lec23 (2) - 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 Wilberforce Pendulum 2.003J/1.053J Dynamics and Control I, Spring 2007 Professor Peacock 5/14/2007 Lecture 23 Vibrations: Two Degrees of Freedom Systems- Wilberforce Pendulum and Bode Plots Wilberforce Pendulum Figure 1: Wilberforce Pendulum. Extension of spring coupled to rotation. Fig ure by MIT OCW.- m : mass, I : moment of inertia, : torsional constant (rotation), k : extension, : coupling of extension and rotation 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 Wilberforce Pendulum Focus on Spring Figure 2: Focus on spring. Figure by MIT OCW. Force: F = kx + 1 (also opposing force in opposite direction) 2 Torque: = + 2 1 x 1 1 and x represents the coupling for small displacements 2 2 Equations of Motion Can use Lagrange, but we will use momentum principles. 1 mx = mg kx (1) 1 I = x (2) Equilibrium Points 1 kx + mg = 0 1 + x = 0 1 = x mg x = 2 k 4 1 2 2 2 2 2 Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007.2007....
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lec23 (2) - Cite as: Thomas Peacock and Nicolas...

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