Suppose that f(t) is periodic with period -T, 7) and has the following real Fourier coefficients:a2 = 3,аз — 3,b2 = -3, b3 = 0,ao4,a1 = 1,b, = 2,(A) Write the beginning of the real Fourier series of f(t) (through frequency 3):f(t) = 2+cost+2sint+3cos2t-3sin2t+3cos3t+0+.(B) Give the real Fourier coefficients for the following functions:(i) The derivative f'(t)ao =, a1 =-1, az =-6, az =-9b, = 2, b2 =-6bz =(ii) The function f(t) – 2ao =, a1 =, az =3, аз —3b1 = 2, b2 =-3bz =(iii) The antiderivative of (f(t)2) (with C0)ao =, a1, a2 =3/2, аз1b1 =-2b2 = 3/2b3 =(iv) The function f(t) + 3 sin(3t) + 3 cos(2t)ao = 2, a1 =1, a2 =6, аз —3b, = 2b2 =-3b3 =3(iv) The function f(2t)an =2, a1, a23, a33b, =2, b2 =-3b3 = 0

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Suppose that f(t) is periodic with period |-, 7) and has the following real Fourier coeficients: do - 4, a, -1, az- 3, ag - 3, b = 2, b = -3, bg = 0, (A) Write the beginning of the real Fourier series of f(t) (through frequency 3) {(t) = 2+cost+2sint+3cos2t-3sin2t+3cos3t+0+. (B) Give the real Fourier coeficients for the following functions: (1) The derivative f'(t) a --1 -6 ... b, - 2 by -6 (H) The function f(e) – 2 de =0 3 3 ... b,-2 -3 by (iii) The antiderivative of (f(t) – 2) (with C = 0) 1 3/2 ... -2 by 3/2 (iv) The function f(t) + 3 sin(3t) +3 cos(2t) đo = 2 1 6. 3 b,-2 by -3 by -3 (Iv) The function f(2t) 2 1 3 3 ... 2 bz -3 by

Suppose that f(t) is periodic with period |-, 7) and has the following real Fourier coeficients: do - 4, a, -1, az- 3, ag - 3, b = 2, b = -3, bg = 0, (A) Write the beginning of the real Fourier series of f(t) (through frequency 3) {(t) = 2+cost+2sint+3cos2t-3sin2t+3cos3t+0+. (B) Give the real Fourier coeficients for the following functions: (1) The derivative f'(t) a --1 -6 ... b, - 2 by -6 (H) The function f(e) – 2 de =0 3 3 ... b,-2 -3 by (iii) The antiderivative of (f(t) – 2) (with C = 0) 1 3/2 ... -2 by 3/2 (iv) The function f(t) + 3 sin(3t) +3 cos(2t) đo = 2 1 6. 3 b,-2 by -3 by -3 (Iv) The function f(2t) 2 1 3 3 ... 2 bz -3 by

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

Suppose that f(t) is periodic with period -T, 7) and has the following real Fourier coefficients:
a2 = 3,
аз — 3,
b2 = -3, b3 = 0,
ao
4,
a1 = 1,
b, = 2,
(A) Write the beginning of the real Fourier series of f(t) (through frequency 3):
f(t) = 2+cost+2sint+3cos2t-3sin2t+3cos3t+0+.
(B) Give the real Fourier coefficients for the following functions:
(i) The derivative f'(t)
ao =
, a1 =
-1
, az =
-6
, az =
-9
b, = 2
, b2 =
-6
bz =
(ii) The function f(t) – 2
ao =
, a1 =
, az =
3
, аз —
3
b1 = 2
, b2 =
-3
bz =
(iii) The antiderivative of (f(t)
2) (with C
0)
ao =
, a1
, a2 =
3/2
, аз
1
b1 =-2
b2 = 3/2
b3 =
(iv) The function f(t) + 3 sin(3t) + 3 cos(2t)
ao = 2
, a1 =
1
, a2 =
6
, аз —
3
b, = 2
b2 =
-3
b3 =
3
(iv) The function f(2t)
an =2
, a1
, a2
3
, a3
3
b, =
2
, b2 =
-3
b3 = 0

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