What is inverse oflaplace (900)/(s^2+90s+900) ?

The answer to inverse oflaplace (900)/(s^2+90s+900) is 12sqrt(5)e^{-45t}sinh(15sqrt(5)t)

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inverse oflaplace (900)/(s^2+90s+900)

inverse laplace

\frac{900}{s ^{2} + 90 s + 900}

125 e^{- 45 t} sinh (155 t)

Solution steps

L^{- 1} {\frac{900}{s ^{2} + 90 s + 900}}

Expand

\frac{900}{s ^{2} + 90 s + 900} : 900 \cdot \frac{1}{( s + 45 ) ^{2} - 1125}

= L^{- 1} {900 \cdot \frac{1}{( s + 45 ) ^{2} - 1125}}

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)}

= 900 L^{- 1} {\frac{1}{( s + 45 ) ^{2} - 1125}}

L^{- 1} {\frac{1}{( s + 45 ) ^{2} - 1125}} : e^{- 45 t} \frac{1}{15 5} sinh (155 t)

= 900 e^{- 45 t} \frac{1}{15 5} sinh (155 t)

Refine

900 e^{- 45 t} \frac{1}{15 5} sinh (155 t) : 125 e^{- 45 t} sinh (155 t)

= 125 e^{- 45 t} sinh (155 t)

\int 8 x + 6 cos (x) d x

\int_{0}^{x} e^{- u} d u

(\frac{1}{sin ( x )})^{^{'}}

\int v^{2} d v

\frac{2 s + 1}{s ^{2} + 9}

What is inverse oflaplace (900)/(s^2+90s+900) ?
The answer to inverse oflaplace (900)/(s^2+90s+900) is 12sqrt(5)e^{-45t}sinh(15sqrt(5)t)