Question

Find a Fourier series expansion of the periodic function 0 - Sts- 2 f(t) = 4x2 cost VI VI st 2 0 .sta 2 f(t)= f (t+2A) Select one: 1 (-1)** cos 2n a. f (0) = 87 +87 4n2 -1 12 12 * (-1) "*l cosnt b. f(t) 2n-1 =+ 7 77 c. f(t) 6 12 - (-1)' cosnt 2n-1 =1 00 d. f(t) = 4A+87 .(-1) "* cos ant 4n2-1

Answer 1

ANSWER:

Given fLE) - ut cost i !! LETT/2 -1/2 L + Cl2 T/2 atau qft) 12 रा 712 7112 f(t) f(t)= Even function a) bn=0 fis of Eſt) = ' trancoscoot) +bosincang + f(t)dt ao = . Z 2 ut cost de D 8T (siento 72 87 E-sin (12-0)} 2 873 (sin 1/2 - sino] = 8T [] ao 2875

ant j'fles cosent)dt 12 1/2 s T cost cosneldt T2 - 41 ] [co CO Dt +los (D 5-19+] at sin (at)t) [sro C0-10 in- 0 Tle anff 45( sin (n+1) 912 SM-117/2 + Dt1 TV2] = f um[nto -ni] ;n=4,8,16min um l hair no. 2, 6, 10- o :: > .n : Odal Replau s' with for Even term . f(t) 87 + 8 ml (199+1 2 cos (ent) un²1 f(t) = ull +8T E wscant) un²-1

Therefore,option D is correct answer.