u = 5 sin(~t) nm. The micro cantilever has a length l = 320 nm, width w = 50 nm, thickness h = 3 nm, Young's modulus E = 150 GPa, mass density t = 5400 kg/m3 and is used in conjunction with a strain gauge (Kg = 2.1) attached to the cantilever root and connected in a Wheatstone bridge (with vi = 20 nV). Knowing that the maximum voltage readout is DV0 = 8 nV, determine the overall coefficient of viscous damping c.