Practice Solving PDEs Using Fourier Sine Transform - 10.7 | 10. Fourier Cosine and Sine Transforms | Mathematics (Civil Engineering -1)
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10.7 - Solving PDEs Using Fourier Sine Transform

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define the Fourier Sine Transform.

💡 Hint: What type of functions does it primarily deal with?

Question 2

Easy

What is the wave equation?

💡 Hint: What are the main variables in the wave equation?

Practice 4 more questions and get performance evaluation

Interactive Quizzes

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

Question 1

What is the primary application of the Fourier Sine Transform?

  • To solve equations in circular domains
  • To analyze wave equations with zero displacement at boundaries
  • To evaluate definite integrals

💡 Hint: Consider what scenarios involve zero values at a boundary.

Question 2

True or False: The Fourier Sine Transform can be used for functions defined over a finite domain.

  • True
  • False

💡 Hint: Think about the definition of the transform.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Consider a wave on a string described by \( u(x,t) = f(x - ct) \) with initial conditions u(0,t) = 0. Use the Fourier Sine Transform to derive the displacement at any point given specific f(x).

💡 Hint: Think about how the Fourier Sine Transform extracts frequency components from your initial function.

Question 2

A vibrating beam with boundary conditions at x=0 and free at the other end is subject to a specific force. Formulate the wave equation and solve using the Fourier Sine Transform.

💡 Hint: Setting up the wave equation correctly is crucial to identify the FST solution.

Challenge and get performance evaluation