Calculus problem

Hello...
Please somebody help me solve this equation.
This is related to vibration

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Please share your thoughts/work with us - so that we know where to begin to help you.
 
The equation is very odd, in that [MATH]a_w[/MATH] appears inside the integral as a function of t, but on the LHS it can't be a function of t. I suppose, as topsquark suggests, they must be reusing the same symbol for both the function and its time average. (Is that standard in this field?)

I think you'll need to show us the source, so we can see what it all means in context. It isn't clear to me that there's anything to solve. As HallsofIvy asked, what are you trying to solve for?
 
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