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The reason for this paper is that most of the modern undergraduate textbooks on linear system analysis present the mechanical network with no proof or justification that it will lead to the correct answers. In most textbooks a procedure for writing down the system network is given and then the method for writing down the system equations is shown. Any connection with previous metholds of solving mechanics problems seems to be ignored. In this paper the mechanical network is presented as a natural abstraction of the free-body diagram used in mechanics. The major advantages of this technique are: 1) it may be presented quickly, 2) it is easily understood by the student, and 3) it demonstrates the physical basis for the network approach.