Practice Rectangular Membrane, Use Of Double Fourier Series (20) - Rectangular Membrane, Use of Double Fourier Series

Practice: Rectangular Membrane, Use of Double Fourier Series

Lesson 20Rectangular Membrane, Use of Double Fourier Series

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8 questions

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3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What does the variable $u(x,y,t)$ represent in the wave equation?
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Think about what is changing in the membrane.
Question 2.
Define what boundary conditions are in the context of a rectangular membrane.
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Consider how the edges of the membrane are held.
3Question 3.
What is the two-dimensional wave equation used to model?
- The motion of a particle
- The vibration of a membrane
- The flow of liquid
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Think about structures that can vibrate.
4Question 4.
True or False: The double Fourier series can be used to model forced vibrations?
- True
- False
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Recall the different analysis conditions.
Question 5.
Given a rectangular membrane of dimensions 2m x 3m and tension resulting in a wave speed of 10 m/s, calculate the first three fundamental frequencies using separation of variables.
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Plug in the dimensions into your eigenvalue expressions.
Question 6.
Design a small rectangular membrane structure to minimize vibrations caused by wind. Which Fourier coefficients would be most critical for ensuring stability?
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Refer back to how lower frequencies relate to stronger vibrations.

4 more questions in this section. Enroll free to practise them all.