18.12 - Application in Beam Vibrations (Wave Equation)
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Practice Questions
Test your understanding with targeted questions
What is the wave equation in the context of beam vibrations?
💡 Hint: Think about how displacement relates to time and position.
What do boundary conditions represent?
💡 Hint: Consider what happens at the ends of a supported beam.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the equation used to represent beam vibrations?
💡 Hint: Remember which equation deals with wave propagation.
True or False: Boundary conditions are not important for beam vibration analysis.
💡 Hint: Think about the constraints imposed at the ends of the beam.
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Challenge Problems
Push your limits with advanced challenges
Apply the wave equation for a beam of length 5 meters, fixed at both ends, with initial displacement given by \( u(x,0) = 10\sin(\frac{\pi x}{5}) \). Derive the Fourier series solution.
💡 Hint: Focus on how the sine function influences the boundary conditions.
A beam has an initial horizontal displacement described by \( u(x,0) = 100\sin(\frac{3\pi x}{10}) \) and zero initial velocity. Determine the expression for \( A_n \) and \( B_n \).
💡 Hint: Revisit the Fourier coefficients and their relationship to the given initial conditions.
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