Science:Math Exam Resources/Courses/MATH307/April 2012/Question 06 (b)
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Question 06 (b) 

Explain the physical significance of the values and how these relate to . If t is measure in days, and the time period T encompasses several years, which values of c_{n} might you expect to be the largest absolute value? (Think about what time scales you expect temperature to fluctuate over.) 
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If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Science:Math Exam Resources/Courses/MATH307/April 2012/Question 06 (b)/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Since is a complex number with real and imaginary part, we write in its complex exponential form = Therefore reflects the original temperature function’s frequency spectrum. If we put the above expression back into the Fourier series representation of y(t), we have
The values of might you expect to have the largest absolute value is the frequency for the maximum temperature swings over the course of years. This would probably be seasonal fluctuations, so it would be for about 12 months. 