Question

Determine the inverse Laplace transform of the function below. se -35 s2 +85 + 25 e Click here to view the table of Laplace transforms. -35 -(41-12) Se s2 +8s + 25 3 (3 cos (3-9) - 4 sin (3-9))h(t-3) (Use parentheses to clearly denote the argument of each function.) L-1

Answer 1

let (A) = 구 (1) 48425 Now, 전 8425 + 2 S. 4 + " + 9 (A+A+ (+4) 시 (3 At 4 3 7/3 (썬t3 (+4) + 3 나 L . {()} 382 { - (+37 3 (432 +시 너 = } { (3 (3

11 e- -96 C's-}-<* { 3 s +3² [using first shifting theorem e at cos (34) 4 é At sin (34) 3 cos (3+) . 4 sim (3+) (34)) -(2) - Now , we state as follows Second shifting theorem If I'{f(3)} = F(*) then I'{eas f(s)}=G(4), 1 > لے 7 a Where G(+) F(-a) ta &ca lie, I'{e-as f(x)} F (A-a) h(t-a) where th' is Heavisida unit step function Now, in this problem L'{+18) 3 cos (34) - 4 sm (3+) 3 [using (2) Using the second shifting theorem stated above e-at we get (7-3) L'{e-3 f(x)} est 3 E Cos (31 -3)) – 4 sim (314-3) h(+3) TA esss S++25 : } e-(4+=12) (31-9].n (4-3) 3 cos (31-9) - 4 sin (34-9) 3 Where h(+-3) is Heavisida unit step function which is defined as follows: h(+-3) when t>3 when & <3. وا o

Please give a thumbs up if you are benefited.