## Damped Forced Oscillations and Beats

Hello,

I know it is possible with the undamped case but is it possible to have beats with a Damped Forced Oscillation?

Graphing a particular instance of the equation:
$y(t)=C_1 e^{- \alpha t}cos(\omega _o t)+C_2 cos(\omega t)$
Resulted in:

Which kind of looks like beats that are fading away.

But I can't find a mathematical representation that describes it like the undamped case:
$y(t)=C sin(\frac{\omega_o + \omega}{2}t)sin(\frac{\omega_o - \omega}{2}t)$
That pesky exponential term from the first equation above keeps on getting in the way.

Any help appreciated,

Scott.