Question

Use the convolution theorem to find the inverse Laplace transform of the given function 10 (2-4) *****.. }o-0 Enter your answer in the answer box Previous

Answer 1

F8) 2 | 0 1 0 63[62 +) 8+22) ? Q 822 - Let, { ; ; ? (9) . 2 8222 . Ir334 E - 2 ? " 3(8) ; 6242 2 1" {ਡੋਡ ਤੋਂ - 5 3 ਤੋ] , • Sin2E :) 5. 13-1 2 (3-1)! - : PC) .: By convolution theorem, ਨੂੰ 2 t 2 -l 82122 m 2 $*f(u) g(t-u) du ; in ੨|b -u) dਘ. -ਪੰin2[t-u) du -( ))

2 - Jau du. -2 Sucos 2(t-u) de. Integrating sinalt-4) du s 2 t 2 2 first wel get, ju² sing (t-uldu. Integrating by parts uteus 2(t-u) Qu. -cos 2(E-) -7 uz ces 216-4) by parts, a useos 2(t-u) usin2(t-u) -2 ulee u? cos2lt-u) + ų sin 2(t-u) [ + cos2lt-u) +2 u² COS 264 -4) + ų sinalt -u) I cos2(t-1) : to uzsin2(t-u) du Cos 2(t-u) + un sin2(t-u) – COS 217-ce) I coso caso + t sino 0 -0 + eos et 2 2 4 t E, €85 2.Lt -c)]* 2 u2 [ u 2 2. +2 Leos2t. + 2 4 this in (1) we have, putting in Policia in} $ + + €952t] 5 cos 2t 15 t² 5 8 + 4

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