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In this study, the numerical solution of the ordinary kind of differential equation for a simple pendulum with large-angle of oscillation was introduced to obtain the time period. The analytical solution is obtained in terms of elliptic functions, and numerical solution of the problem was achieved by using two numerical quadrature methods, namely, Simpson?s 3/8 and Boole?s method. The period of a simple pendulum with large angle is presented; a comparison has been carried out between the analytical solution and the numerical integration results. In the case of error analysis, absolute and relative errors of the problem have been presented. A numerical algorithm has been developed by Matlab software 2013R and used for analyzing the result. It is established that the results of the comparison guaranty the ability and the accuracy of the present method.

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.

The paper describes the X-ray attenuation in materials according to their atomic number, using six different materials from low atomic number to higher atomic number, Iron (Fe-26) as low atomic number, silver (Ag-47), tin (Sn-50), platinum (Pt-78), gold (Au-79) and lead (Pb-82) as high atomic number. Using the data were taken from the NIST Standard Reference Database 126. From the J. H. Hubbell and S. M. Seltzer work, a table of contents was used. Whereas The mass attenuation coefficient for the above six elements was taken and compared with each other.

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