<![CDATA[Spring mechanical vibration motion system with a damped degree of freedom and influenced by external forces, is mathematically expressed as an ordinary differential equation of order of two linear constant coefficients that are not homogeneous. If an external force acts on a stationary system expressed as a continuous function f(t) for any time t, then the system will experience mechanical vibrational motion which mathematically the equation of motion can be expressed as a superposition. The equation consists of as a solution to a homogeneous form with mechanical vibrations as a solution to a particular form. In terms of the particular solution this article will show a mathematical way when f(t) is a continuous function section by part which is defined at an interval, such that the mechanical vibration motion equation is at the same time a special solution of the equation the mechanical vibration system. Keywords: Vibration, Impulse Functions, ConvolutionMSC2020: 34A37]]>
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