Question 2. The Fourier series representation, FS(t), of a periodic function of period 4 is given by 00 nat nnt ao FS(t) = + b, sin 4 a, cos n-1 In this particular case the Fourier series coefficients are given by ao = 1.5 5(-1)" an = 2(1 - 2(-1)") b, = n272 Compute the Fourier series coefficients for n = 1, 2, 3 correct to 4 decimal places and hence, using these entered values, compute FS3(4) correct to 3 decimal places. Enter the values in the boxes below.

Question 2. The Fourier series representation, FS(t), of a periodic function of period 4 is given by 00 nat nnt ao FS(t) = + b, sin 4 a, cos n-1 In this particular case the Fourier series coefficients are given by ao = 1.5 5(-1)" an = 2(1 - 2(-1)") b, = n272 Compute the Fourier series coefficients for n = 1, 2, 3 correct to 4 decimal places and hence, using these entered values, compute FS3(4) correct to 3 decimal places. Enter the values in the boxes below.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question 2. The Fourier series representation, FS(t), of a periodic function of period 4 is given by FS(t) Nnt -() Nat %3| an cos + b, sin In this particular case the Fourier series coefficients are given by ao = 1.5 6(-1)" an = 6(1 2(-1)") n²#² Compute the Fourier series coefficients for n = 1,2, 3 correct to 4 decimal places and hence, using these entered values, compute FS,(2) correct to 3 decimal places. Enter the values in the boxes beloW. Enter a, correct to 4 decimal places: Enter az correct to 4 decimal places: Enter az correct to 4 decimal places: Enter b correct to 4 decimal places: Enter b correct to 4 decimal places: Enter by correct to 4 decimal places: Enter FS3(2) correct to 3 decimal places:
QUESTION 9.43 Assuming f is the fourier series g(t) = 6t+5 for -12
This question is about trigonometric Fourier Series.
Question 4 Given that f(x) = x³, where -1 ≤ x ≤ 1. What is the coefficient b,, of the Fourier series of f? Select one: O A. O B. -sinx C. sinx O D. -1
Question 6. The complex Fourier series representation of a periodic function of period 2 is given by FS(t) = Σ n= ∞ Cne-int where cn = 4+ I 6 n³ (4-5(-1)")j. Find, to three decimal places, the amplitude |c₂| and phase on for n=1,2. Enter the real and imaginary values of c-₁ in the appropriate boxes below. Enter ₁ correct to 3 decimal places: Enter correct to 3 decimal places: Enter |c₂| correct to 3 decimal places: Enter 2 correct to 3 decimal places: Enter the real part of c_₁: Enter the imaginary part of c_₁: C-1
Q1. Find the Fourier Series in Trigonometric format (sine/cosine format). f(t) = (2. rs and f(t) has a period of T. _I << I 10. 4 otherwise Q2. Find the Fourier Series in Trigometric format (sine/cosine format) Accessibility Unavailable nors I
hello , I am just going through homework answers my lecturer has written and have a question on the fourier series. when writing the values of an, a3 is negative. why is that ? and when he puts an into the equation he has turned sine to cosine.
handwritten solution for part c
Solve
= 1) The function f(x) periodic on the interval [0, 2л] has complex Fourier series f(x): Σ(1/n²) einx where the sum over n goes from - infinity to infinity. Convert this to cosine and sine Fourier Series by finding the values of A's and B's in the expression Ao + ΣAn cos(nx) + Σ Bn sin(nx) where each sum goes from 1 to infinity. Hint: consider the n and -n term together in the complex Fourier Series or use Euler's identity.
Needed to solved all parts of questions correctly in 30 minutes and get the thumbs up please show neat and clean work