Practice Fourier Sine Transform (FST) - 15.3.2 | 15. Fourier Integral to Laplace Transforms | Mathematics (Civil Engineering -1)
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15.3.2 - Fourier Sine Transform (FST)

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the mathematical expression for the Fourier Sine Transform?

💡 Hint: Recall the integration limits for the sine-transform.

Question 2

Easy

What type of functions does the Fourier Sine Transform primarily work with?

💡 Hint: Consider what 'piecewise' means in terms of function behavior.

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Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is the definition of the Fourier Sine Transform?

  • A method to convert a time function into a frequency function using sine functions
  • A method to convert a time function into a frequency function using cosine functions
  • A graphical representation of functions over a finite interval

💡 Hint: Focus on the function's behavior in relation to sine.

Question 2

Is the Fourier Sine Transform useful only for periodic functions?

  • True
  • False

💡 Hint: Consider the definition's focus on non-periodic functions.

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Challenge Problems

Push your limits with challenges.

Question 1

Using the Fourier Sine Transform, compute the transformed integral for f(x) = x over the interval [0,∞].

💡 Hint: Consider using integration by parts, where u = x and dv = sin(ωx) dx.

Question 2

Given a function f(x) = e^(-ax) for x >= 0, compute its Fourier Sine Transform.

💡 Hint: The integral can be solved using a standard table of integrals or through integration by parts.

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