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Unformatted text preview: Physics 140 Fall 2007 lecture #22: 20 Nov Midterm exam #3 is next Thursday, 29 November covers chapters 912 (rotation through gravity) bring three 3x5 notecards, calculator, #2 pencils Review on Monday, 26 Nov, 8:009:30pm in 182 Dennison Ch 13 topics: restoring forces produce oscillations simple harmonic motion (SHM) damped harmonic motion natural frequency, driven oscillations and resonance Live from Ann Arbor, its Tuesday Morning! Which is your favorite FM station? A: 88.1 B: 88.3 C: 88.7 D: 95.5 E: 97.9 F:107.1 Things that Oscillate mass on spring pendulum e in antenna Things that Oscillate: I masses on springs A restoring force leads to oscillations about a point of equilibrium. A linear restoring force tends to push a system back toward a point of stable equilibrium, with a magnitude that varies linearly with the displacement away from equilibrium. An example is Hookes law for an ideal spring Applying Newtons second law gives a secondorder ordinary differential equation the solution of which is a sinusoidal variation of position in time Any system with displacement following this form is said to be undergoing simple harmonic motion (SHM) . F = " kx d 2 x dt 2 = " k m x x ( t ) = x m cos( " t + # ) ( " = k / m ) Linear Restoring Forces and Simple Harmonic Motion Descriptive features of SHM Although the causes of SHM will vary from one system to another, the sinusoidal variation is a common element. All solutions are directly characterized by three...
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This note was uploaded on 04/03/2008 for the course PHYSICS 140 taught by Professor Evrard during the Fall '07 term at University of Michigan.
 Fall '07
 Evrard
 Force, Simple Harmonic Motion

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