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10/06/2014PHY 711 Fall 2014 -- Lecture 181 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 18: Finish reading.

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Presentation on theme: "10/06/2014PHY 711 Fall 2014 -- Lecture 181 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 18: Finish reading."— Presentation transcript:

1 10/06/2014PHY 711 Fall 2014 -- Lecture 181 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 18: Finish reading Chapter 4 and start reading Chapter 7 1.Coupled motion of extended systems; relationship to continuum models & wave equation 2.Analytic methods for solving Sturm- Liouville equations

2 10/06/2014PHY 711 Fall 2014 -- Lecture 182

3 10/06/2014PHY 711 Fall 2014 -- Lecture 183 Returning to linear case; continuum limit -- Longitudinal versus transverse vibrations Images from web page: http://www.physicsclassroom.com/class/waves/u10l1c.cfm

4 10/06/2014PHY 711 Fall 2014 -- Lecture 184 m m m Longitudinal case: a system of masses and springs:

5 10/06/2014PHY 711 Fall 2014 -- Lecture 185 system parameter with units of (velocity) 2

6 10/06/2014PHY 711 Fall 2014 -- Lecture 186  x,t)  Transverse displacement:

7 10/06/2014PHY 711 Fall 2014 -- Lecture 187

8 10/06/2014PHY 711 Fall 2014 -- Lecture 188

9 10/06/2014PHY 711 Fall 2014 -- Lecture 189

10 10/06/2014PHY 711 Fall 2014 -- Lecture 1810

11 10/06/2014PHY 711 Fall 2014 -- Lecture 1811

12 10/06/2014PHY 711 Fall 2014 -- Lecture 1812

13 10/06/2014PHY 711 Fall 2014 -- Lecture 1813

14 10/06/2014PHY 711 Fall 2014 -- Lecture 1814

15 10/06/2014PHY 711 Fall 2014 -- Lecture 1815

16 10/06/2014PHY 711 Fall 2014 -- Lecture 1816

17 10/06/2014PHY 711 Fall 2014 -- Lecture 1817

18 10/06/2014PHY 711 Fall 2014 -- Lecture 1818 Example initial profile --  (x):


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