Practice Numerical Solution Techniques (17.14) - Modelling – Vibrating String, Wave Equation

Practice: Numerical Solution Techniques

Lesson 17.14Modelling – Vibrating String, Wave Equation

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9 questions

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2 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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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What does the Finite Difference Method (FDM) do?
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Think about how it transforms a differential equation into manageable parts.
Question 2.
What is the main advantage of numerical methods?
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No hint provided
3Question 3.
What does the Finite Difference Method (FDM) approximate?
- Time only
- Space only
- Both space and time
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Remember that FDM deals with both dimensions.
4Question 4.
Is the Finite Element Method suitable for complex geometries?
- True
- False
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Think about the capability of FEM discussed in class.
Question 5.
Using the Finite Difference Method, derive the iterative formula to approximate the wave equation on a string of length L and tension T. Assume small displacements and use a grid of 10 segments.
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Think about how the grid influences your calculations based on previous steps.
Question 6.
Evaluate a structure using FEM. Consider a beam with varying cross-section under a static load. Discuss how you would set up the problem including nodes and elements.
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Make sure to think about where each change occurs in the structure to set the elements effectively.

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