L	cantilever length
w	cantilever width
h	cantilever thickness
t	time
x	space coordinate (distance from the cantilever support)
$q\left(x,t\right)$	time-varying distributed load acting on the beam at a distance x from the support, per unit length
$W\left(x,t\right)$	time-varying deflection of the beam at a distance x from the support
$F_z$	shear forces acting on the element of the beam
$M_y$	bending moment acting on the element of the beam
$\rho$	density of the structural material
$A$	area of rectangular beam cross section
$I_z$	second moment of area of the rectangular cross section beam
E	Young’s modulus of the structural material
$\psi \left(t\right)$	temporal term solution of harmonic oscillation
$\mathsf{\Phi }\left(x\right)$	spacial term solution of harmonic oscillation
$c_{1,2,3,4}$	constants of spacial term solution of harmonic oscillation
$f_{0,n}$	natural (undamped) resonance frequency of mode n
${\omega }_{0,n}$	natural (undamped) radial resonance frequency of mode n
$z$	displacement of the one-degree-of-freedom microcantilever from the equilibrium position (z = 0)
$\dot{z}$	velocity of the one-degree-of-freedom microcantilever
$\ddot{z}$	acceleration of the one-degree-of-freedom microcantilever
$k_{\mathrm{eff}}$	effective spring constant of the microcantilever
$m_{\mathrm{eff}}$	effective mass of the nth resonant mode of the microcantilever
$m_c$	total mass of the microcantilever
$c$	intrinsic viscous damping coefficient
Q	quality factor
$\omega$	excitation frequency
$F_0{e}^{i\omega t}$	excitation harmonic force at $\omega$, with amplitude $F_0$
$A_0$	amplitude of the motion at $\omega$
$\varphi$	phase between the applied external force and the motion at $\omega$
${\omega }_{res}$	resonance frequency of the nth mode of intrinsically damped resonators
$m_0$	mass of the cantilever per unit length
$c_0$	intrinsic viscous damping coefficient per unit length
$F_{hydro}\left(x,t\right)$	time-varying distributed hydrodynamic load, acting on the beam at a distance x, per unit length
$m_A$	added mass by interactions with the surrounding fluid, per unit length
$c_V$	added damping coefficient by interactions with the surrounding fluid, per unit length
${\omega }_{R,n}$	resonance frequency of the nth mode of extrinsically damped resonators with added mass and damping
$Q_n$	quality factor of the nth mode
${\mathsf{\Gamma }}_{rect}{}^{\text{'}}\left(\omega \right)$	real part of the hydrodynamic load acting on a microcantilever with rectangular cross section
${\mathsf{\Gamma }}_{rect}{}^{″}\left(\omega \right)$	imaginary part of the hydrodynamic load acting on a microcantilever with rectangular cross section
${\rho }_f$	density of the fluid
$\eta$	viscosity of the fluid
$\delta$	thickness of the layer in which the velocity of the fluid drops by a factor of 1/e
$Re$	Reynolds number
a1, a2, b1, b2	Maali’s constants for ${\mathsf{\Gamma }}_{rect}\left(\omega \right)$
τ	integration time
${\sigma }_y\left(\tau \right)$	Allan deviation for time windows of duration τ
$f_i$	consecutive ith frequency measurements
$f_c$	nominal carrier frequency
$S_y\left(f\right)$	spectral density of frequency fluctuations
$S_{\Phi }\left(f\right)$	spectral density of phase fluctuations
$y_{rms}\left(f\right)$	measured root mean squared (rms) value of normalized frequency
${\mathsf{\Phi }}_{rms}\left(f\right)$	measured root mean squared (rms) value of normalized phase
$BW$	width of the frequency band in Hz
$P_{noise \left(1 Hz\right)}\left(f\right)$	power density in one single sideband due to phase modulation by noise, for a 1 Hz bandwidth (dBm/Hz)
$P_{signal }$	total power of the carrier (dBm)
$ℒ\left(f\right)$	single-sideband phase noise, the ratio of $P_{noise \left(1 Hz\right)}\left(f\right)$ to $P_{signal }$(dBc/Hz)
$f_h$	cut-off frequency of an infinitely sharp low-pass filter
$h_{-2}$, $h_{-1}$, $h_0$, $h_1$, $h_2$	constants to fit power-laws to random walk frequency noise, flicker of frequency, white frequency noise, flicker of phase and white phase noise, respectively
$A$, $B$, $C$, $D$, $E$	numerical constants for conversion between frequency (spectral densities) and time (Allan deviation) domains
$\delta f_{min}$	minimum measurable frequency shift
LoD	limit of detection
$\delta f_0$	shift in the natural (undamped) resonance frequency
$\delta f_R$	shift in the damped resonance frequency of microcantilevers with added mass and damping;
$\delta k_{\mathrm{eff}}$	infinitesimal change of the effective stiffness of the cantilever induced by the adsorbate
$\delta m_{\mathrm{eff}}$	infinitesimal change of the effective mass of the cantilever induced by the adsorbate
$\delta m_A$	infinitesimal change of the added mass induced by the fluid
$\delta \eta$	infinitesimal change in the viscosity of the fluid
$\delta {\rho }_f$	infinitesimal change in the density of the fluid
S	sensitivity
$S_{mass,vac}$, $S_{mass,fluid}$	mass sensitivity in vacuum and in fluid
$S_{viscosity,fluid}$	viscosity sensitivity
${\tau }_A$, ${\dot{\tau }}_A$	applied shear stress and shear stress rate
${\delta }_D$, ${\dot{\delta }}_D$	shear strain and shear strain rate of a viscous dashpot
${\delta }_S$, ${\dot{\delta }}_S$	shear strain and shear strain rate of an elastic spring
${\delta }_{tot}$, ${\dot{\delta }}_{tot}$	shear strain and shear strain rate of the spring-dashpot series
$G_0$	elasticity constant of the fluid
$\lambda$	characteristic relaxation time of the fluid
$\omega$	frequency of the applied shear stress and induced total strain response
$\phi$	phase between applied stress and total strain response
${\tau }_0$	amplitude of the shear stress
${\delta }_0$	amplitude of the total strain response
$G^{*}$	dynamic elastic modulus
$G^{\prime }$, $G^{″}$	elastic and viscous parts of the dynamic elastic modulus
${\eta }^{*}$	complex dynamic viscosity
${\eta }^{\prime }$, ${\eta }^{″}$	viscous and elastic parts of the dynamic viscosity
$\left|\frac{H\left(\omega \right)}{H_0}\right|$	general ratio of amplitudes of the transfer function