1. 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
PHYS page 1

2. 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
PHYS page 2

3. 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 )
PHYS page 3

4. PHYS page 4

5. PHYS page 5

6. 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)
PHYS page 6

7. PHYS page 7