Time averages. Charge density wave systems

[LagrangeEuler]

Homework Statement

How to get equation
$\frac{d \theta}{dt}=-\omega_d+\omega_1\cos (\omega t)$
where $\omega_d$ is the average drift frequency and $\omega_1$ is proportional to the amplitude of the ac current.
from
$\frac{d \theta}{dt}=\omega_{co}(\frac{V(t)}{V_T}-\sin \theta)$
where $\omega_{co}$ is classical crossover frequency and $V_T$ is the dc treshold voltage,

Homework Equations

Time averages
$\langle A \rangle=\frac{1}{T}\int^{T}_0 Adt$

The Attempt at a Solution

I do not see the way how to calculate averages
$\langle V(t) \rangle=\frac{1}{T}\int^{T}_0 V(t)dt$
and
$\langle \sin \theta(t) \rangle=\frac{1}{T}\int^{T}_0 \sin \theta(t)dt$
Any idea?

 

[Greg Bernhardt]

I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?