Resonating angular frequency

The basis of the RFR technique is that a probe photon at a resonance angular frequency oares can be absorbed under the resonance condition... 

In the case of a purely elastic deposited layer the viscosity coefficient is equated to zero and the resonant angular frequency after mass loading co, can be found from the expression ... 

Ot resonating angular frequency of the optical mode of lattice vibration transverse waves, y attenuation constant, co angular frequency... 

There are two kinds of popular relaxation times, spin-lattice relaxation time and spin-spin relaxation time T2. Dipolar interactions between nuclear spins in polymers predominantly govern relaxation times. According to the Bloembergen-Purcell-Pound (BPP) theory [5], and T2 vary against the correlation time (t ) of the molecular motion, as indicated in Figure 8.1. Tj has the minimum at = 1/ , in which CO is the resonance angular frequency. If the Tj minimum is observed, the absolute correlation time of the molecular motion can be obtained. On the other hand, T2 decreases with an increment of From these behaviors of the relaxation times, the dynamics of polymer chain can be obtained. 

Eigure 1 shows a simple seismometer that will detect vertical ground motion. It consists of a mass suspended from a spring. The resonance angular frequency of the mass-spring system is (Do = where coq = 2jiITq and Tq is the... 

Here E(t) denotes the applied optical field, and-e andm represent, respectively, the electronic charge and mass. The (angular) frequency oIq defines the resonance of the hamionic component of the response, and y represents a phenomenological damping rate for the oscillator. The nonlinear restoring force has been written in a Taylor expansion the temis + ) correspond to tlie corrections to the hamionic... 

Figure B2.5.13. Schematic representation of the four different mechanisms of multiphoton excitation (i) direct, (ii) Goeppert-Mayer (iii) quasi-resonant stepwise and (iv) incoherent stepwise. Full lines (right) represent the coupling path between the energy levels and broken arrows the photon energies with angular frequency to (Aco is the frequency width of the excitation light in the case of incoherent excitation), see also [111].

Figure 6.1 Nonlinear optical responses, (a) Second-order SF generation, the transition probability is enhanced when the IR light is resonant to the transition from the ground state g to a vibrational excited state V. CO is the angular frequency of the vibration, (b) Third-order coherent Raman scheme, the vibrational coherence is generated via impulsive stimulated...

In electrical circuits die above analysis can be applied by adding an alternating voltage of angular frequency co in serts with the circuit -shown jp Bg. 3. However, the results in (bis case are normally less dramatic. In fact the condition of resonance, at which... 

A useful equivalent way of looking at the resonance phenomenon is in a coordinate system rotating with the angular frequency of Hi about the z axis which coincides with the direction of Ho, the applied static field 44)-In this rotating coordinate system the effective fields are Hi, which is now time-independent, and a field Ho — u/y, where w is the angular frequency... 

Since the s orbitals do not have orbital magnetic moment, g — ge — 2.0023. A is an eneigy, which in SI units is expressed in joule. Sometimes it is convenient to have it expressed in frequency units, i.e. in hertz or in radians per second, and then we have to divide A by h or by h (ft = h/2n). In magnetic resonance there often is a factor 2jt which complicates life. The frequency which we refer to is the angular frequency or the Larmor precession frequency. Such frequency co is... 

Fig. 7.1. Two equivalent ROA experiments involving Stokes vibrational Raman scattering at angular frequency oj — ojv in incident light of angular frequency oj far from resonance, a The ICP ROA experiment measures JR - JL, where JR and JL are the scattered intensities (shown here as unpolarized) in right- and left-circularly polarized incident light, respectively, b The SCP ROA experiment measures hi-h., where Jr and JL are the intensities of the right- and left-circularly polarized components, respectively, of the scattered light using incident light of fixed polarization (shown here as unpolarized)...

Figure 2.38 illustrates that in the case of an ionic solid the optical mode of the lattice vibration resonates at an angular frequency, co0, in the region of 1013Hz. In the frequency range from approximately 109-10nHz dielectric dispersion theory shows the contribution to permittivity from the ionic displacement to be nearly constant and the losses to rise with frequency according to... 

A major use of high-quality pot-core inductors is in combination with capacitors in filter circuits. They were once extensively used in telephone systems but solid state switched systems have replaced them. The soft MnZn and NiZn ferrite systems are dominant for pot-core manufacture, although metal dust cores are used for certain applications. The important design principles can be understood by reference to a simple series LCR circuit to which a sinusoidal voltage U of angular frequency co is applied (Fig. 9.46). The circuit impedance Z = R+](coL - 1/coC) is a minimum when ojZ, = /<<>C. Thus the resonant frequency o0 is given by... 

Here, co is the angular frequency of the bending mode involved in the Fermi resonance. Next, within the exchange approximation [69], the coupling Hamiltonian (220) involved in the Fermi resonance is... 

Besides, the ff are the coupling parameters involved in the Fermi resonances expressed as angular frequencies, whereas the Af are the angular frequency gap ... 

---