Short Answer

Determine the inverse Laplace transform of the given function.
$\frac{1}{s^{5}}$ .

The inverse laplace transform of the given function is $\frac{t^{4}}{24}$ .

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Determining the inverse laplace transform

For a given transfer function H, the Inverse Laplace Transform takes the output Y(s) and determines what X(s) it is in terms of (s).
Consider a function F(s), if there is a function f(t) that is continuous on $[0, \infty)$ and satisfies $L {f} = F$ then we say that f(t) is the inverse Laplace transform of F(s) and employ the notation
localid="1662725690417" $f = L^{- 1} {F}$
localid="1662725700279" $L^{- 1} \{\frac{n!}{{(s - a)}^{n + 1}}\} = e^{at} t^{n}, n = 1, 2, \dots$
Constant multiplication property of inverse laplace transform, for function and constant.
localid="1662725707425" $L^{- 1} {a \cdot f (t)} = a \cdot L^{- 1} {f (t)}$

Find inverse laplace transform for the given function

The given function is $\frac{1}{s^{5}}$ .

Find the inverse laplace transform of $\frac{1}{s^{5}}$ using localid="1662725728091" $L^{- 1} {a \cdot f (t)} = a \cdot L^{- 1} {f (t)}$ and $L^{- 1} \{\frac{(n)!}{s^{n + 1}}\} = t^{n}$ as:

localid="1662725718604" $\begin{array}{rcl} L^{- 1} \{\frac{1}{s^{5}}\} & = & L^{- 1} \{\frac{1}{24} \cdot \frac{24}{s^{5}}\} \\ = & \frac{1}{24} L^{- 1} \{\frac{24}{s^{5}}\} \\ = & \frac{t^{4}}{24} \end{array}$

Therefore, the inverse laplace transform of the given function is $\frac{t^{4}}{24}$ .

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Fundamentals Of Differential Equations And Boundary Value Problems

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Short Answer

Determine the inverse Laplace transform of the given function.
$\frac{1}{s^{5}}$ .

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Determining the inverse laplace transform

Find inverse laplace transform for the given function

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Fundamentals Of Differential Equations And Boundary Value Problems

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Determine the inverse Laplace transform of the given function.1s5.

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Determining the inverse laplace transform

Find inverse laplace transform for the given function

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Determine the inverse Laplace transform of the given function.
$\frac{1}{s^{5}}$ .