Chapter 7: Q7.4 - 1E (page 375)

Determine the inverse Laplace transform of the given function.

$\frac{6}{{(s - 1)}^{4}}$ .

Short Answer

Expert verified

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

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 $\frac{6}{{(s - 1)}^{4}}$ .

Find the inverse laplace transform of $\frac{6}{{(s - 1)}^{4}}$ using as $L^{- 1} \{\frac{n!}{{(s - a)}^{n + 1}}\} = e^{a t} t^{n}, n = 1, 2, \dots$ as

$\begin{array}{rcl} L^{- 1} \{\frac{6}{{(s - 1)}^{4}}\} & = & L^{- 1} \{\frac{3!}{{(s - 1)}^{3 + 1}}\} \\ = & e^{t} t^{3} \end{array}$

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Determine the inverse Laplace transform of the given function.

$\frac{6}{{(s - 1)}^{4}}$ .

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

Decision Maths

Mechanics Maths

Calculus

Statistics

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Determine the inverse Laplace transform of the given function.6(s-1)4.

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

Decision Maths

Mechanics Maths

Calculus

Statistics

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Determine the inverse Laplace transform of the given function.

$\frac{6}{{(s - 1)}^{4}}$ .