Question 7.The Fourier series representation, FS(t), of a function f(t),where f(t + 8) = f(t) is given byaonπtFS(t) = a + 2ª, cos (17²) + b., sin (14).Σanbn2n=1In this particular case the Fourier series coeffcients are given byao = 0.75an =5(1-2(-1)")n²π²Compute the Fourier series coefficients for n = 1, 2, 3 correct to 4 decimal places and hence, using these entered values, compute FS3 (2) correct to 3 decimal places.Enter the values in the boxes below.bn3(-1)"Nπ=Enter a₁ correct to 4 decimal places:Enter a correct to 4 decimal places:Enter a correct to 4 decimal places:Enter b₁ correct to 4 decimal places:Enter b₂ correct to 4 decimal places:Enter b3 correct to 4 decimal places:Enter FS3 (2) correct to 3 decimal places:

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Answered: Question 7. The Fourier series…

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 4. The Fourier series representation, FS(t), of a function f(t), where f(t + 4) = f(t) is given by ao nπt = PS(() - +, cos (17) + A, sin (17) (nat) = = an COS bn 2 2 2 n=1 In this particular case the Fourier series coeffcients are given by ao an bn = 0.25 3(−1)n NTT 2(1 – 2(−1)n) n²π² Compute the Fourier series coefficients for n = 1, 2, 3 correct to 4 decimal places and hence, using these entered values, compute FS3(0) correct to 3 decimal places. Enter the values in the boxes below. Enter 1 correct to 4 decimal places: Enter a correct to 4 decimal places: Enter a correct to 4 decimal places: Enter b₁ correct to 4 decimal places: Enter b₂ correct to 4 decimal places: Enter b3 correct to 4 decimal places: Enter FS3(0) correct to 3 decimal places:
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
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.
QUESTION 1 In the Fourier series of f(x)=9x² + 1 for 0
P4 Derive the Fourier Series of Following signal (2 = x 010 = 7 mont *5m2 2 = x x(1)₁ V NNN -A altanut tot sulev 0
= 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.
Question 6. The complex Fourier series representation of a periodic function of period 2π is given by FS(t) = = ∞ n=1x Cne-int I where c = 2 + (5 – 6(−1)”)j . 2 Cn N³ Find, to three decimal places, the amplitude c and phase on for n = 1, 2. Enter the real and imaginary values of c-₁ in the appropriate boxes below. Enter |c₁| correct to 3 decimal places: Enter ₁ 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:
Please I need a full solution
Question 4. The Fourier series representation, Fs(t), of a function f(t), where f(t + 4) = f(t) is given by cos (17²) - FS(t) = = ao = 0.75 an = bn ao 2 In this particular case the Fourier series coeffcients are given by = an cos 4(-1)" nn in (17²). 2(1-2(-1)") n²π² + b sin Compute the Fourier series coefficients for n = 1,2,3 correct to 4 decimal places and hence, using these entered values, compute FS3 (2) correct to 3 decimal places. Enter the values in the boxes below. Enter a correct to 4 decimal places: Enter a correct to 4 decimal places: Enter a3 correct to 4 decimal places: Enter b₁ correct to 4 decimal places: Enter b2 correct to 4 decimal places: Enter bg correct to 4 decimal places: Enter FS3 (2) correct to 3 decimal places:
(1 point) for 0 Bn sin S(7) = 0 • S(-3) = -1 S(11) = 0

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