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# lec22 - Live fromPhysics 140 Fall 2007 Ann Arbor lecture#22...

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Physics 140 – Fall 2007 lecture #22: 20 Nov Midterm exam #3 is next Thursday, 29 November covers chapters 9-12 (rotation through gravity) bring three 3x5 notecards, calculator, #2 pencils Review on Monday, 26 Nov, 8:00-9:30pm in 182 Dennison Ch 13 topics: • restoring forces produce oscillations • simple harmonic motion (SHM) • natural frequency, driven oscillations and resonance Live from Ann Arbor, it’s 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

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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 Newton’s second law gives a second-order 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

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Descriptive features of SHM
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lec22 - Live fromPhysics 140 Fall 2007 Ann Arbor lecture#22...

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