Question

Consider the 2-periodic function given on the interval [0,27) by if 0 <<< 2 (x - 72 if <<< 27. 1. Sketch the graph of this function. 2. Find its Fourier series.

Answer 1

Solved using basics of Fourier Series

ΣΚΟΥΤΕ 5 HOO

25 T 27 floc-x)? doc a l doodx 쓸 40 = ocdat160-x)? dac # T T txc²_200+2²) da T 2 T? 23 - Tx² + 3x 2 = 7+1 873 8 T3 - 4K3 +2T 473 +273_73 +73-73) 3 (62) 2K + #3 XX2+1 -233 - 3 I + (773 -2A3 = a + T² 3 27 20 an= = Syacos(nodoc - I s secas (no Odx + 1 G²-27x +7²) Lastnoldi x sin (nx) + Los (nx +1 66²-27x+7²) sin(x) + (2x-27) cos(na n n2 T n 5?

2T +2 6-sinfon) 1 7 o +(-in - h² 0-0 - (2x-22) (-1) n² nz 7 an I (-10-1 27 n2 TL n² an= (-10-1+27 Tn² bn= 15 Jx) sin(x) dx x sinchalda (x²270 +7²) sin(nada (27 + T

T b + HK nz 27 13 bota cos(nx) + sin(nx) (0²-27x+2²) C-casino) + (22-27) sin(ooo +2005 (1x)] *bn=1 -I-ID (47² 47² 7²) (-1) Cute (23-24+?)(-(-10%) + 0 +0 - 26-09 -(-09 A +211-6-1) to-o-o + n T +0+ 2 53 n3 bn + 1 TL n n HE n3

2 20) = at fo)= aşan cos Chol) + bn sin(n) = 7+3+(021+27).65cm) 2(1+4-07))Sino) n=1 Gun + 1-T² T n n3