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===== Complex Representations; Initial conditions revisited (20 minutes) =====


Notes for representing harmonic motion, including complex numbers: {{courses:lecture:oslec: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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