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PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103

PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 15: Start reading Chapter 4 Small oscillations about equilibrium Normal modes. Please use this time to complete all outstanding assignments.

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PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103

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  1. PHY 711 Classical Mechanics and Mathematical Methods • 10-10:50 AM MWF Olin 103 • Plan for Lecture 15: • Start reading Chapter 4 • Small oscillations about equilibrium • Normal modes PHY 711 Fall 2013 -- Lecture 15

  2. Please use this time to complete all outstanding assignments PHY 711 Fall 2013 -- Lecture 15

  3. Motivation for studying small oscillations – many interacting systems have stable and meta-stable configurations which are well approximated by: PHY 711 Fall 2013 -- Lecture 15

  4. PHY 711 Fall 2013 -- Lecture 15

  5. Example – linear molecule m1 m2 m3 PHY 711 Fall 2013 -- Lecture 15

  6. PHY 711 Fall 2013 -- Lecture 15

  7. PHY 711 Fall 2013 -- Lecture 15

  8. PHY 711 Fall 2013 -- Lecture 15

  9. PHY 711 Fall 2013 -- Lecture 15

  10. Digression: PHY 711 Fall 2013 -- Lecture 15

  11. Digression on matrices -- continued Eigenvalues of a matrix are “invariant” under a similarity transformation PHY 711 Fall 2013 -- Lecture 15

  12. Example of transformation: PHY 711 Fall 2013 -- Lecture 15

  13. PHY 711 Fall 2013 -- Lecture 15

  14. PHY 711 Fall 2013 -- Lecture 15

  15. m1 m1 m1 m2 m2 m2 m3 m3 m3 PHY 711 Fall 2013 -- Lecture 15

  16. PHY 711 Fall 2013 -- Lecture 15

  17. Additional digression on matrix properties Singular value decomposition PHY 711 Fall 2013 -- Lecture 15

  18. Singular value decomposition -- continued PHY 711 Fall 2013 -- Lecture 15

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