is used. Mostly frequency will be used, and the use of angular frequency will be limited to terms like sin ( ωt ) and cos ( ωt ) where the factor 2 π -as in sin (2 πνt )-would be unnecessary bulky. In particular spectral densities -as in 6- are referred to frequency and not to angular frequency. [24] S. Rast, C. Wattinger, U. Gysin and E.Meyer, Nanotechnology 11 169-172 (2000). [25] S. Rast, U. Gysin, P. Ruff, C. Gerber, E. Meyer and D.W. Lee, Nanotechnology 17 (7) S189- S194 (2006). [26] D. Rugar and P Gruetter, Physical Review Letters 67 (22), 699-902 (1991). [27] This may seem evident since we assume that the system is at resonance. Mathematically, however, it is important that a finite oscillation amplitude ”defines” the mean angle: 〈 ϕ ( t ) 〉$_{τ}$ ≃ − π/ 2 + 〈 x ( t ) /y ( t ) 〉$_{τ}$ ≃ − π/ 2 + 〈 x ( t ) 〉$_{τ}$ / 〈 y ( t ) 〉$_{τ}$ = − π/ 2 + 0 / ( Qa$_{exc}$ ) = − π/ 2, for a$_{exc}$ = 0 , while for a$_{exc}$ = 0 this relation -and thus the mean angle- is undefined. [28] Nanotec Electronica, E-28760 Tres Cantos, www.nanotec.es. [29] Stanford Research Instruments model:dual channel 102kHz digital lock-in amplifier. [30] Note, however, that an optional oscillation amplitude gain control, usually used in DSFM to measure dissipation, is not included in figure 1. For the frequency noise measurements to be discussed here the gain control of the DSFM electronics was disabled and is thus not relevant in the present context. [31] Olympus Optical Co. LDT, OMCL-RC series, short, hard cantilever (length 100 µm , width 20 µm ), nominal force constant: 0 . 4 N/m . For more information see www.olympus.co.jp/probe. [32] R. Luethi, E. Meyer, M. Bammerlin, A. Baratoff, L. Howald, C. Gerber and H.J. Guentherodt, Surf. Rev. Lett. 4 , 1025-1027 (1997). [33] F.J. Giessibl, M. Herz and J. Mannhart, PNAS Vol. 99 (19) 12006-12010 (2002). [34] A. Gannepalli, A. Sebastian, J. Cleveland and M. Salapaca, Applied Physics Letters 87 , 111901-1 - 111901-3 (2005). [35] J. Colchero, Procedures in Scanning Probe Microscopy, Chapter 1.3.3.12 ”Force Calibration”, pp. 133-138, Editors:.A. Engel, J. Frommer, H. Gaub, A. Gewirth, R. Guckenberger, M-H. Hara, W. Heckel and B. Parkinson, John Wiley & Sons (1998). [36] H.J. Butt, B. Capella and M. Kappl, Surface Science Reports 59 , 1-152 (2005). [37] More precisely: only for constant noise density the increase of total noise with will have a square root dependence. Note that if the noise density has essentially two ranges, one where 25