What is inverse oflaplace (450)/(s(s+3)^2) ?

The answer to inverse oflaplace (450)/(s(s+3)^2) is 50\H(t)-50e^{-3t}-e^{-3t}*150t

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inverse oflaplace (450)/(s(s+3)^2)

inverse laplace

\frac{450}{s ( s + 3 ) ^{2}}

50 H (t) - 50 e^{- 3 t} - e^{- 3 t} \cdot 150 t

Solution steps

L^{- 1} {\frac{450}{s ( s + 3 ) ^{2}}}

Take the partial fraction of

\frac{450}{s ( s + 3 ) ^{2}} : \frac{50}{s} - \frac{50}{s + 3} - \frac{150}{( s + 3 ) ^{2}}

= L^{- 1} {\frac{50}{s} - \frac{50}{s + 3} - \frac{150}{( s + 3 ) ^{2}}}

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{50}{s}} - L^{- 1} {\frac{50}{s + 3}} - L^{- 1} {\frac{150}{( s + 3 ) ^{2}}}

L^{- 1} {\frac{50}{s}} : 50 H (t)

L^{- 1} {\frac{50}{s + 3}} : 50 e^{- 3 t}

L^{- 1} {\frac{150}{( s + 3 ) ^{2}}} : e^{- 3 t} \cdot 150 t

= 50 H (t) - 50 e^{- 3 t} - e^{- 3 t} \cdot 150 t

y = x^{x} + 1

t \to 0 lim (\frac{2}{t} - \frac{2}{t ^{2} + t})

5^{3 x}

(- 2, - 1), (4, 2)

\int e^{\frac{x}{100}} d x

What is inverse oflaplace (450)/(s(s+3)^2) ?
The answer to inverse oflaplace (450)/(s(s+3)^2) is 50\H(t)-50e^{-3t}-e^{-3t}*150t