10.7 - Solving PDEs Using Fourier Sine Transform
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Practice Questions
Test your understanding with targeted questions
Define the Fourier Sine Transform.
💡 Hint: What type of functions does it primarily deal with?
What is the wave equation?
💡 Hint: What are the main variables in the wave equation?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the primary application of the Fourier Sine Transform?
💡 Hint: Consider what scenarios involve zero values at a boundary.
True or False: The Fourier Sine Transform can be used for functions defined over a finite domain.
💡 Hint: Think about the definition of the transform.
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Challenge Problems
Push your limits with advanced challenges
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.
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.
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