What is inverse oflaplace 4/(5s) ?

The answer to inverse oflaplace 4/(5s) is 4/5 \H(t)

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inverse oflaplace 4/(5s)

inverse laplace

\frac{4}{5 s}

\frac{4}{5} H (t)

Solution steps

L^{- 1} {\frac{4}{5 s}}

= L^{- 1} {\frac{1}{5} \cdot \frac{4}{s}}

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{1}{5} L^{- 1} {\frac{4}{s}}

Use Inverse Laplace Transform table:

L^{- 1} {\frac{a}{s}} = a H (t)

Where

H (t)

is Heaviside step function

= \frac{1}{5} \cdot 4 H (t)

= \frac{4}{5} H (t)

What is inverse oflaplace 4/(5s) ?
The answer to inverse oflaplace 4/(5s) is 4/5 \H(t)