Lecture 4 Notes

Lecture 4 Notes - Recap of last lecture Chapter 13,...

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Recap of last lecture Chapter 13, Periodic motion A simple pendulum’s period is given by g L T = The period of a physical pendulum is
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Damped oscillations The decrease in the amplitude due to dissipative forces is called damping and these oscillations are called damped oscillation. In case of motion in a viscous medium the damping force is usually proportional to velocity F x = -bv x The net force is: x x bv kx F - - = dt dx b kx dt x d m 2 2 - - = or Solutions is: ) cos( ) 2 / ( φ ϖ + = - t Ae x t m b 2 2 4 m b m k - = &
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Damped oscillations Amplitude decreases exponentially ϖ > 0 when km 2 b < (under-damped) ϖ = 0 when km 2 b = (critically damped) ϖ ’ 2 < 0 when km 2 b (over damped)
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Damped oscillations Look at the following applet http://lectureonline.cl.msu.edu/~mmp/applist/damped/d.htm
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An Unique Damped Oscillator The Taipei 101 Damper ball (730 tons, on the 93 rd floor) Saved the building during the 2008 Sichuan earthquake in China
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Lecture 4 Notes - Recap of last lecture Chapter 13,...

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