2. Determine the inverse Laplace transform of the function below. 9 (2s + 9)5 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. 2- 1 - 9 ( 25 + 9)5 / 3: Table of Laplace Transforms f(t F(S) = 1{f)(s) 1 5: S >0 e at 1 2, S>0 n! to , n= 1,2,... b sin bt S cos bt 52 + 2 : 530 nI eaten , n = 1,2,... S - ajn + 1 : $>a b e asin bt (s - a)2 + b2 > > > a s - a e at cos bt (s - a)2 + 2 . S > a 4: Properties of Laplace Transforms {{f + g} = fff} + fig) ((cf) = cuff) for any constant c Leaf(t) (s) = {(f)(s - a) { {f} (s) = siff}(s) - f(0) f(f') ( 5 ) = 52 eff] (s) - sf(0 ) - f' ( 0 ) { {f()}(s) = s" eff)(s) -s" -f(0) - sn -2f'(0) - ... - f(n - 1) (0) I{if(1 ) ) ( s ) = ( - 1) 0 - ( 2 (f) (s ) ) dsn 2- 1( F 1 + F 2 ) = 2-' ( F 1 } + 2-1 ( F 2 } 2- 1( CF ) = Cy-1( F )3. Determine the inverse Laplace transform of the function below. 6s + 50 S + 8s + 52 Click here to view the table of Laplace transforms." Click here to view the table of properties of Laplace transforms. 2 - 1/ 5s + 50 54 + 85 + 52 6: Table of Laplace Transforms f(t) F(s) = 1{f)(s) 1 e at S-a: $>0 n! to , n = 1,2, ... gn+ 1 : 5>0 b sin bt 52 + 2: 5 0 S cos bt eatth, n = 1,2,... (s - a)n + 1 : $>a b e at sin bt (s - a)2 + 2 , $ > a s - a e at cos bt (s - a)2 + 2 > > > a 6: Properties of Laplace Transforms { {f + g} = (f) + fig) { {cf) = cf (f) for any constant c {{eatf(t)} (s) = {{f)(s - a) I (f'} (s) = SI(f)(s) - f(0 ) f(f') (s ) = s' eff)(s) - sf(0) - f' (0 ) e(f()} (s) = s" eff,(s) - sn-1f(0) - s"-2f'(0) - ... - f(n- 1)(0) { {t" f(1 ) ( s ) = ( - 1 ) n - dan ({ {)(s)) 2 - 1 ( F 1 + F 2 ) = 1- 1 ( F 1 ) + 2- ( F 2 } 1- ( CF ) = Cy-1{F }1. Determine the inverse Laplace transform of the function below. 9 $2 + 49 Click here to view the table of Laplace transforms. 1 Click here to view the table of properties of Laplace transforms.2 9 132 + 49 ) : Table of Laplace Transforms f(t) F(s) = 1{f)(s) 1 1 e at s- a: $>0 n! to , n = 1,2,. gn + 1: 5>0 b sin bt S cos bt +62:520 e atth, n = 1,2,.. S - a)n+ 1 : $>a b e at sin bt (s - a)2 + b2 > > > a 6- a e at cos bt (s - a)2 + 2 > > > a 2: Properties of Laplace Transforms fff + g) = {{f) + fig) {{cf) = cf {f) for any constant c the atf(1)} (s) = {{0)(s - a) * (f) (s) = SI (f)(s) - f(0 ) f (f') ( s ) = 52 elf, (s ) - sf ( 0 ) - f' (0 ) e(f()} (s) = s" eff)(s) - s- f(0) - s" -2f'(0) -... - f(0-1) (0) I(if(1 ) ( s ) = ( - 1 ) n - ( 2 (0 (5 ) ) dsn 2 - 1 ( F 1 + F 2 ) = 2 1 { F 1 } + 2- 1 ( F 2 } 1 {CF ) = Cy {F ]