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Unformatted text preview: 1 Slide Sets Material on vibrations is covered in Sets 13, 14, and 15 and textbook sections 3.7 and 3.8. Material on Laplace transforms is covered in Sets 16, 17, 18 and 19 and textbook Chapter 6. Material on systems of first order ODEs is covered in Sets 20 and 21 and pieces of textbook sections 7.1, 7.4, 7.5 and 7.6. The associated material on linear algebra is in textbook sections 7.2, and 7.3. 2 Differential Equations for Mechanical Vibrations mu 00 + u + ku = f ( t ) form differential equations from modeling of mass-spring system F = ma k spring constant determines force due to spring attempting to return to equilib- rium m mass of object combines with e.g. gravity to exert a force on system damping of system due to e.g. atmospheric drag types of vibration undamped free vibrations: mu 00 + ku = 0 damped free vibrations mu 00 + u + ku = 0 undamped forced vibrations mu 00 + ku = f ( t ) damped forced vibrations mu 00 + u + ku = f ( t ) 3 Behavior of Mechanical Vibrations 3.1 Undamped Free Vibrations ODE mu 00 + ku = 0 persistent sinusoidal oscillation natural frequency natural period T 1...
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- Fall '09