Number Of Resonant Frequencies Research Articles

Modèles intégro-différentiels en électrodynamique linéaire des continus

In this paper, we propose a purely macroscopic theory of the complex refractive index based on dielectric models defined by constitutive equations which are linear differential equations in the electric field, the polarization vector and their time derivatives up to the orders m and n respectively. Meixner's thermodynamics restrictions impose 0 ≤ n — m ≤ 2 and a set of inequalities on the constitutive coefficients. In the special case m = 2, n — 4, the expression of the complex refractive index shows the existence of two optical resonances. In the general case, it seems that the number of resonance frequencies is the greater integer contained in n/2

Zur Theorie der erzwungenen Schwingungen des symmetrischen Kreisels

The object of this paper is to give a theory of the experiments described in the foregoing paper. The applied system of non-linear differential equations byA. Foppl is first solved approximately for ‘small angles’, that means small deviations of the axis of the gyroscope from the verticaldirection, the cases without and with consideration of damping force being discussed separately. All characteristic features of the motion observed in the experiments are explained.—After that, an exact particular solution is given for the case of a circular periodic force. An approximate calculation is carried out for the case of a periodic elliptical force acting on afast rotating gyroscope. The solution contains an infinite number of resonance frequencies (subharmonic resonances and resonances with sums and differences of the forced and natural frequencies).