Question

mechanical engineering analysis help, get from problem to solution, pls show all work, thanks.

Problem 1. Find the Fourier series expansion of a half-wave rectified sine wave depicted below. ft) Answer: л f(t) = 1+ 5 sinat - cos 2nt 2 Ecos 4nt -: - cos баt + ... 2 ДІЛ 35 0 2; 3;

Answer 1

0 fet) = (* Sinta) oct 0 I It ca fets a sinkt) 1 oct</ <tca 0 fourier series of fit is given by fut) 5 do + (en cok (enHoa sindano T-2 fit) = lote an costant) + bn Sin (and (and - n=1 T ao = If fit fit) dd ao = est Sasinat)dA L costat, 0 - est let (-COB*tcoso) (1+1) Po =) T an = fit) costat de T

an ' st a Sincat) Cos Cant) of when nal = han Sin en+) nt – 90 (021) 874 Sin(nat) et de 'memudad de = a J - R Cos (0-1) at (n-it Cozintl) at Tntija 0 = le Ź Cos (nt) - Corf (n+1) 7-” - nti n-1 let ntlanti - T-EU (Cor[n+1)* (n+1)* -| when nfl = an na-1 bn = 9 T f(t) sin(ant) dt = a sind) Sinnat) dt when no a

a * Sintat) costat dt Fab Sincat) Costa Adh 5 Sincant) dt * أفع (os(ant) ga - klos Cosqa taso 22 a kloro 중xo - o bi = a Sintat) Sincat) dd I sinent) dh = 7T K 11 -CBQat) de 2 Sin (and Ia klor klos no Sinan Sino ga = Kloo

bn = 2 Cos(next Có 3 (21)x+){ if (cos(n-1) IS GR (n-1) and (0-1)ad dr - Scaunulat - comenjat de T 2 Isin(n-1) at _ - T klor frQCnulat nila (n-1)* 11 let Sin (0-1)- Sino (nra Sin (NH)a -sino (AHIA = lot (0-0) when noa (bn = caspat) fet) It n=9 IMB Mo cos(n+1)* -I. COB (mat) ) + +by Sinnat n? Cosental Cos (nat) + 2 sinat fut) = 1 + ItE n- fit) = 1+ A sinkt) & Co8(gat) IS CO3(QAT) - Coffbut)+----