Practice Boundary and Initial Conditions - 19.4 | 19. Modelling – Membrane, Two-Dimensional Wave Equation | Mathematics (Civil Engineering -1)
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19.4 - Boundary and Initial Conditions

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the condition of a membrane at its boundary?

💡 Hint: Think about the fixed edges of a drum.

Question 2

Easy

What does the initial condition u(x, y, 0) = f(x, y) represent?

💡 Hint: Consider how the membrane looks before it starts vibrating.

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 mathematical representation of fixed boundary conditions for a vibrating membrane?

  • u(0,y,t)=0
  • u(x,y,t)=0
  • u(a,y,t)=f(x,y)

💡 Hint: Think about how the edges of a membrane would behave.

Question 2

True or False: Initial conditions only describe the shape of the membrane.

  • True
  • False

💡 Hint: Consider what happens when the membrane starts vibrating.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Consider a circular membrane fixed at the edges. Describe how you would apply boundary and initial conditions to model the vibrations under a sudden force applied at the center.

💡 Hint: Start with defining u(r,0)=f(r) for the shape after the force.

Question 2

Imagine a rectangular membrane with varying tension along different edges. How might you adjust the boundary conditions while still keeping the essence of fixed edges?

💡 Hint: Explore conditions where tension can influence displacement at edges while still maintaining overall fixed conditions.

Challenge and get performance evaluation