What is inverse oflaplace (1000)/(s+1000) ?

The answer to inverse oflaplace (1000)/(s+1000) is 1000e^{-1000t}

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inverse oflaplace (1000)/(s+1000)

inverse laplace

\frac{1000}{s + 1000}

1000 e^{- 1000 t}

Solution steps

L^{- 1} {\frac{1000}{s + 1000}}

= L^{- 1} {1000 \cdot \frac{1}{s + 1000}}

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)}

= 1000 L^{- 1} {\frac{1}{s + 1000}}

Use Inverse Laplace Transform table:

L^{- 1} {\frac{1}{s - a}} = e^{a t}

L^{- 1} {\frac{1}{s + 1000}} = e^{- 1000 t}

= 1000 e^{- 1000 t}

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What is inverse oflaplace (1000)/(s+1000) ?
The answer to inverse oflaplace (1000)/(s+1000) is 1000e^{-1000t}