Practice Determination Of Coefficients Using Fourier Series (17.5) - Modelling – Vibrating String, Wave Equation
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Determination of Coefficients Using Fourier Series

Practice - Determination of Coefficients Using Fourier Series

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the formula for calculating A_n?

💡 Hint: Consider the role of sine functions in Fourier series.

Question 2 Easy

How do you represent the initial velocity in terms of Fourier series?

💡 Hint: Think about which initial condition corresponds to velocity.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does A_n represent in the context of the Fourier series?

Initial velocity
Initial displacement
Frequency component

💡 Hint: Think about what initial conditions refer to.

Question 2

True or False: B_n is calculated using the integral of initial displacement.

True
False

💡 Hint: Recall the definitions of A_n and B_n.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Consider a vibrating string with f(x) = x(2-L+x) on the interval [0, L]. Determine A_n.

💡 Hint: Use integration by parts if necessary.

Challenge 2 Hard

Given g(x) = sin(x) and L = 2π, find B_n for a vibrating string.

💡 Hint: Consider orthogonality properties of sine functions.

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Reference links

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