Q9P Use L23聽of the Laplace Transfor... [FREE SOLUTION]

Chapter 12: Q9P (page 593)

Use L23of the Laplace Transform Table (page 469 ) to evaluate ${鈭�}_{0}^{鈭�} {tJ}_{0} (2 t) e \hat{} - tdt$ .

Short Answer

Expert verified

The equation by use of Laplace theorem is ${鈭�}_{0}^{鈭�} [({tJ}_{0}) (2 t)] e^{- 1} dt = \sqrt{5}$ .

Step by step solution

Concept of Laplace Transform

The Laplace transform is an integral transform in mathematics that turns a function of a real variable (typically time) to a function of a complex variable. It is named after its inventor Pierre-Simon Laplace. (Complex periodicity)

Determine equations with proof:

The given equation is as follow.

${鈭�}_{0}^{鈭�} [{tJ}_{0} (2 t)] e^{- 1} dt$ 鈥�.. (1)

Let $g (t) = ({tJ}_{0}) - (2 t)$

Therefore,

${鈭�}_{0}^{鈭�} [{tJ}_{0} (2 t)] e^{- 1} dt = L (g (t))$

Thus,

$L (g (t)) = L [({tJ}_{0}) (2 t)] = - \frac{d}{dp} L [\frac{1}{\sqrt{P^{2} + 4}}] = p \sqrt{P^{2} + 4}$

At p = 1

$L (g (t)) = 1 脳 \sqrt{{(1)}^{2} + 4} = \sqrt{5}$

Hence, the solution is role="math" localid="1659263208798" ${鈭�}_{0}^{鈭�} [({tJ}_{0}) (2 t)] e^{- 1} dt = \sqrt{5}$ .

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91影视

Use L23of the Laplace Transform Table (page 469 ) to evaluate ${鈭�}_{0}^{鈭�} {tJ}_{0} (2 t) e \hat{} - tdt$ .

Short Answer

Step by step solution

Concept of Laplace Transform

Determine equations with proof:

One App. One Place for Learning.

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91影视

Use L23of the Laplace Transform Table (page 469 ) to evaluate 鈭�0鈭�tJ0(2t)e^-tdt.

Short Answer

Step by step solution

Concept of Laplace Transform

Determine equations with proof:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electric Charge Field and Potential

Astrophysics

Oscillations

Circular Motion and Gravitation

Wave Optics

Electricity and Magnetism

Study anywhere. Anytime. Across all devices.

Use L23of the Laplace Transform Table (page 469 ) to evaluate ${鈭�}_{0}^{鈭�} {tJ}_{0} (2 t) e \hat{} - tdt$ .