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Unformatted text preview: ME 530.343: Design and Analysis of Dynamic Systems Spring 2009 Lecture 5 – Mass-Spring Systems and Equivalent Mechanical Systems Wednesday, February 11, 2009 1 Today’s Objectives Purpose of today’s lecture: • Degrees of freedom • Identify equivalent systems: m eq ¨ x + b eq ˙ x + k eq x = f eq • Springs and dampers in series and in parallel Reading: Palm Chapter 4.1, 4.2, 4.4, 4.5 (ignore Laplace transform examples for now) 2 Degrees of Freedom To begin modeling any dynamic system, you first know how many degrees of freedom there are in the system. This will tell you: • How many equations of motion you will finding • The size of the matrix equation describing the system (if you need to put it in that form, as we will in the last half of this course) • How many and which system variables you will select The number of degrees of freedom is the number of parameters that can be independently varied in a system . Test for simple mass-spring-damper systems: Can you hold one mass in a mechanical system at a constant position, but still move another mass in the system? m m k For complex or continuous systems (e.g., buildings), the concept of (finite) degrees of freedom is not as well defined. You typically want to create a model that has enough degrees of freedom to appro- priately characterize the system’s behavior, but not so many that the computational requirements are too high....
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This note was uploaded on 03/02/2010 for the course MECH 530.343 taught by Professor Sun during the Spring '08 term at Johns Hopkins.
- Spring '08