Complex Representations; Initial conditions revisited (20 minutes)

Notes for representing harmonic motion, including complex numbers: reps_initcond_complexnumbers_wiki.ppt

  • Introduce the use of complex numbers to represent oscillatory motion, and stress that the representation is still real (in quantum mechanics, the representation may be complex).

\[ \hbox{“C-form”}\qquad f\left( t \right)=Ce^{i\omega t}+C^{*}e^{-i\omega t}\]

\[ \hbox{“D-form”}\qquad\qquad f\left( t \right)=\Re\left( De^{i\omega t} \right)\]

  • Introduce the term phasor in context of Argand plane representations
  • Revisit initial conditions example and show relationships among all coefficients of the 4 representations.
  • Discuss where different representations might be useful.

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