Explanation Formula used: Linearity property: The transform of a sum of functions is the sum of the transforms and is written as L [ a f ( t ) + b g ( t ) ] = a L ( f ) + b L ( g ) The Laplace transform of the function f ( t ) is defined by the function F ( s ) . The Laplace transform is denoted by L ( f ) and is given by the formula F ( s ) = L ( f ) = ∫ 0 ∞ e − s t f ( t ) d t The Laplace transform of the function f ( t ) = e − a t cos b t for any a, is given by. L ( e − a t cos b t ) = s + a ( s 2 + a 2 ) 2 + b 2 The Laplace transform of the function f ( t ) = t sin a t for any a, is given by L ( t sin a t ) = 2 a s ( s 2 + a 2 ) 2 . Calculation: The given function is f ( t ) = 2 t sin 3 t + e − 3 t cos t . Compare the given equation with f ( t ) = e − a t cos b t and f ( t ) = t sin a t and obtain the values of a , b as shown below: a = 3 , b = 1

11th Edition

ISBN: 9780134508290

Author: Evans

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

See similar textbooks

Videos

Question

Chapter 31.11, Problem 10E

To determine

The Laplace transform of the function f(t)=2tsin3t+e−3tcost.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 31.11, Problem 9E

Chapter 31.11, Problem 11E

Students have asked these similar questions

18. If m n compute the gcd (a² + 1, a² + 1) in terms of a. [Hint: Let A„ = a² + 1 and show that A„|(Am - 2) if m > n.]

2. (5 points) Let f(x) = = - - - x² − 3x+7. Find the local minimum and maximum point(s) of f(x), and write them in the form (a, b), specifying whether each point is a minimum or maximum. Coordinates should be kept in fractions. Additionally, provide in your answer if f(x) has an absolute minimum or maximum over its entire domain with their corresponding values. Otherwise, state that there is no absolute maximum or minimum. As a reminder, ∞ and -∞ are not considered absolute maxima and minima respectively.

Let h(x, y, z) = — In (x) — z y7-4z - y4 + 3x²z — e²xy ln(z) + 10y²z. (a) Holding all other variables constant, take the partial derivative of h(x, y, z) with respect to x, 2 h(x, y, z). მ (b) Holding all other variables constant, take the partial derivative of h(x, y, z) with respect to y, 2 h(x, y, z).

Chapter 31 Solutions

EBK BASIC TECHNICAL MATHEMATICS

Ch. 31.1 - Show that is a solution of . Is it the general...Ch. 31.1 - Prob. 1E Ch. 31.1 - In Exercises 1 and 2, show that the indicated...Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 4E Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 6E Ch. 31.1 - In Exercises 7–10, show that each function y =...Ch. 31.1 - Prob. 8E Ch. 31.1 - In Exercises 7–10, show that each function y =...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The Laplace transform of the function f ( t ) = 2 t sin 3 t + e − 3 t cos t .

Videos

The Laplace transform of the function f(t)=2tsin3t+e−3tcost.

Want to see the full answer?

Chapter 31 Solutions