The Doppler effect is a phenomenon which relates the frequency of the harmonic waves generated by a moving source with the frequency measured by an observer moving with a different velocity from that of the source. The classical Doppler effect…

The asymptotic behaviours for small and large amplitudes, A, of the period for a nonlinear oscillator, where the square of the angular frequency depends quadratically on the velocity, are obtained. These asymptotic expressions are compared with the exact period, T(A),…

Two Lidstedt-Poincaré perturbation based methods are used to solve the nonlinear differential equation of a nonlinear oscillator having the square of the angular frequency depends quadratically on the velocity. Mickens published two interesting papers [1, 2] about this oscillator and…

The first-order harmonic balance method via the first Fourier coefficient is used to construct two approximate frequency–amplitude relations for a conservative nonlinear oscillatory system in which the restoring force has an irrational form. This system corresponds to the motion of…

Obtaining holographic volume gratings with high diffraction efficiencies that can be used under white light has been a serious problem for the polyvinyl alcohol-acrylamide-based photopolymers developed by other researchers. In this paper we propose to eliminate the residual monomer in…

Bleached holograms are one of the most interesting techniques used to produce phase holograms of high quality on photographic emulsions. Of particular interest is the method of fixation-free rehalogenating bleaching. Using Kogelnik's coupled-wave theory we shall obtain information about the…

Kogelnik's coupled-wave (CW) theory has been used for decades to predict the diffraction efficiency of volume diffraction gratings. Although this theory has been applied with success to volume diffraction gratings recorded under a great variety of experimental conditions, its predictions…

The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a simple pendulum, and an approximate expression for its period is obtained. Only one iteration leads to high accuracy of the solutions…

We present three ways of treating the problem of fluid flow in a hollow cylinder. One method involves a differential equation, and the other two involve more physical insight. We discuss the relative advantages of each method., The following article…

Cables are one of the common structures studied in a first-year engineering mechanics course (statics), since the flexible cable is one of the usual methods of supporting loads. For example, the suspension bridge has been used for many centuries and…