## MIT 1803 lecture 10

This lecture covered the homogeneous second order equation as it applied to the damped harmonic oscillator.  The characteristic equation was extracted, and explored a little bit.

$y'' = 2py' - w_0^2y = 0$

$r^2 + pr + w_0^2 = 0 \quad \quad r = -p +- (p^2 -w_0^2)^{1/2}$
$\cos \theta = \frac{e^{i\theta} + e^{-i\theta}}{2}$