(a) Assume that Theorem 7 3 1 holds when the symbol a is replaced by ki, where k is a real number and i 2 1 Show that te kti can be used to deduce (b) Now use the Laplace transform to solve the initial value problem x ' ' 2 x cos t, x(0) 0, '(0) 0 Theorem 7 3 1 If f(t) F(s) and a is any real number...

a From theorem 76 Lite because L1e1e ds d 1 ds ski 1 ski 1 ski Now by Eu ...

(a) Assume that Theorem 7.3.1 holds when the symbol a is replaced by ki, where k is...

Question:

(a) Assume that Theorem 7.3.1 holds when the symbol a is replaced by ki, where k is a real number and i² = -1. Show that ℒ{te^kti} can be used to deduce

- k L{t cos kt} (s? + k2)? 2ks L{t sin kt} (s? + k)2

(b) Now use the Laplace transform to solve the initial value problem x'' + ω²x = cos ωt, x(0) = 0, '(0) = 0.

Theorem 7.3.1

If ℒ{f(t)} = F(s) and a is any real number, then

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

A First Course in Differential Equations with Modeling Applications

ISBN: 978-1111827052

10th edition

Authors: Dennis G. Zill

See More Books

Question Posted: Nov 02, 2020 04:33 AM

The convolution of two functions g and fis the function g *f defined by vf (v)du The aim of this project is to show how convolutions can be used to obtain a particular solution to a nonhomogeneous...
A company faces the following demands during the next three weeks: week 1, 2000 units; week 2, 1000 units; week 3, 1500 units. The unit production costs during each week are as follows: week 1, $130;...
The Philbrick Company has two plants on opposite sides of the United States. Each of these plants produces the same two products and then sells them to wholesalers within its half of the country. The...
Explain the nature of stress at work Describe the health consequences of stressful work Explain how to use hardiness theory to reduce stress List three ways to use Banduras self-efficacy theory to...
Sheri is a warehouse worker for a small grocery market. As she was moving some merchandise, the loading dock door unexpectedly fell and injured her. What legal provisions does Sheri have for this...
Increasing the amount of information provided to potential applicants reduces the number of inappropriate applications. LO1
12. Health care entities frequently provide charity care to qualified individuals. How is charity care reported in the financial statements of a hospital?
Mary Janus is developing a transfer price for the housing section of an automatic pool-cleaning device. The housing for the device is made in Department A. It is then passed on to Department D, where...
Show Me How Calculator 258 Sales and Production Budgets Son Inc. manufactures two models of speakers, Rumble and Thunder. Based on the following production and sales data for June prepare(a) a sales...
Wood-Mode Company is involved in the design, manufacture, and installation of various types of wood products for large construction projects. Wood-Mode recently completed a large contract for Stadium...
Discuss how you would fix up each of the following functions so that Theorem 7.3.2 could be used directly to find the given Laplace transform. Check your answers using (16) of this section. (a) {(2t...
Fill in the blanks. The vector is a solution of for k = __________. X = k (5) 4.
Which inventory method is the correct one? Can a company change inventory methods? pg25
K ints: 0 of 3 Save The height of women ages 20-29 is normally distributed, with a mean of 64 inches. Assume = 2.7 inches. Are you more likely to randomly select 1 woman with a height less than 65.2...
CASE 11-23 Balanced Scorecard LO11-4 Haglund Department Store is located in the downtown area of a small city. While the store had been profitable for many years, it is facing increasing competition...
0.1 points Sert Avne Your monthly Cable/Internet payment increases to $104 for the month of March and on. What is the new annual total you pay for Cablemed $1,178 $1,192 $1,206 $1,220
Tax issues are definitely a concern of consolidated entities. Using external resources, please explain some of the challenges faced by the accountant for tax purposes regarding consolidated entities....
Ownership of 51% of the outstanding voting common stock of a company would usually result in a. the use of the cost method b. the use of the lower of cost or market method c. the use of the equity...
The following are the balance sheets for Plate and Salad immediately prior to Plates September 1, 20X1, acquisition of Salad: Consider the following cases: Case 1 Plate buys 100% of Salads common...
Consider the reaction of acetic acid in water CH 3 CO 2 H(aq) + H 2 O(l) CH3CO 22 (aq) + H 3 O + (aq) where Ka 5 1.8 3 1025. a. Which two bases are competing for the proton? b. Which is the stronger...
(i) What is a prospective study? What are its advantages? (ii) What is a randomized study? What are its advantages? (iii) What is a double-blind study? Are there advantages vs. other approaches?...
Implement a test to assess whether the incidence of hearing loss is different between the groups. State clearly which test you are using, and report a two-sided p-value? After 2 weeks of treatment,...
Interpret the results of your test in Problem 10.120? After 2 weeks of treatment, 14 of the placebo patients and 3 of the ASA patients developed clinically significant hearing loss.
A stock is expected to pay a dividend of $1.50 at the end of the year (i.e., D 1 = $1.50), and it should continue to grow at a constant rate of 10% a year. If its required return is 14%, what is the...
The Hobby Shop has a checking account with a ledger balance of $1,700. The firm has $2,400 in uncollected deposits and $4,200 in outstanding checks. What is the amount of the disbursement float on...
An investment will pay you $34,000 in 11 years. If the appropriate discount rate is 6.1 percent compounded daily, what is the present value? (Use 365 days a year. Do not round intermediate...

(a) Assume that Theorem 7.3.1 holds when the symbol a is replaced by ki, where k is...

Question:

- k L{t cos kt} (s? + k2)? 2ks L{t sin kt} (s? + k)2"

Step by Step Answer:

a From theorem 76 Lite because L1e1e ds d 1 ds ski 1 ski 1 ski Now by Eu...View the full answer

A First Course in Differential Equations with Modeling Applications

Students also viewed these Mathematics questions