Question

Laplace transform for the function below

- f(+) 8+ sin 3t 10

Answer 1

er fets dt o Non, 3C0S 34. St.Tusing we know that Laplace transformation of fet) is defined by į (foto) = -St and denoted by L($(+) = =F(S) St dt 8 est at ut Sinate at It e st dt = 8. Jest - 8 2 Sim3t. e dt integration -S s [by parts_ 3 cos 3t. est et 2 where ra 12 8 ∞ -- (0-1) = 8 J = J Simatrest at [coszą e st) * -Sassins? *[(0-1)]- en s J= 11 est dt S ts CH ma

Now, 32 J 52 52 J- 3 J+33-95 (123) 3% 기 J 52 a (3²4 432 I =%7 313 S2 ㅋ JE $²432 sr 3 87 > JE Х 5²3? 3 a J = 3 s²+32 Thus using and 3 2 that is the value of I and I in the equation o then we get f(s) I tJ 8 3 + S 5432 Hence 3 L( 84 Sin 34 8 S f 5²432