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Resonance - from Feynman lectures

  1. Sep 15, 2014 #1
    Good afternoon,

    I am working my way through the Feynman lectures and I am stumped at Chapter 23, Resonance. Specifically, the derivation of equation 23.12. I have followed up to that point but the appearance of tan (theta) baffles me. The equation is below:

    2s8jx3a.png

    Any help would be greatly appreciated.

    Ryan
     
  2. jcsd
  3. Sep 15, 2014 #2

    DrClaude

    User Avatar

    Staff: Mentor

    You have to use Euler's formula along with a separation of the real and imaginary parts:
    $$
    \begin{align}
    e^{-i \theta} &= \omega_0^2 - \omega^2 + i \gamma \omega \\
    \cos \theta - i \sin \theta &= \omega_0^2 - \omega^2 + i \gamma \omega
    \end{align}
    $$
    from which you get that ##\cos \theta = \omega_0^2 - \omega^2## and ##\sin \theta = -\gamma \omega##
     
  4. Sep 15, 2014 #3
    Thanks DrClaude. That's very helpful.
     
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