Chapter 7: Q7.4 - 3E (page 374)

Determine the inverse Laplace transform of the given function.

$\frac{s + 1}{s^{2} + 2 s + 10}$ .

Short Answer

Expert verified

The inverse laplace transform of the given function is $e^{- t} \cos 3 t$ .

Step by step solution

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
$f = L^{- 1} {F}$
$L^{- 1} \{\frac{n!}{{(s - a)}^{n + 1}}\} = e^{a t} t^{n}, n = 1, 2, \dots$

Find inverse laplace transform for the given function

The given function is $\frac{s + 1}{s^{2} + 2 s + 10}$ .

Find the inverse laplace transform of $\frac{s + 1}{s^{2} + 2 s + 10}$ using $L^{- 1} \{\frac{s - a}{{(s - a)}^{2} + {(b)}^{2}}\} = e^{a t} \cos b t$ as:

$\begin{array}{rcl} L^{- 1} \{\frac{s + 1}{{(s + 1)}^{2} + {(3)}^{2}}\} & = & L^{- 1} \{\frac{s - (- 1)}{[s - {(- 1)}^{2} + {(3)}^{2}}\} \\ = & e^{- t} \cos 3 t \end{array}$

Therefore, the inverse laplace transform of the given function is $e^{- t} \cos 3 t$ .

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Determine the inverse Laplace transform of the given function.

$\frac{s + 1}{s^{2} + 2 s + 10}$ .

Short Answer

Step by step solution

Determining the inverse laplace transform

Find inverse laplace transform for the given function

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Short Answer

Step by step solution

Determining the inverse laplace transform

Find inverse laplace transform for the given function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Determine the inverse Laplace transform of the given function.

$\frac{s + 1}{s^{2} + 2 s + 10}$ .