Resonance natural frequency

The Weissenbetg Rheogoniometer is well suited to research on homogeneous viscoelastic fluids and elastic melts. For oscillatory shear a second motor-drive mechanism is added. This allows the use of 60 frequencies in the range of 7.6 x 10 to 40 Hz at ampHtudes between 2 x 10 and 3 X 10 rad. An electronic circuit improves the precision of oscillatory measurements, particularly at frequencies neat the natural resonance frequency of the instmment itself (298). 

Multiples of running frequency Harmonic resonance Multiples of component natural frequencies (rotor casing, foundation, bearing housing, diaphragms, etc.)... 

Quasi-resonant converters utilize an T-C tank circuit, which rings at its natural resonance frequency in response to a step change in its terminal voltage or current. The tank circuit is placed between the power switch and the transformer and/or the transformer and the output filter. 

Next, decide the natural resonance frequency of the tank circuit. For the available quasi-resonant controller ICs on the market, the range is between 1 and 2 MHz. This limit should be considered the maximum limit within conventional QR designs. So 1 to 1.5 MHz is a typical choice. Lower frequencies can be used and some efficiencies can be gained. The equation for the resonance frequency is... 

A number of studies (Kristoff and Guilbault 1983 Milanko et al. 1992) have investigated the use of coated and uncoated piezoelectric crystals in the detection and analysis of diisopropyl methylphosphonate in air samples. Piezoelectric crystals have a natural resonant frequency of oscillation that can be utilized to detect... 

The most simple, but general, model to describe the interaction of optical radiation with solids is a classical model, due to Lorentz, in which it is assumed that the valence electrons are bound to specific atoms in the solid by harmonic forces. These harmonic forces are the Coulomb forces that tend to restore the valence electrons into specific orbits around the atomic nuclei. Therefore, the solid is considered as a collection of atomic oscillators, each one with its characteristic natural frequency. We presume that if we excite one of these atomic oscillators with its natural frequency (the resonance frequency), a resonant process will be produced. From the quantum viewpoint, these frequencies correspond to those needed to produce valence band to conduction band transitions. In the first approach we consider only a unique resonant frequency, >o in other words, the solid consists of a collection of equivalent atomic oscillators. In this approach, coq would correspond to the gap frequency. 

In general for small P /Ph ratios, with (the resonant bubble radius), oscillations take place at approximately the excitation frequency (Fig. 2.21). For R > Rj, bubble oscillation has a strong component of its ovm natural resonant frequency (Fig. 2.22). However for very small bubbles, R. << R, transient conditions are attained as P increases beyond Pjj (Fig. 2.23, P = 4 and 10 atm). It may be that as... 

Thus on applying rapidly reversing charges to a piezoelectric material fluctuations in dimensions will be produced. This effect can be harnessed to transmit ultrasonic vibrations from the crystal section through whatever medium it might be in. However it is not possible to drive a given piece of piezoelectric crystal efficiently at every frequency. Optimum performance will only be obtained at the natural resonance frequency of the particular sample - and this depends upon its dimensions. In the... 

Once the tube scanner was invented (Binnig and Smith, 1986), it soon became the primary choice of piezo scanners in STM. Its small size and high natural resonance frequency make the mechanical design and vibration isolation much easier. Currently, most of the commercial STMs as well as home-made STMs use tube scanners. 

The anisotropic nature of the dipolar, quadrupolar and chemical shift anisotropy interactions requires that the isotropy of molecular orientation relative to the applied magnetic field be broken in order to allow their direct observation in terms of shifts in the frequencies of resonances.20,32,38 40 For high resolution NMR studies this has meant, thus far, that some degree of alignment of the molecule needs to be established. Almost all molecules will align to a small extent due to the anisotropy of their magnetic... 

When the room is highly idealized, for instance if it is perfectly rectangular with rigid walls, the reverberant behavior of the room can be described mathematically in closed form. This is done by solving the acoustical wave equation for the boundary conditions imposed by the walls of the room. This approach yields a solution based on the natural resonant frequencies of the room, called normal modes. For the case of a rectangular room shown in figure 3.3, the resonant frequencies are given by [Beranek, 1986] ... 

Here, the electrons on each molecule create transient dipoles. They couple the directions of their dipoles to lower mutual energy. "Dispersion" recognizes that natural frequencies of resonance, necessary for the dipoles to dance in step, have the same physical cause as that of the absorption spectrum—the wavelength-dependent drag on light that underlies the dispersion of white light into the spectrum of a rainbow. 

As described in earlier sections, any two material bodies will interact across an intermediate substance or space. This interaction is rooted in the electromagnetic fluctuations— spontaneous, transient electric and magnetic fields—that occur in material bodies as well as in vacuum cavities. The frequency spectrum of these fluctuations is uniquely related to the electromagnetic absorption spectrum, the natural resonance frequencies of the particular material. In principle, electrodynamic forces can be calculated from absorption spectra. 

A detailed analysis of electroacoustic quartz crystal impedance was presented by Doblhoffer and Soares [63] to study the viscoelastic properties of overlayers [64] who showed that the resonance frequency of a crystal electronic oscillator is very close to a quartz crystal natural resonant frequency. 

Quartz Crystal Microbalance. The shift Av (Hz) from the natural resonant frequency of the "unloaded" quartz v0 (Hz it depends on the "cut" of the quartz crystal) as molecules are adsorbed onto the crystal can be used to measure small increase of mass Am (g). The Sauerbrey95 equation (1959) is... 

The piezoelectric crystals are patterned with two excitation electrodes (electronic surface films) on their opposite sides. Due to the converse piezoelectricity phenomenon, when -> alternating voltage is applied to the attached electrodes mechanical oscillations occur within the crystal lattice. These oscillations are stable only at the natural resonant frequency of the crystal. 

Tip life can be best extended by polishing the tip — its radiation surface only — with abrasive paper or cloth. The face should never be lathed as too much material will be removed and, taking into account that the tip is a part of a finely tuned resonant body, the removal of material will shorten the tip length and thus raise the natural resonant frequency. 

This relaxation time is very important as it is associated to the natural linewidth . However the time constant T2 cannot be directly quantified, because there are other factors which also contribute to the dephasing process. These factors are experimental factors and are related to the inhomogeneity of the Bo field in the sample. As different molecules in the sample experience slightly different Bo fields, their precession frequency (and resonance frequency, vo) is slightly different, thus the dephasing is faster, T2 becomes shorter, and the actual line in the spectrum is artificially broadened. 

The lowest level of abstraction, here called the geometry level, is the closest to physical reality, in which the physics is described by partial differential equations. This level is the domain of finite-element, boundary-element or related methods (e.g., [7-9]). Due to their high accuracy, these methods are well suited for calculating, for example, the distribution of stresses, distortions and natural resonant frequencies of MEMS structures. But they also entail considerable computational effort. Thus, these methods are used to solve detailed problems only when needed, whereas simulations of complete sensor systems and, in particular, transient analyses are carried out using methods at higher levels of abstraction. 

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