L4_13.pptx - Topics for Today Third exam is Wednesday April...

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Topics for Today Third exam is Wednesday, April 20 Third exam will cover chapters 11-15. Damped simple harmonic oscillator (15-5) Forced oscillations and resonance (15-6)

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When you start an oscillator in motion, it eventually stops because it dissipates energy. We call this “damping”. Damping is often described as force that is proportional to velocity, Since the force is always opposite the direction of motion, such a force always does negative work and decreases the kinetic energy: The “damping constant” = b , depends on the geometry of the oscillator and the viscosity of the fluid (air, water, …) it is moving in. Damped Simple Harmonic Motion
Now we have two forces Hooke’s law (spring force): Damping: Newton’s second law: This is a second order differential equation: , Solution is with With b = 0, we get previous result for . Damped Simple Harmonic Motion

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Displacement is with Damping shifts the frequency/period of oscillation.
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• Spring '12
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