What is inverse oflaplace (280)/(s^2+14s+245) ?

The answer to inverse oflaplace (280)/(s^2+14s+245) is 20e^{-7t}sin(14t)

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inverse oflaplace (280)/(s^2+14s+245)

inverse laplace

\frac{280}{s ^{2} + 14 s + 245}

20 e^{- 7 t} sin (14 t)

Solution steps

L^{- 1} {\frac{280}{s ^{2} + 14 s + 245}}

Expand

\frac{280}{s ^{2} + 14 s + 245} : 280 \cdot \frac{1}{( s + 7 ) ^{2} + 196}

= L^{- 1} {280 \cdot \frac{1}{( s + 7 ) ^{2} + 196}}

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)}

= 280 L^{- 1} {\frac{1}{( s + 7 ) ^{2} + 196}}

L^{- 1} {\frac{1}{( s + 7 ) ^{2} + 196}} : e^{- 7 t} \frac{1}{14} sin (14 t)

= 280 e^{- 7 t} \frac{1}{14} sin (14 t)

Refine

280 e^{- 7 t} \frac{1}{14} sin (14 t) : 20 e^{- 7 t} sin (14 t)

= 20 e^{- 7 t} sin (14 t)

\int m + n x d x

\frac{d}{d x} ((1 - 5 x)^{- 2})

y = e^{3 x} cos (π x), (0, 1)

\frac{\partial}{\partial y} (sin (yz))

\int - \frac{2 x}{( x ^{2} - 2 ) ^{3}} d x

What is inverse oflaplace (280)/(s^2+14s+245) ?
The answer to inverse oflaplace (280)/(s^2+14s+245) is 20e^{-7t}sin(14t)