Question

n=2

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

Answer 1

3. Griven function & (n) = ( 2 ) solncn nanaan Here 10=2 So the function is f (n) = 20; OLAL2 4; 2LnL4 we know f(n)= a + nal the fourier Series expansion E ancos nan bn Sin in Where T be period. ar fong da ana * J fon) cos han de Tfen) Sin nanda bra Here The Geraph of this function YA -y=4 2 XIT Y' This is a step function where T=2 Here the domein of this function (0,4) 1229 Ž J f (x) da - Ž[ { tem dat { " fond de - ₃ [ot suuda] = ₃ [142 (4-2) = 2.(2) = 4

- 2 Sinnan da 4 (-1+1) if n is even ana 4 놀 l'Acon) f(n) Cos nA a da Ź J & (n) cos han det 16M) cos nanda + Z J & coB nanda 0 4 ( (na = 28 me nenda (sin nan = u ha [sin yon _ sin 2nx] = u ha [sin(204) - Sin (na) bn - for sin nanda = z Jrf in Singanon + Ź J (n) senganda =Ź je 4 sinnanda 4 = 2 + Cobana 2 na 2 [ cos na may [- Cos una = 1 / [- (08 (242) + (osnx] u ha [-2 + (-on na u 1-1-1) If no odd.