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In one cycle there is a positive variation from equilibrium, a return to equilibrium, then a negative variation, and return to equilibrium. This relationship is often described in terms of the sine wave, and the frequency referred to is that of an equivalent sine-wave variation in the ...
Equation (I.1.5) reflects the fact that the FT is a unitary transform and as a consequence, the norm (|⋅|2) is preserved when shifting from the t domain to the f domain and vice versa. These equations show also that |s(t)|2 is an energy time density, while |S(f)|2 is an...
Equation 5.20 can be modified to display this role: (12.9)σd/σa=∑=[(3.2/Δ)+0.9](α+μ)+σb[1−(μr/α)(1−r)−1]. It should also be noted that relatively brittle wires may actually break on contact with the capstan where the tensile bending stress adds to the drawing...
In a self-excited sine-wave generator, frequency division is achieved by synchronizing the generator’s frequency with a subharmonic oscillation of the frequency of the external periodic signal by means of the locking effect. In a regenerative frequency divider for sine waves, the periodic signal of...
Equation (7.3) gives the frequency response in polar form. For completeness, recall the transformations between polar and rectangular forms (i.e., for converting real and imaginary parts to magnitude and angle, and vice versa): Going the other way from polar to rectangular (using Euler's formu...
Rearranging the above equation to solve for frequency error:Frequency error (fe) = signal frequency (fs) * frequency accuracy (fa). Additional InformationExamples:Consider a case in which you are measuring a precise 100kHz sine wave, using a device with a frequency accuracy of 25 ppm. The fr...
This will be followed by a discussion of how to establish frequency response functions from base excitation data. 6.6.1.1 External force excitation The matrix differential equation of motion of a constrained (grounded), linear elastic structure is (6.6-1)[m]{w¨(t)}+[c]{w˙(t)}+[k]{w...
In this equation, x(t) is the displacement of the body as a function of time. X, which dictates the magnitude of the response, is a constant of integration that must be determined from the initial conditions and is given by (8.5)X=x0sinφ The damping ratio ζ is given by two equat...
Without loss of generality, sinceN> > 4 and Δf < <f0, and supposeφ0 = 0, such in-equation of 0 < cos[(2N + 1)πΔfTs] < 1 can be fulfilled. We have $$ \left\{\begin{array}{c}{f}_0<{f}_{\mathrm{meas}}\le {f}_0+\Delta f,\kern0.5em...