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Unformatted text preview: 1 AE 383 System Dynamics Lecture Notes 6 (July 4 th 2006) First Order Systems We will analyze certain combinations of the basic elements of mechanical and electrical systems. We have found analogies between elements. We will also encounter analogies between systems. Two classes of systems are found to be of fundamental importance: “First-order” and “Second order” systems. Mechanical First-order systems In the figure below some combinations of masses, springs and dampers are shown. These are all “first-order” systems. The differential equation relating input and output will have exactly the same form for each of these examples. Since these systems are mathematically identical, it will be efficient to study the general properties of the solution. Before we begin to write the equations of motion for the systems we should define coordinate systems and sign conventions. As an example, for the mass damper system shown in Figure (a) the positive direction for x o is chosen to the right. is chosen to the right....
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This note was uploaded on 10/24/2011 for the course AEE 463 taught by Professor Melin during the Spring '11 term at Middle East Technical University.
- Spring '11