1.SecondOrderSystems

1.SecondOrderSystems - Second Order Systems 1. Governing...

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Second Order Systems 1. Governing equations All mechanical systems are governed by Newton's laws of motion, the most familiar of which is Fm dx dt = 2 2 ( l ) where m is the mass and x is the displacement and the F components are the forces acting on the system. Since the forces are usually proportional to x and d x /d t , eq.(1) shows that such mechanical systems are always second order. These are called linear second order systems as long as no nonlinear forces proportional to x 2 , (d x /d t ) 2 ,... are disturbing the system. This turns out to be of great practical significance, since almost all dynamical mechanical systems are indeed linear second order, so that knowledge acquired about one system can be readily transferred to another problem. [Brief translation: Learn this stuff, and you will find it useful for more than just this lab/report/class/degree. Really!] k m c x The simplest mechanical system is the mass-spring dashpot problem shown in the figure. When displaced from its equilibrium at x
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This note was uploaded on 07/20/2009 for the course AME 341BL taught by Professor Spedding during the Spring '08 term at USC.

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1.SecondOrderSystems - Second Order Systems 1. Governing...

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