Practice Application in Beam Vibrations (Wave Equation) - 18.12 | 18. Separation of Variables, Use of Fourier Series | Mathematics (Civil Engineering -1)
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18.12 - Application in Beam Vibrations (Wave Equation)

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the wave equation in the context of beam vibrations?

💡 Hint: Think about how displacement relates to time and position.

Question 2

Easy

What do boundary conditions represent?

💡 Hint: Consider what happens at the ends of a supported beam.

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 equation used to represent beam vibrations?

  • Wave Equation
  • Heat Equation
  • Laplace Equation

💡 Hint: Remember which equation deals with wave propagation.

Question 2

True or False: Boundary conditions are not important for beam vibration analysis.

  • True
  • False

💡 Hint: Think about the constraints imposed at the ends of the beam.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

Question 2

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.

Challenge and get performance evaluation