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 Recognitions: Gold Member Homework Help Science Advisor Staff Emeritus Section 1.1 Rationale The first thing to establish is why one would want to learn how to model dynamic systems, and why one would put such a diverse array of such systems all together in the same discussion. The first answer comes almost instantly upon asking the question: System models are valuable heuristic devices to estimating the response of engineering systems before they are built. This enables engineers to predict whether or not a system is up to the task for which it is designed before any precious material resources are committed to the project. Second, there is a need to educate engineers in the analysis of systems that components of different types, such as mechanical, electrical, thermal, and hydraulic (the four types that will be discussed in this thread). It is essential that a mechanical engineer, for instance, knows how his system will interface with electrical components, such as controllers. It may even be desirable that he learn how to design controllers himself. Neither does an electrical engineer work in a vacuum. Any electrical system generates heat, and the engineer designing the system must know how to include the thermal aspect of his system into the system model. Third, the equations that describe the different types of systems are strikingly similar, and learning how to analyze one type automatically gives the student the ability to analyze the others. For instance, consider the equation: c1(d2u/dt2)+c2(du/dt)+c3u=0 The above equation models a damped mechanical oscillatorif: u=x, the displacement of the oscillator from equilibrium c1=m, the mass of the oscillator c2=b, the damping coefficient c3=k, the spring constant. The same models an LRC circuit if: u=q, the charge on the capacitor c1=L, the inductance c2=R, the resistance c3=1/C, the reciprocal of the capacitance. As we shall come to see, the above equation has analogs in rotational mechanical systems, thermal systems, and hydraulic systems as well. Given both the necessity of analyzing systems outside of one's explicit discipline, and of the mathematical similarity of such diverse system models, it only makes sense to include discussion of the various types all in one place. edit: fixed superscript bracket