What is inverse oflaplace (m*s)/(s^2+s/(n*m)) ?

The answer to inverse oflaplace (m*s)/(s^2+s/(n*m)) is me^{-t/(mn)}

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inverse oflaplace (ms)/(s^2+s/(nm))

inverse laplace

\frac{m \cdot s}{s ^{2} + \frac{s}{n \cdot m}}

m e^{- \frac{t}{mn}}

Solution steps

L^{- 1} {\frac{m s}{s ^{2} + \frac{s}{mn}}}

Expand

\frac{m s}{s ^{2} + \frac{s}{nm}} : \frac{m ^{2} n}{mn s + 1}

= L^{- 1} {\frac{m ^{2} n}{mn s + 1}}

= L^{- 1} {m \frac{1}{s + \frac{1}{mn}}}

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)}

= m L^{- 1} {\frac{1}{s + \frac{1}{mn}}}

Use Inverse Laplace Transform table:

L^{- 1} {\frac{1}{s - a}} = e^{a t}

L^{- 1} {\frac{1}{s + \frac{1}{mn}}} = e^{- \frac{t}{mn}}

= m e^{- \frac{t}{mn}}

\frac{\partial}{\partial x} (y^{2} (2 x e^{2 x y} + e^{2 x y} \cdot 2 y x^{2}))

\frac{\partial}{\partial x} (2 y^{3})

x \to 0 lim (\frac{4}{x ( x + 2 )})

(5 x - 3)^{4} (2 x - 7)^{- 3}

x \to 0 + lim (\frac{8}{x} - \frac{8}{∣ x ∣})

What is inverse oflaplace (m*s)/(s^2+s/(n*m)) ?
The answer to inverse oflaplace (m*s)/(s^2+s/(n*m)) is me^{-t/(mn)}