A Numerical Quadrature Solution for Time Period of Simple Pendulum Under Magnetic Action

Abstract

In the present study, a simple approximation expression is given for the relationship between the period and amplitude of a simple pendulum under magnetic action. The analytical solution presented for the given problem. Two numerical quadrature methods Simpson's and Boole's method were utilized to demonstrate a new approximation of the problem. The results of the numerical quadrature have been compared to the exact solution. Absolute and relative mistakes of the problem have been presented. The Matlab program 2013R has created a numerical method that is used to analyze the outcome, It has been determined that the comparison's outcomes attest to the method's suitability and correctness. Moreover, the results show that numerical solution is suitable for the problem.

Numerical Solution for Time Period of Simple Pendulum Under Magnetic Field

“…There are many numerical integration methods to evaluate composite integrals; in this paper, we use two numerical quadrature methods, Simpsons 3/8 method, and Boole's method [16,[30][31][32][33][34].…”

“…They have several approximation methods which are different from each other [8][9][10][11][12]. Many numerical methods have been applied for solving linear and non-linear differential equations [13][14][15][16]. One of the most popular physical models encountered in undergraduate courses is the simple pendulum and the differential equation describing its motion [14,15,[17][18][19][20][21][22][23][24][25].…”

“…One of the most popular physical models encountered in undergraduate courses is the simple pendulum and the differential equation describing its motion [14,15,[17][18][19][20][21][22][23][24][25]. Historically, the equation arises when studying the oscillations of a pendulum clock, but also appears in various other areas of physics, since problems often can be reduced to a differential equation similar to that describing the pendulum [16,21,22,26,27]. The exact solution to the equation of motion of the undamped pendulum is well known in the literature and involves the Jacobi elliptic functions [15,21,22,28].…”

On the Numerical Solution for Two Dimensional Laplace Equation with Initial Boundary Conditions by using Finite Difference Methods

“…is called Poisson's equation. This equation has been extensively studied by mathematicians and physicists [5,16,37]. In the present study, we consider Laplace equation under initial boundary conditions, as follow:…”

“…Many methods for the exact solution have been presented for solving Differential equations [10][11][12][13][14]. Although the exact solution of some types of DE can be found [1][2][3]5]., many numerical methods have been applied for solving linear and non-linear differential equations [15,16]. In the case of Partial differential equations, much attention has been given in the works to test the reliability and accuracy of the approximation and numerical techniques [17].…”