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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.

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.

Advanced Engineering Mathematics
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

Exercise 6.2.11: Define (t−1)² f(t)=3-t 0 if 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.
Transcribed Image Text:Exercise 6.2.11: Define (t−1)² f(t)=3-t 0 if 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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