- Determine { {F} S2 F(S) + SF(s) - 30F(s)= 25- +6 S + S Click here to view the table of Laplace transforms. 13 Click here to view the table of properties of Laplace transforms. 14 1 (F) = 13: Table of Laplace Transforms F(t F(s) = 1{f)(s) 1 S S >0 e at S- a: $30 n! 1" , n= 1,2,. sn + 1 : $>0 b sin bt S cos bt n! eatth, n = 1,2,... (S - ajn + 1 : $>a b e at sin bt (s- a)+ 2 , S>a e at cos bt (s- a)2 + 2> > > a 14: Properties of Laplace Transforms { {f + g) = {{f) + Lig { {cf} = cf {f) for any constant {{e atf(t)} (s) = {{f)(s -a) { {f) (s ) = si (f) (s ) - f(0 ) I(f') ( s ) = $2 eff} (s) - sf( 0 ) - f' (0 ) e(f )} (s) = s" elf,(s) - sn-1f(0) - s -2f'(0) - ... - f(n- 1)(0) I ( if(1 ) ( s ) = ( - 1) n - ( 2(1} (5) ) 2- 1 ( F 1 + F 2 ) = 2- 1 ( F 1 } + 2-1 { F 2 }7. Determine ~ {F} 85- - 17s +3 F(S) = = s(S - 3)(s - 7) Click here to view the table of Laplace transforms.9 Click here to view the table of properties of Laplace transforms. 10 e - 1( F ) = 9: Table of Laplace Transforms f(t) F(s) = 1{f)(s) 1 eat 1 S-: S>0 to , n = 1,2, ... sn +1 : >0 b sin bt 52 + 2: 530 S cos bt 52 + 62 : s nl e att , n = 1,2,.. (S - a) + 1 : $ >a b e at sin bt (s - a)2 + 2 , S > a - a e at cos bt (s - a)2 + b2 , $ > a 10: Properties of Laplace Transforms (ff + g} = {{f) + fig} {{cf} = cf {f) for any constant c Le atf(t)) (s) = {{f)(s - a) {{f'} (s) = self)(s) - f(0) { {f') ( s ) = 52 eff, (s ) - sf ( 0 ) - f' ( 0 ) effin)} (s) = shelf)(s) - sn - 1f(0) - s-2f'(0) - ... - f(n-1)(0) * (if(1 ) ) ( s ) = ( - 1) n -({ {f) (s)) dsn * ( F 1 + F 2 } = 2 { F 1 } + 2 { F 2 } 2 ( CF ) = ce ( F )8. Determine ~ {F} $4 + 5s+ 10 F (s ) : (5 + 1)2 (5 + 2) Click here to view the table of Laplace transforms. 11 Click here to view the table of properties of Laplace transforms. 12 2- 1(F) = 11: Table of Laplace Transforms fit F(S) = 1{f)(s) 1 1 at 1 6-a: $>0 n! to , n = 1,2, ... sh + 1 : $30 b sin bt 52 + 2: 520 S cos bt 52 + 62: $30 eatth, n = 1,2,... (S - a)n+ 1 : $>a b e at sin bt (s- a)2 + 2 . s = a - a e at cos bt (s - a) 2 + b2 's 12: Properties of Laplace Transforms { {f + g} = {{f) + fig} {{cf) = cf (f) for any constant c the alf(t)} (s) = {{f)(s -a) f(f} (s) = siff}(s) - f(0) { {f'') ( s ) = $2 2(f) (s) - sf( 0 ) - f' ( 0 ) e(f()} (s) = s" eif)(s) - s-1f(0) - s -2f'(0) - .. - f(n-1)(0) I {FF(1 ) } ( 5 ) = ( - 1 ) n - ( 2 (0) (5 ) ) ds" 2 - 1 ( F 1 + F 2 ) = 1 ( F 1 ) + 2 { F 2 ) { {CF ) = CA (F )