Mastering Inverse Laplace Transforms: Homework 12 Guide
School
University of Illinois, Urbana Champaign**We aren't endorsed by this school
Course
MATH 220
Subject
Mathematics
Date
Dec 11, 2024
Pages
1
Uploaded by BaronAtomEmu24
Math 220, Spring 2022Homework 12, due Thu, Apr 71Reminder: All work submitted must be YOUR OWN. Please, write clearly, show all steps, stateyour answer and remember to properly assign page numbers to each question. We can only gradethe calculations that are shown. Calculators may be used for simple arithmetic, but use of CAS orother mathematical or graphing software is not permitted.In problems involving Laplace transforms, label all properties, formulas and the correspondingparameters (use the official table of Laplace transforms on Blackboard). State the domain ofsinyour answers.Consult the syllabus for the academic integrity policy and Blackboard for tutorials on how tosubmit to Gradescope. Please, remember to match the pages and questions.1. Calculate the inverse Laplace transformL-1-3s2+ 2s+ 4(s2-4s+ 5)(s-2).2. Solve the initial value problem by the method of Laplace transforms:y00-3y0-4y= 12e2t, y(0) = 2, y0(0) =-13. Solve the initial value problem by the method of Laplace transforms:y00+ 4y= 2, y(0) = 4, y0(0) = 14. Consider the following piecewise-defined functionf(t) on [0,∞):f(t) =0,0≤t <22t-4,2≤t <310e-t,t≥3(a) Sketch the graph off(t).(b) Rewritef(t) as a linear combination of multiples of shifted Heaviside functionsu(t-a),where the coefficients are functions oft.(c) Calculate the Laplace transform off(t).
