4. Determine the inverse Laplace transform of the function below. Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. 7: Table of Laplace Transforms f(t) F(s) = 2{f)(s) 1 5 : S >0 e at S- a S >0 n! to , n = 1,2,... b sin bt 52 + 62 : 5 >0 S cos bt 52 + 2, 5>0 n! earth , n = 1,2, S - ajn + 1 : $>a b e at sin bt (s - a)2 + b2 : $ >a - a e at cos bt (s- a)2 + b2 " 2, S>a 8: Properties of Laplace Transforms {{f + g} = {{f) + fig} {{cf) = cf (f) for any constant c the atf(t)} (s) = (f)(s- a) { {f} (s) = SI (f)(s) - f(0 ) * (f" ) ( s ) = 52 (f) (s ) - sf (0 ) - f' ( 0 ) e (f( )} (s ) = shelf, (s ) - sn - 1f(0 ) - sn - 2f' (0 ) -... - f(n- 1)(0 ) * {if(1 ) ( s ) = ( - 1 ) 0 -( 2 (1 (s ) ) 2- 1 ( F 1 + F 2 ) = 2-1 (F 1 ) + 2- ( F 2 } 2- 1 ( CF ) = CR-1 ( F } 5. Determine the partial fraction expansion for the rational function below. - 4s - 32 (5+ 2) (52 + 4) - 45 - 32 (s+ 2) ($2 + 4) . Determine the partial fraction expansion for the rational function below. 3s (s - 4) ($2 - 16) 3s (s - 4) (s2 - 16)