Question

Please give me a step-by-step solution for this with use of "the convolution theorem"!

18. Find 18. Find (6) - · Asa ਭੂt coast + sin $t ਮੈਗ , ( 3 . 79. Find A8. (a) ਮੈਂ (3 - 2) sin t - 3t cost}, (b) ਛੰst(sin 2t - 2t cog 2t)

Answer 1

solue ® Let C Qusi = se (1²+4)² Let us assume that Filma Ontless and Gisi = rot use FIA) - - and GIA) - ^2+(212 - s2+ (2² then f1t) = ['] Flail = cos(2+) and g(t) = ['{G1031 = cos(2+) - By Convolution theorem, we get L'{QW1 = Fus) Gussi = (*g) (t) زرنا بل (20) م - +$ 2100(27-20) cos(20) du 2 t - 20) los (20) du Il cos I cos (27-20+20) + los(27-20-20) du

151691 + * corlat) + korlat-quy de 12 los (t) + cos/2t-40) cho colae) (U14+ ( ain fet-Ray)* 7 = It los(2+) + 124 I sin (2+) ula Used - For mula Used - " L a colats 2 cos (al costb) = ... cos (a+b) + cosla-b) sin(2t - 14 ) = sin(-2+1 = -sin (24)

Solve @ @ Let Qisa (32+1)3 Let us assume that Flos = woorja and Glass FISI = (12+12 and 141 - - St ! $2+1 then flu = 14 life wise } = {(sint – A conto) and 2141 = ["latit = sin(t) 1. By convolution theorem , we get L"{qust = 5 + (sia - U cores) sin(40) du sinlu) sin(t-u) -uvoslu) sinlt-ul du

2 sin lu) sin tuj - zucos(u) sinlt-u) do cos(U-x+u)-cos(utt-u) .du luksinlutt-u)- sinlu-ttu)) du ( silou.cento)** (0 (ustavu te co *** uainet + color:#) dit usin Lt) + los(20-t) dt t² sinltltt cosit) | = $( sin tu) t loslt) + sin(t)-0) +(tºsint! ++ 20,00) + + ( uzining central - * in - + 2014) - Elesinus touty 1 Vesinlt), sin(2v-t) 42 + * ( * 9in(!) + sinut - 0 + sintets) (3-+2) sinltl-3t cosity Formula Used - winter sin b) = cos(4-) - Losla+b) la sin lb) = sin(a+b) - sin(a-b)

Solve 79 ② het Qus= 64933 Fusta FI = lotters and 6191 = Tewasa $+(212 and GIA = 12+ (2) 2] 2 then flt = ["Flande sin bhd and glt) = ['IGIA) = t sin (2+). t - I sin (24) 2X2 12(t-U) Upin (20) 2 4. 1"{019) = 1* sin(21-0). U minly do et t'u sinlat-su) simtes du de su (cos(z »Do) – Lov/2t » +9) do 1(2+-20-20) - los(2+-

2) t op (24) sin (2+-40) U lot du It sin(24) (101124-40) - cod 24)) du tal (ul din lat, gy - veten) Saints ou encore **(taiplay) – trebuje prin cap-49, vanud * * (taime) - 42000] * * ( sauter oy), warganya * ( toimis. Praesen) to continue to you = H ( tapis Poco) +i (trantasy = 6** (sin(1) = 24 2013+)) -t² cos(2+)/ + los (2+-40), ulos(2+) + tsin(at) 4 16 I cos (24) 16 t²cos(2+) los (24) t sin (2+)-t² cos (2+) / +2 101/2t) 165 1-2t cos/ 69
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