Question

Question 3 3 pts Find the Fourier Sine series for the function defined by f(x) = { 0, 2n, 0 <*n n<<2n and write down, 1. The period T and the frequency wo of the Fourier Sine series 2. The coefficients for r = 1,2,3,...

n=7

Answer 1

for n=7 f(oc) - 0 < x < 7 7<x514 14 (1) f(x) is defined in the period (O) = (0,14) Then, Denied T of the fourier sine senes- 2l=2814 T= 29 frequency we z 2A 즈 14 2T 28 (2) bn- 2 l 4462) sin ning sin nax dx I bn: 2174fosin nax dx + " f(x) sin naxdx] 14 l e 0 7 ly bna o Sinnāx dxt I 14. Sinnax dx? e 7 o 7 ty - bn= X 14 sin nax dr. 14 7 7 14 bna 14 COS Қх 14 nt 7 bn : - 28 NT cos na Cos na 2 bna 28 f cos no - cos no] 기자

NOW when n is odd COS na 2 = -1; when n +212n-1) when nacan) بلت And, cos na = -1, when nis odd when a wis even i.e. when n→ 2 (2n-1) and also when n=2(2n). bn = S 28 NT cosAN 2 28 [o-(-1)] when nis odd ien:1,3,5,7-.. n = 28 [-1-1] when 7 > 2(2n-1) i-e. n = 216,10,14 NC 28 [i-1] when + 2(2n) i.e. n = 4, 8, 12, 16 na bn = for - هديل : لا 28 na - 56 na for n=2,6,10,14 0 for no 4, 8, 12, 16