Damped resonance

In Fig. 62a we demonstrate by solid lines the absorption dependence (463) in the R-band calculated for liquid H2O (a) and liquid D20 (b) at temperature 22.2°C the ordinates are fitted in such a way that the magnitude of the Astr(v) peak is equal to 1. The chosen dimensionless collision frequency Y is chosen 0.6 for H20 and 1.32 for D20, with correspondingly the lifetimes xstr 0.071 and 0.036 ps. These curves exhibit a damped resonance, since the fitted lifetime xstr is very short they resemble the dashed curves g(vstr) in Fig. 60d and 61d. 

As expected, the intermediate case, i.e. strongly damped resonant transitions, is most difficult to treat accurately. 

Orifice plates are often applied to damp resonant oscillations in existing installations. Their effect is based on frictional losses. Therefore orifice plates shall be placed at pipe positions with a maximum of flow pulsation. 

Tani discusses the dynamics of displacive ferroelectrics and obtains a damped-resonant response. 

The dielectric response shown in Fig. 43a resembles a highly damped resonance curve with the peak frequency v m located in the THz region. The s// L(v) spectra in Fig. 43b are compared for y =2.8 (curve 1) andy L = 2 (curve 2), for which the lifetimes t are respectively 0.089 and 0.14 ps. For greater y L (i.e., for shorter lifetime t l) the absorption curves become shallower. The frequency vj m of the loss-peak intensity, marked in Fig. 43b by the vertical lines, agrees with the estimate (193) only approximately. It is worthwhile to emphasize the following ... 

The discussion in this section is applicable to any polar solid (i.e., one that has a permanent dipole) in which relaxation of the permanent dipoles occurs. In principle this approach could be applicable to piezoelectric and ferroelectric solids at temperatures above their transition temperature as well (see next chapter). However, the same response, as shown in Fig. 14.11, can also occur as a result of heavily damped resonance. This is easily seen in Fig. 14.7a as /. which is a measure of the damping, increases, the resultant resonance curves become flatter. Experimentally it is not easy to distinguish between the two phenomena. 

The electrical characteristics of a QCM are well represented by a simple RLC damped resonator equivalent circuit [8], termed the Butterworth-Van Dyke equivalent circuit (Figure 11). 

FIGURE 14.5 Pressure step response computed from the model (tq = 2, Tsm = 5, and G = 10). The step was produced by altering the initial condition for pressure at t = 0. Note that pressure and resistance are 180° out of phase. A damped resonant response is evident with a resonant frequency of 0.1 Hz. 

Figure 4.17 Shift and change of the resonance frequency of a quartz crystal microbalance, real part of the admittance versus frequency, /q, Wq, resonance frequency and full width at half maximum (FWHM) of the initial gold electrode,/j, w, resonance frequency and FWHM of a gold electrode after formation of a rigid and smooth surface film (no damping), resonance frequency and FWHM of a gold electrode after formation of a viscoelestic and/or rough surface film (strong damping).

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