Lecture Wednesday 6. February 2008

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Presentation transcript:

Lecture Wednesday 6. February 2008 Room 316, 14:15 – 16:00 Topics: Eigenmodes of Coupled Vibrations Algebraic method for Harmonic Oscillator Accompanying text: SolidState-HarmOsc-2008.pdf Comment: Including the party puzzles; Edited version 07.02.2008 PHYS208 06.02.2008 page 1

Two popular party puzzles Homework: Now we know how the C changes with temperature, const T^3 How is life in the cold world? heat_1_and_2 is naturally the heat in block 1 when the two blocks share their heat PHYS208 06.02.2008 page 2

Eigenmodes of Coupled Vibrations Transforming the most general matrix expression ( N x N matrices and N-dim column vectors ) to a sum of N independent terms (independent terms -> DIAGONAL MATRIX ) PHYS208 06.02.2008 page 3

PHYS208 06.02.2008 page 4

PHYS208 06.02.2008 page 5

Algebraic method for Harmonic Oscillator This is about superposition of eigenmodes. (previous slides) Guitar string – initial «triangular» displacement is «decomposed» into eigenmodes (see theory of musical instruments) PHYS208 06.02.2008 page 6

PHYS208 06.02.2008 page 7