https://scholar.ptuk.edu.ps/handle/123456789/102 2026-04-29T15:34:49Z https://scholar.ptuk.edu.ps/handle/123456789/931 Title: Exact Solution for Nonlinear Oscillators with Coordinate-Dependent Mass Authors: Abu-As'ad, Ata; Asad, Jihad Abstract: In this work, we aim to obtain an exact solution for a nonlinear oscillator with coordinate position- dependent mass. The equation of motion of the nonlinear oscillator under investigation becomes exact after making reduction of order. The obtained solution was expressed in terms of position and time. Initial conditions were applied, in addition to modified initial condition. Finally, fixed points where studied with their stability, and some plots describing the system where presented. Description: Simple oscillating systems are modeled in general as a mass attached to a spring (i.e., simple oscillators). The equation of motion describing such systems are obtained either using Newtonian mechanics or Lagrangian method, and it can be solved exactly in some simple cases. Unfortunately, no such systems present in the macroscopic world and this is due to dissipative forces that are always present in nature. Dissipative forces can be ignored if they have small effects, but in many cases they lead to damping oscillators. Linear oscillators are those that oscillate with one frequency and its motion is sinusoidal and periodic, for more information related to oscillators (simple and damped) we advise interested people to refer to some classical mechanics texts [5, 9, 10]. Nonlinear oscillators result in complex motion and there are mainly two important features for such systems: as the amplitude increases then the non linearity motion becomes more important, and in some cases, the frequency will change with amplitude. In real world one can find many such nonlinear oscillators and one has to note that coupled nonlinear oscillators are a subject founded in many branches of science as: biology, physics, and many others. In literature there are a lot of efforts paid on studying these systems [13, 16, 20]. An important example is the van der Pol oscillator which is an oscillator with nonlinear damping introduced in the 1920’s by Balthasar van der Pol (1889 - 1959).The van der Pol oscillator is considered as an example of an oscillator with nonlinear damping, energy being dissipated at large amplitudes and generated as low amplitude, and it attracts the attention of many researchers where many method have been applied in dealing with this oscillator either analytically using Homotopy analysis method (HAM) as in[4, 14]. Homotopy perturbation method (HPM) as in [18] or numerically using for example perturbation algorithm combining the method of Multiple Scales and Modified Lindstedt–Poincare Techniques as in [15], A domain decomposition method (ADM) as in [2, 8] and many other methods. Nonlinear oscillations have been of paramount importance in practical engineering, physics, applied mathematics, and several real-world requirements for many years. In literature, one can find many various analytical approaches for solving nonlinear systems, such as the iteration perturbation method [7], the homotopy perturbation method (HMP) [21], the variational method [17], and many other methods[6]. Interested researchers in this topic can refer to [12, 12] therein. In principle, the solution for such nonlinear oscillators is difficult to obtain analytically and researchers resort to use different numerical methods [1, 3, 21, 21]. In [21] the authors consider a nonlinear oscillator with coordinate-dependent mass, where they proposed a nonlinear oscillator with negative coefficient of linear term (see Eq. 3 in [21]) and apply the homotopy perturbation method to find an approximate period for their equation. In this paper we are going to find an exact solution for the above equation in section 2, while in section 3 the exact solution with modifying in the potential function will be presented and explained, an equilibrium points of the system and their stability with graphical simulation are given finally close the paper with a conclusion . 2022-04-22T00:00:00Z https://scholar.ptuk.edu.ps/handle/123456789/730 Title: CLASSICAL FEATURES OF THE MOTION OF A HEAVY BEAD SLIDING ON A ROTATING WIRE Authors: Abu-Asa'd, Ata Abstract: In this paper, we study the motion of a heavy bead sliding on a rotating wire. Our first step was constructing the classical Lagrangian of the system. Secondly, we derived the Euler- Lagrange equation (ELE). Thirdly, we solve the obtained ELE, which is a non-homogenous second order linear differential equation. Finally, by using MATLAB the equation is solved numerically for some selected parameters, and for specified initial conditions. Description: Lagrangian and Hamiltonian mechanics play an important role in solving a wide range of classical physical systems [1–3]. This branch of classical mechanics is based on scalars concepts (i.e. kinetic and potential energies). Classical mechanics books contain many such systems, and for more details one can refer to the three references [1–3] above. Solving such systems by this technique results in obtaining differential equations called equations of motions (i.e. Euler-Lagrange equations). These equations have to be solved for some given initial conditions either analytically or numerically in some cases. In under graduate level mathematician and physician students study an interesting course called ordinary differential equations (ODE). In this course students study techniques that enable them to solve many branches of ODE, see for example [4–7]. Numerical solution of ODE’s are powerful because they help scientists in solving many kinds of DE’s without the need of knowing their analytical solutions due to difficulty, or insufficient data. In literature one can find many numerical methods and techniques that has been considered [8–12]. In this paper, we choose an interesting physical system (a heavy bead sliding in a rotating wire). The importance of this example is due to the fact that the kinetic 2019-07-08T00:00:00Z https://scholar.ptuk.edu.ps/handle/123456789/701 Title: Project Review Solution-Directed Model: Using System Dynamics Modeling Authors: Eleyan, D Abstract: Project review is an essential part in project management. It consists of two main processes, Evaluation and Prediction. Evaluation aims to assess the performance achieved between successive reviews and portrays a clear picture about the project's current situation. Prediction takes the outcomes of the evaluation process and produces a forecast for the project's future. Project review needs criteria to evaluate the situation of the project. The standard criteria in project management are time, work, quality and resources. This research augments current techniques in project review by developing a method that incorporates the techniques of earned value and balanced scorecard. The integration of these techniques within the context of project review presents an innovative approach that should enable decision makers more accurately to predict the performance of a project Description: Project review is an essential part in project management. It consists of two main processes, Evaluation and Prediction. Evaluation aims to assess the performance achieved between successive reviews and portrays a clear picture about the project's current situation. Prediction takes the outcomes of the evaluation process and produces a forecast for the project's future. Project review needs criteria to evaluate the situation of the project. The standard criteria in project management are time, work, quality and resources. This research augments current techniques in project review by developing a method that incorporates the techniques of earned value and balanced scorecard. The integration of these techniques within the context of project review presents an innovative approach that should enable decision makers more accurately to predict the performance of a project 2010-01-01T00:00:00Z https://scholar.ptuk.edu.ps/handle/123456789/700 Title: Project Review in the Project Management Authors: Sawalhi, N; Eleyan, D Abstract: project review plays an essential role in the project management. Balanced scorecard and earned value are prominent project management techniques, which can be used to perform a project review. Each one of these techniques has its own weaknesses, which forbid it from performing an effective project review. This paper propose analytical framework to investigate these techniques and highlights the weaknesses for each. This framework has proposed a project review processes, project review techniques and project review criteria. Description: project review plays an essential role in the project management. Balanced scorecard and earned value are prominent project management techniques, which can be used to perform a project review. Each one of these techniques has its own weaknesses, which forbid it from performing an effective project review. This paper propose analytical framework to investigate these techniques and highlights the weaknesses for each. This framework has proposed a project review processes, project review techniques and project review criteria. 2010-01-01T00:00:00Z