What is inverse oflaplace 5/(pis^2) ?

The answer to inverse oflaplace 5/(pis^2) is (5t)/pi

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inverse oflaplace 5/(pis^2)

inverse laplace

\frac{5}{π s ^{2}}

\frac{5 t}{π}

Solution steps

L^{- 1} {\frac{5}{π s ^{2}}}

= L^{- 1} {\frac{5}{π} \cdot \frac{1}{s ^{2}}}

Use the constant multiplication property of Inverse Laplace Transform:

For function

f (t)

and constant

a : L^{- 1} {a \cdot f (t)} = a \cdot L^{- 1} {f (t)}

= \frac{5}{π} L^{- 1} {\frac{1}{s ^{2}}}

Use Inverse Laplace Transform table:

L^{- 1} {\frac{( n ) !}{s ^{n + 1}}} = t^{n}

L^{- 1} {\frac{1}{s ^{2}}} = t

= \frac{5}{π} t

= \frac{5 t}{π}

What is inverse oflaplace 5/(pis^2) ?
The answer to inverse oflaplace 5/(pis^2) is (5t)/pi