# Resonance - from Feynman lectures

1. Sep 15, 2014

### rpthomps

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:

Any help would be greatly appreciated.

Ryan

2. Sep 15, 2014

### 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 $\sin \theta = -\gamma \omega$

3. Sep 15, 2014