What is inverse oflaplace 1/(s(s^2+200)) ?

The answer to inverse oflaplace 1/(s(s^2+200)) is 1/200 \H(t)-1/200 cos(10sqrt(2)t)

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inverse oflaplace 1/(s(s^2+200))

inverse laplace

\frac{1}{s ( s ^{2} + 200 )}

\frac{1}{200} H (t) - \frac{1}{200} cos (102 t)

Solution steps

L^{- 1} {\frac{1}{s ( s ^{2} + 200 )}}

Take the partial fraction of

\frac{1}{s ( s ^{2} + 200 )} : \frac{1}{200 s} - \frac{s}{200 ( s ^{2} + 200 )}

= L^{- 1} {\frac{1}{200 s} - \frac{s}{200 ( s ^{2} + 200 )}}

Use the linearity property of Inverse Laplace Transform:

For functions

f (s), g (s)

and constants

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

= L^{- 1} {\frac{1}{200 s}} - L^{- 1} {\frac{s}{200 ( s ^{2} + 200 )}}

L^{- 1} {\frac{1}{200 s}} : \frac{1}{200} H (t)

L^{- 1} {\frac{s}{200 ( s ^{2} + 200 )}} : \frac{1}{200} cos (102 t)

= \frac{1}{200} H (t) - \frac{1}{200} cos (102 t)

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What is inverse oflaplace 1/(s(s^2+200)) ?
The answer to inverse oflaplace 1/(s(s^2+200)) is 1/200 \H(t)-1/200 cos(10sqrt(2)t)