lec20 (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]. 1 Single Degree of Freedom System 2.003J/1.053J Dynamics and Control I, Spring 2007 Professor Thomas Peacock 5/2/2007 Lecture 20 Vibrations: Second Order Systems with One Degree of Freedom, Free Response Single Degree of Freedom System Figure 1: Cart attached to spring and dashpot. Figure by MIT OCW. mx ¨ + cx ˙ + kx = F ( t ) System response? What is x ( t )? Use 18.03 Background. x ( t ) = Free Response + Response Due to Forcing Complementary Solution, when F ( t )=0 Particular Solution This lecture will cover the Free 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. Downloaded on [DD Month YYYY]. 2 Free Response Free Response Look at k → Figure 2: Cart with dashpot only. Figure by MIT OCW. mx ¨ + cx ˙ = 0 Assume conditions x (0) = x and ˙ x (0) = v . mx ¨ + cx ˙ = mv ˙ + cv = 0 v = v e ( − ct/m ) already used ˙ x (0) = v Integrate v ( t ) once. Using x (0) = x , we obtain: x = x + mv 1 − e − c t m c Figure 3: Solution to differential equation. Solution attenuates to a steady state value. Figure by MIT OCW. 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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lec20 (1) - Cite as Thomas Peacock and Nicolas...

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