Practice Standard Fourier Cosine And Sine Transform Pairs (10.5) - Fourier Cosine and Sine Transforms

Practice: Standard Fourier Cosine and Sine Transform Pairs

Lesson 10.5Fourier Cosine and Sine Transforms

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6 sample questions

Question 1.
Define Fourier Cosine Transform.
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Think of the functions defined and their nature.
Question 2.
What type of functions does the Fourier Sine Transform typically use?
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Consider boundary conditions.
3Question 3.
What is the Fourier Cosine Transform of $e^{-ax}$ ?
- \$ \\frac{2a}{\\pi(a^2+s^2)} \$
- \$ \\frac{2s}{\\pi(as^2)} \$
- \$ \\frac{2}{a^2+s^2} \$
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Remember the form of the transform.
4Question 4.
True or False: The Fourier Sine Transform is used for functions that are even.
- True
- False
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Think about the nature of sine functions.
Question 5.
For the function $f(x) = e^{-3x}$ , calculate both the Fourier Cosine and Sine transforms and use them in a practical engineering problem such as heat diffusion.
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Consider how temperature changes with distance from the source.
Question 6.
Discuss how the choice between FCT and FST could change the outcome in solving a boundary value problem for a beam fixed at one end versus a string fixed at both ends.
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Think about how boundary conditions affect physical properties.

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