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)

\frac{\partial}{\partial x} (4 x^{3})

f (x) = 8 x - x^{2}, at x = 1

\int (2 + 3 x^{2} - 8 x^{3}) d x

y^{^{''}} + 3 y^{^{'}} + 2 y = 15 + e x

\int x - x^{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)