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Let f (t) be a periodic function with period r. Explain

Chapter 5, Problem 5.54

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QUESTION:

Let f (t) be a periodic function with period r. Explain clearly why the average of f over one period is not necessarily the same as the average over some other time interval. Explain why, on the other hand, the average over a long time T approaches the average over one period, as T --->- co.

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QUESTION:

Let f (t) be a periodic function with period r. Explain clearly why the average of f over one period is not necessarily the same as the average over some other time interval. Explain why, on the other hand, the average over a long time T approaches the average over one period, as T --->- co.

ANSWER:

Step 1 of 2

Considering the following sin function:

 

The period of the above sin function is  

Calculating the average value of the considering sin function in a period in the interval  as,

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