Question 4. The Fourier series representation, FS(t), of a function f(t), where f(t + 6) = f(t) is given by Σ nat 3 n=1 FS(t) ao 2 ag=0.75 an= bn + In this particular case the Fourier series coeffcients are given by an cos 2(-1)" TUTT 3(1-2(-1)") 1²7² +b, sin nat 3 Compute the Fourier series coefficients for n = 1, 2, 3 correct to 4 decimal places and hence, using these entered values, compute FS3(1.5) correct to 3 decimal places. Enter the values in the boxes below. عالم جانتا 25°C 15 م اكتب هنا للبحث 1
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- QUESTION 9.43 Assuming f is the fourier series g(t) = 6t+5 for -12The Fourier series representation, FS(t), of a function f(t), where f(t + 10) = f(t) is given by FS(t) = 2 + Σª, cos (757) + an 71 a0 = 1.25 In this particular case the Fourier series coeffcients are given by an= b₁ 2(-1) (15²) 4(1-2(-1)") 7²π² + b, sin Compute the Fourier series coefficients for n=1,2,3 correct to 4 decimal places and hence, using these entered values, compute FS, (2.5) 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 a correct to 4 decimal places: Enter b, correct to 4 decimal places: Enter by correct to 4 decimal places: Enter b3 correct to 4 decimal places: Enter FS (2.5) correct to 3 decimal places: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:Find at least three nonzero terms (including ao and at least two cosine terms and two sine terms if they are not all zero) of the Fourier series for the given function, and sketch at least three periods of the function. Which of the following is the Fourier series for the given function? O A. f(x)= O B. f(x) = O C. f(x)= 9 18 + 2 9 9 2 9 ——— OD. f(x) = - 2 - + π 18 F π 18 π 18 π 6 sin x + - sin 3x + ... π cos x X- sin x- COS X + 6 π 6 π 6 - π cos 3x - ... sin 3x - ... cos 3x + ... - 18 π 6 sin x - - sin 3x - ... π f(x) = {: 0 9 ≤x≤0 0≤xPls help ASAPQuestion 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-1QUESTION 1 80 1.1 f(t) = nt - t, 0Question 3. The Fourier series representation, FS(t), of a function f(t), where f(t + 8) = f(t) is given by rs(t) = a + Σα ao = 0.25 an bn ∞ In this particular case the Fourier series coeffcients are given by - 2(−1)n Nπ n=1 an cos nπt (not). +b, sin (nt). 4 6(1 – 2(−1)") n²π² 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:Question 4. The Fourier series representation, FS(t), of a function f(t), where f(t + 8) = f(t) is given by nπt FS(t) = 4+ [a, cos(xt) - Σ 2 4 n=1 an In this particular case the Fourier series coeffcients are given by ao 1 bn = = = 3(-1)" Nπ + bn sin 3(1-2(−1)n) n²π² nπt 4 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 decimal places. Enter the values in the boxes below. 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:QUESTION 1 In the Fourier series of f(x)=9x² + 1 for 0Question 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: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:Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. 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