A new analytical approximate expression for the period of the simple pendulum is obtained by using a heuristic but pedagogical derivation. This formula depends on two parameters obtained by comparing term-by-term the power-series expansions of the approximate and exact expressions…

We have determined “effective” Bethe coefficients and the mean excitation energy of stopping theory (I-value) for multiwalled carbon nanotubes (MWCNTs) and single-walled carbon nanotube (SWCNT) bundles based on a sum-rule constrained optical-data model energy loss function with improved asymptotic properties.…

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…

The classical problem of deflection of a cantilever beam of linear elastic material, under the action of an uniformly distributed load along its length (its own weight) and an external vertical concentrated load at the free end, is experimentally and…

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…

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…

A closed-form approximate expression for the solution of a simple pendulum in terms of elementary functions is obtained. To do this, the exact expression for the maximum tension of the string of the pendulum is first considered and a trial…

In this paper, we analyze the relation between the surface curvature of an isolated charged conductor and resultant electrostatic potential. The study will be performed for a long conductor with uniform cross section. It will be demonstrated by geometric arguments…