Exercise 6.2.11 Exercise 6.2.11: Define(t−1)²f(t)=3-t0if 1≤t<2,if 2 < t < 3,otherwise.a) Sketch the graph of f(t).b) Write down f(t) using the Heaviside function.c) Solve x" + x = f(t), x(0) = 0, x'(0) = 0 using Laplace transform.

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Answered: Exercise 6.2.11: Define (t−1)²_ if 1≤t<…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Exercise 6.2.11: Define (t−1)²_ if 1≤t< 2, if 2 ≤ t <3, otherwise. f(t)=3-t 0 a) Sketch the graph of f(t). b) Write down f(t) using the Heaviside function. c) Solve x" + x = f(t), x(0) = 0, x'(0) = 0 using Laplace transform.