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How do I find the time average of $\cos^2(3-wt)$ ?

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closed as too localized by Lord_Farin, Michael Albanese, 23rd, TMM, Davide Giraudo Apr 26 '13 at 12:58

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What is the definition of time average, and is "w" a constant? –  dezign Apr 26 '13 at 11:39
    
What is the definition of time average of a function? And have you seen trigonometric identities such as $2\cos^2x= 1+\cos 2x$? –  Dilip Sarwate Apr 26 '13 at 11:39

1 Answer 1

For a one variable function $f(t)$ with period $T$ the time average function is defined as

$$\frac{1}{T} \int_{0}^{T} dt f(t)$$

so what you need to compute is the following integral

$$\frac{1}{T}\int_{0}^{T}dt\cos^2(3-\omega t) $$

where $T$ is the smallest strictly positive number such that:

$$f(t+T)=f(t) $$

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Important: T is the smallest strictly positive number verifying $f(t+T)=f(t)$! –  moray95 Apr 26 '13 at 11:59
    
@moray95 thank you –  Jorge Apr 26 '13 at 12:02

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