lec24 (1) - Cite as: Thomas Peacock and Nicolas...

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Unformatted text preview: Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. Forced Response of Multi-Degree-of-Freedom Systems 1 2.003J/1.053J Dynamics and Control I, Spring 2007 Professor Peacock 5/16/2007 Lecture 24 Vibrations: Forced Response of Multi-Degree-of-Freedom Systems Forced Response of Multi-Degree-of-Freedom Systems Figure 1: Two carts connected by two springs. Motion only in the x direction. Generalized coordinates x 1 and x 2 . Figure by MIT OCW. Equations of Motion m 1 x 1 + k 1 x 1 k 2 ( x 2 x 1 ) = F 1 ( t ) m 2 x 2 + k 2 ( x 2 x 1 ) = 0 Rewrite in matrix form. m 1 x 1 k 1 + k 2 k 2 x 1 F 1 ( t ) + = (1) m 2 x 2 k 2 k 2 x 2 Let: F 1 ( t ) = F cos t What is the response? Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology....
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This note was uploaded on 11/29/2011 for the course CIVIL 1.018j taught by Professor Markusbuehler during the Fall '08 term at MIT.

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lec24 (1) - Cite as: Thomas Peacock and Nicolas...

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