What is inverse oflaplace 7/(s^2+42) ?

The answer to inverse oflaplace 7/(s^2+42) is sqrt(7/6)sin(sqrt(42)t)

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inverse oflaplace 7/(s^2+42)

inverse laplace

\frac{7}{s ^{2} + 42}

\frac{7}{6} sin (42 t)

Solution steps

L^{- 1} {\frac{7}{s ^{2} + 42}}

= L^{- 1} {\frac{7}{6} \frac{42}{s ^{2} + ( 42 ) ^{2}}}

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)}

= \frac{7}{6} L^{- 1} {\frac{42}{s ^{2} + ( 42 ) ^{2}}}

Use Inverse Laplace Transform table:

L^{- 1} {\frac{a}{s ^{2} + a ^{2}}} = sin (a t)

L^{- 1} {\frac{42}{s ^{2} + ( 42 ) ^{2}}} = sin (42 t)

= \frac{7}{6} sin (42 t)

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

\frac{\partial}{\partial x} (x^{2} - 7 x y + y)

\int csc^{2} (\frac{x}{5}) d x

\frac{\partial}{\partial x} (sin (x^{2} - 7 x y))

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

What is inverse oflaplace 7/(s^2+42) ?
The answer to inverse oflaplace 7/(s^2+42) is sqrt(7/6)sin(sqrt(42)t)