7.8 Mechanical Devices 151 7.8 MECHANICAL DEVICES The spring constant (stiffness) k of a nanocantilever varies with its characteristic linear dimension l, and its mass m as l 3 . Hence the resonant frequency of its vibration p ! 0 D k=m (7.22) varies as 1=l. This ensures a fast response--in effect, nanomechanical devices are extremely stiff. Since the figure of merit (quality factor) Q equals ! 0 divided by the drag (friction) coefficient, especially for devices operating in a high vacuum Q can be many orders of magnitude greater than the values encountered in conven- tional devices. On the other hand, under typical terrestrial operating conditions water vapor and other impurities may condense onto moving parts, increasing drag due to capillary effects (cf. Figure 3.1), and generally degrading performance. The simplest mechanical device is probably the vibrating cantilever; we may use this to fix ideas (Figure 7.21; see Figure 7.22 for a more picturesque representation). From equation (7.22), the fundamental (resonant) frequency is the square root of the quotient of the spring constant and the mass, i.e., p ! 0 D Yl=m eff (7.23)