Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the Laplace...

 

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Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the Laplace transform of the function below. te cos 6t Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. P{te¹ cos 6t} = Properties of Laplace Transforms L{f+g} = L{f} + L{g} L{cf} = c{f} for any constant c L{e atf(t)} (s) = L{f}(s − a) L{f'} (s) = sh{f}(s) - f(0) 2 Lf''(s) = s² {f}(s)-sf(0) - f'(0) n {f(n)} (s) = s¹ s^ s′ 2{tf(t)} (s) = (-1) (Af}(s)) {f}(s)-sn-1f(0)-s-2f'(0)-... -f(n-1) (0) dn n ds Table of Laplace Transforms f(t) 1 e e t", n = 1,2,... at sin bt cos bt e atên, n = 1,2,... at at e sin bt cos bt F(s) = {f}(s) 1 - 5. S> 0 S 1 s-a' n! n+1 S b s² + b² 2 S>0 S>0 S>0 S s² + b² 2 n! (s-a)n +1,s>a b (s− a)² + b²¹S² s-a S>0 " (s-a)² + b² s>a s>a Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the Laplace transform of the function below. te cos 6t Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. P{te¹ cos 6t} = Properties of Laplace Transforms L{f+g} = L{f} + L{g} L{cf} = c{f} for any constant c L{e atf(t)} (s) = L{f}(s − a) L{f'} (s) = sh{f}(s) - f(0) 2 Lf''(s) = s² {f}(s)-sf(0) - f'(0) n {f(n)} (s) = s¹ s^ s′ 2{tf(t)} (s) = (-1) (Af}(s)) {f}(s)-sn-1f(0)-s-2f'(0)-... -f(n-1) (0) dn n ds Table of Laplace Transforms f(t) 1 e e t", n = 1,2,... at sin bt cos bt e atên, n = 1,2,... at at e sin bt cos bt F(s) = {f}(s) 1 - 5. S> 0 S 1 s-a' n! n+1 S b s² + b² 2 S>0 S>0 S>0 S s² + b² 2 n! (s-a)n +1,s>a b (s− a)² + b²¹S² s-a S>0 " (s-a)² + b² s>a s>a