Question

dan Multiplication by t. 8. Find the following Laplace transforms using the formula L[t"f(t)] = (-1)", (a) [t3e-36] (b) C[(t + 2)2e'] (c) C[t(3 sin 2t - 2 cos 2t)] (d) L[tsin t] (e) C[t cosh 3t) (1) [(t-1)(t - 2) sin 3t] (g) [t3 cost] 9. Applying L[t"f(t)] = (-1)", , calculate (a) Sºte-3t sin t dt (b) Scºt?e-t cost dt recimento e contato Llegarsim 225 (-1)" IEC d'Fs) dsh

Answer 1

dan Now (8) (9) Llt - 3t) = ? Now Lit" 814) = 65" d' FUN! Now 811) eat, L18!!))= 543 Now Lit'3+) = -13° 4 (1) = (- 19453") = ( 8+3 - (-2).(-3) (x+3)= 6 - 117€) - etusi 373 (8+3) 4 (6) L[ (2+2) et] =? -[(42+4+2+) et]. Lltet) + L (4et) + [etety Now ultet) = (-1 dh (6) [:lle) = 1 +7 8-1 (-1) (-)(0-) Lluet)= 4 Llet) 4. s-l

H latet)= alltet) - 2 (-1) d (6) = 2.4-16-1863-15 are (s-12 Now , {(t+1) et] = alt et) + Llyet) + 2(dtet) co to +3932 a s-1 2+4(5-)"+2(3-1) nnah (3-1)3 112 - 2 + 48² +4 -85 +25-2 11 (313 L[[t+'et] = 48-60+4. (81)3 () {[+1 38inat - 2 Casat)] = ? Now Ll3t sinat - 2t casat] =32 t. sinat)-2. 117. (08&t) Aleo Llaingt) = 4, +(012+) = x+y en eltsinat) = (-) d ( 4 ) e da Loto) - (-2) 1/4 aina t)

& 1lt larat) = -1-1) (-1) 1 s +4-282 (+4). 1 - 8 (28) 1 I (3²+4)2 1 (2+4) 2 11+(12+) - szy 1844)? So, L[t (3 sinat - 2 carat) 7= 3.2 lt.sinat) -2 Lt. Laat) = 3. us (5²+4)2 – 2132-4) 8² +42 128 - 25+ 8 - - 25 + 128+ 8 (8474) (3²74) 2 - 28²7 128+8 Sog L[t13 einat - 2 C12t) ] = 73 274) 2 Ll teint) = ? (sint) = 34 L (th sint) = (-1) a (1) Law"). (prests)

21tsint) = 42). da list) = (-2)./ (3471).1 - 8.2(371). 23 (32+1)9 2 as – 45-48. =(-2) (3 + 1 + 25% - 43" _482 (3+1) 4 a - 2 (-34 -25² + 1 7 18²7199 - 68 +48²-2 (2+1) 4 Llit sint) = 65+45 -2.

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