A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analyzed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force and this allows us to approximate the original nonlinear differential equation…

In their comment, Qing-Yin and Pei derived another analytical approximate expression for the large-angle pendulum period, which they compare with other expressions previously published. Most of these approximate formulas are based on the approximation of the original nonlinear differential equation…

An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the generalized harmonic balance method in which analytical approximate solutions have rational form. This approach gives us not only a truly periodic solution but…

The analytical approximate technique developed by Wu et al. for conservative oscillators with odd nonlinearity is used to construct approximate frequency-amplitude relations and periodic solutions to the relativistic oscillator. By combining Newton's method with the method of harmonic balance, analytical…

A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analyzed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid…

An approximation scheme to obtain the period for large amplitude oscillations of a simple pendulum is analysed and discussed. The analytical approximate formula for the period is the same as that suggested by Hite (2005 Phys. Teach. 43 290), but…

Based on the results of the coupled-wave theory the diffraction efficiency is calculated for thick phase transmission holographic gratings taking into account the chemical processing of the recording material. Three effects of processing are considered: variations in the average refractive…

Silver halide sensitized gelatin (SHSG) is one of the most promising techniques for the fabrication of transmission holographic optical elements, achieving relatively high sensitivity of photographic material with the low scattering and high light stability of dichromated gelatin. In this…

The experimental results of diffraction efficiency as a function of the geometrical disposition of recording beams in bleached silver halide transmission thick-holographic gratings are presented. Two variables have been used to relate these results with certain geometric parameters. These variables…

A statistical model is used to study the formation of noise gratings in holograms and the mechanism that causes radiation scattering in them. The theoretical model presented describes noise scattering in terms of diffraction due to the high number of…