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Written for senior-year undergraduates and first-year graduate students with solid backgrounds in differential and integral calculus, this paper is oriented toward engineers and applied mathematicians. Consequently, this paper should be useful to senior-year undergraduates the finite element method . The scaled direct approach is adopted for this purpose and each step in the finite element solution process is given in full detail. For this reason, all students must be exposed to (and indeed should master). This paper provides the general framework for the development of nearly all (nonstructural) finite element models. The finite element method of analysis is a very powerful, modern computational tool. Applications range from deformation and stress analysis of automotive, aircraft, building, and bridge structures to field analysis of beat flux, fluid flow, magnetic flux, seepage, and other flow problems. This paper presents study and comparison of numerical methods which are used for evaluation of dynamic response. A Single Degree of Freedom (SDF)-linear problem is solved by means of Newmark’s Average acceleration method , Linear acceleration method , Central Difference method [6,7] with the help of MATLAB. The advantages, disadvantages, relative precision and applicability of these numerical methods are discussed throughout the analysis.