QuestionQuestion

Transcribed TextTranscribed Text

Part A (15 pts). (True/False Questions). Choose true or false. 1) The Laplace transform of cos 3𝑡 is ! !!!!! □ True □ False 2) The Laplace transform of 𝑒!!"! is ! !!!". □ True □ False 3) ℒ{3 + 4 t + 5 sin 2𝑡} is equal to 3ℒ{1} +4 ℒ{ 𝑡}+5ℒ{sin 2𝑡}. □ True □ False 4) ℒ!!{ !" !!!!} is equal to ℒ!!{15} ℒ!!{ ! !!!!}. □ True □ False 5) The inverse Laplace transform of 𝐹 𝑠 = !! !! is 𝑡!. □ True □ False Part B (25 pts). (Multiple Choice Questions). Chose the correct answer. 1) The Laplace transform of sin 4𝑡 is a) 𝟒 𝒔𝟐!𝟒𝟐 b) !! !!!!! c) !! !!!!! d) ! !!!!! e) None of them 2) The Laplace transform of 4 − 5 sin 𝑡 + 6 𝑐𝑜𝑠𝑡 − 7𝑒! is is Type equation here. a) 𝟒 𝒔 + 𝟓 𝒔𝟐!𝟏 + ! 𝒔 𝒔𝟐!𝟏 − ! 𝒔!𝟏 b) 𝟒 𝒔 − 𝟓 𝒔𝟐!𝟏 − ! 𝒔 𝒔𝟐!𝟏 − ! 𝒔!𝟏 c) 𝟒 𝒔 − 𝟓 𝒔𝟐!𝟏 + 𝟔𝒔 𝒔𝟐!𝟏 + ! 𝒔!𝟏 d) None of them e) 𝟒 𝒔 − 𝟓 𝒔𝟐!𝟏 + ! 𝒔 𝒔𝟐!𝟏 − ! 𝒔!𝟏 3) The inverse Laplace transform of 𝐹 𝑠 = ! !!! + ! !!!! is a) 𝑒!! − 5 𝑠𝑖𝑛𝑡 b) 𝑒!!! + 5 𝑐𝑜𝑠 𝑡 c) 𝑒!! + 5 𝑠𝑖𝑛𝑡 d) 𝑒!! + 5 𝑐𝑜𝑠 𝑡 e) None of them 4) The inverse Laplace transform of 𝐹 𝑠 = ! (!!!!) + !! (!!!!) is a) 2sin 𝑡 + 4 cos 𝑡 b) 2sin 2𝑡 + 4 cos 3𝑡 c) 2sin 2𝑡 − 4 cos 3𝑡 d) 4sin 2𝑡 + 12 cos 3𝑡 e) None of them 5) When the Laplace transform is applied to the problem y! + 5𝑦 = 1, y 0 = 0, the resulting transformed equation is a) 𝑠 + 5 𝑌 𝑠 = ! !! b) 𝑠 − 5 𝑌 𝑠 = ! ! c) 𝑠 + 5 𝑌 𝑠 = −! ! d) s + 5 Y s = ! ! e) None of them Part C (60 pts). (Workout Problems). Solve the following problems. Show your work clearly. 1) a) Find the Laplace transform of 𝑒! + 𝑒!! ! + sin 2𝑡 + 3 b) Find the inverse Laplace transform of 𝐹 𝑠 = ! !(!!!!). 2) Given initial value problem 𝑦! + 5𝑦 = 𝑒!!, y 0 = 1 a) Use the Laplace transform to solve the above initial value problem b) How do you solve the above initial value problem if we replace y 0 = 1 with y 1 = 1. (Justify your answer) 3) Given initial value problem 𝑦!! − 5y! + 6𝑦 = 𝑒!! , y 0 = 0, y! 0 = 1 a) Use the Laplace transform to solve the above initial value problem b) Do you know another method to solve the above initial value problem besides the Laplace transform? (Justify your answer)

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:
    Solution.pdf.

    $33.00
    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Decision:
    Upload a file
    Continue without uploading

    SUBMIT YOUR HOMEWORK
    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats