Amplitude ratio

In the absenee of damping the amplitude ratio beeomes infinite at tu =... 

By substituting these into the differential equations, two equations for the amplitude ratio, A1/A2, can be found ... 

Fig. 26—Amplitude ratio for line contacts ( , 0, O) and point contacts ( , , ), taken from Ref. [59], (a) Transversal roughness (b) isotropic roughness and (c) longitudinal roughness.

Vary the magnitude of the frequency in the forcing disturbance and study its effect on the phase angle and amplitude ratio of the system. Use the information to construct the Bode diagram for the system, i.e., plots of phase angle and amplitude ratio versus frequency. 

With gain or phase margin, calculate proportional gain. Can also estimate the peak amplitude ratio, and assess the degree of oscillation. The peak amplitude ratio for a chosen proportional gain. Nichols chart is usually constructed for unity feedback loops only. 

The photodecomposition of isopropyl alcohol on silica gel produces a seven-line spectrum having a hyperfine separation of 20.7 G and an amplitude ratio of 1 6.7 20.2 31 21.1 7.4 1.5 (68). This spectrum was attributed to SiOCMe2 formed from the ether surface groups. In addition to this spectrum the spectrum of the methyl radical was also observed. Irradiation of adsorbed tert-butyl alcohol produced a three-line spectrum which was attributed to SiOMe2OCH2 (68). Apparently the splitting from the methyl protons was too small to be observed. 

Basic data of the thickness of the adsorbed layer, t, and the refractive index, n, of the adsorbed layer were calculated from the experimental data of the phase difference, A, and the azimuth angle, i >, of the amplitude ratio by computer. The computer program proposed by McCrackin (10) was used. 

The Bode diagram (Figure 7j) shows plots for GW, G2(s) and G(s) as amplitude ratio against frequency. Only the asymptotes (Section 7.10.4, Volume 3) are plotted. 

CVSF = conduction velocity of slow = motor fibers dSCV = distal sensory nerve conduction velocity MAP k/a = proximal to distal amplitude ratio of muscle action potentials MMCV = maximal motor nerve conduction velocity MNCV = mixed nerve conduction velocity RL = residual latency of motor nerve conduction... 

Figure 4.15. Effect of chloroquine on linear pBR322 DNA. Torsion constant (top) and fluorescence amplitude ratio of the slow (intercalated) and fast (free) components in the decay of the ethidium fluorescence intensity (hottom) versus ln(added chl/bp). The DNA is present in 0.1 M NaCl, 10 mM Tris, 10 mM EDTA, pH 8.5, at 20°C, and ethidium is present at 1 dye per 300 base pairs. The points at the left of the figure apply for zero added chloroquine. The best-fit...

K e = 22 x 10s M Linear pBR322 remains uniform and independent of added chloroquine up to chl/bp = 25. The decline in the amplitude ratio at large chl/bp is due to competition between ethidium and chloroquine for binding sites on the DNA and is used to determine the chloroquine binding constant. 

These are all complex variables since the susceptibilities are complex. We obtain the amplitude ratio at the top (exit) of the layer, X, in terms of that at the bottom (entrance),X.-... 

The variable z is the depth above the depth w at which the amplitude ratio is the known value X, in effect the thickness of the layer or lamella. We know the amplitude ratio deep inside the crystal here, both the diffracted intensity and the incident amplitude are zero, but since their ratio must always be <1 then the amplitude ratio X=D f, ID q ( z ) must also be zero. Using the above we may derive the reflectivity of a thick crystal,... 

Thus we calculate the reflectivity of a whole layered material from the bottom up, using the amplitude ratio of the thick crystal as the input to the first lamella, the output of the first as the input to the second, and so on. At the top of the material the amplitude ratio is converted into intensity ratio. This calculation is repeated for each point on the rocking curve, corresponding to different deviations from the Bragg condition. This results in the plane wave reflectivity, appropriate for synchrotron radiation experiments and others with a highly collimated beam from the beam conditioner. 

Instead of considering the dispersion surface as a variable and the reciprocal lattice as invariant, it is usually easier to consider the reciprocal lattice as the variable. Then equation (8.30) determines the variation of the amplitude ratio of the reflected and transmitted components as the wavefield propagates through the crystal. The ratio R characterises a particular tie-point on the dispersion surface and if R varies the tie-point must migrate along the dispersion surface branch. This results in a change in the intensity of the transmitted and diffracted... 

The first term on the right-hand side of eqn. (11) decays away and, after a time approximately equal to 5t, the second term alone will remain. Note that this is a sine wave of the same frequency as the forcing function, but that its amplitude is reduced and its phase is shifted. This second term is called the frequency response of the system such responses are often characterised by observing how the amplitude ratio and phase lag between the input and output sine waves vary as a function of the input frequency, k. To recover the system RTD from frequency response data is more complex tnan with step or impulse tests, but nonetheless is possible. Gibilaro et al. [22] have described a short-cut route which enables low-order system moments to be determined from frequency response tests, these in turn approximately defining the system transfer function G(s) [see eqn. (A.5), Appendix 1]. From G(s), the RTD can be determined as in eqn. (8). 

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