Transcribed TextTranscribed Text

1. [12 marks] Find the inverse Laplace transforms of = 2s-2 2. [16 marks] Solve the following initial value problems using Laplace transforms, where u (t) is the Heaviside step function (a) y" + 2y' + 2y = 2t with y (0) = 0 and y' (0) = 1 (b) y" - 6y' + 8y = 22 (t - 2 t with y(0) = 2 1 and y' (0) = 0 3. [8 marks] Suppose the location of a particle is given by t € [0,3]. (1) (a) Sketch the path indicating the starting point at t = 0 and the direction of movement with an arrow. (b) Find the velocity of the particle v(t) and hence the speed s(t) = |v(t)]. (c) Find the acceleration of the particle at any time. 4. [7 marks] Let F(t) = (e-t, cos t) and G (t) = (t,2t²). Find d G(t) and 5. [7 marks) If y = 3z and X = sin Z (with 0 < Z < 3), find the arclength of the curve. You may evaluate the integral in any way you choose (including numerically) but you need to explain how you did it. The answer should be given to 2 decimal places.

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:

    for this solution

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

    Find A Tutor

    View available Advanced Math Tutors

    Get College Homework Help.

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

    Fast tutor response requires as much info as possible.

    Upload a file
    Continue without uploading

    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