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MEM423Sp10_11.2.sDOF

MEM423Sp10_11.2.sDOF - MEM423 Mechanics of Vibrations(1.10...

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MEM423 Mechanics of Vibrations (1.10, 2.1-2.3, 2.6) Dr. Ajmal Yousuff Dept. Mech. Engg. & Mechanics Drexel University
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Vibrations (1-DOF) Degrees of Freedom: The (minimum # of) variables needed to describe the dynamics of the system. need not be unique. Yousuff MEM423 Vibrations 2 mass support spring support (fixed) Elastic rod M 1 M 2 support (pinned) rigid rod x 1 support M 1 K 1 M 2 K 2 x 1 x 2
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Spring Consider an ideal spring: Mass-less Linear No damping Yousuff MEM423 Vibrations 3 F x reference F kx F x Slope = k k: force/unit distance
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Illustration (static) Yousuff MEM423 Vibrations 4 s reference m Free Body Diagram F = ks W = mg mg ks If m (or, W = mg ) is known, and s is measured, If k and s are known, / k mg s W ks
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Dynamics Yousuff MEM423 Vibrations 5 s unstrectched m f(t) X (>0) equilibrium Newton’s 2 nd Law : (mass)(acceleration) = (sum of external forces)
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Equation of Motion Yousuff MEM423 Vibrations 6 2 2 ( ) ( ) d x m mg k x s f t dt But mg = ks (static equilibrium)
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Solution Rewrite:
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