1. Come up with a combination of Heaviside functions whose graph: has a constant height of 0 until t = 4, jumps up to 3 until t = 6, and then falls to 2 thereafter. b) has a constant height of 8 until t = 1, falls to -1 from t = 1 to t = 2, and has a height of 0 thereafter. c) follows the line y = t until t = 4, and then has a height of 1 thereafter.
1. Come up with a combination of Heaviside functions whose graph: has a constant height of 0 until t = 4, jumps up to 3 until t = 6, and then falls to 2 thereafter. b) has a constant height of 8 until t = 1, falls to -1 from t = 1 to t = 2, and has a height of 0 thereafter. c) follows the line y = t until t = 4, and then has a height of 1 thereafter.
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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Please explain how to do 1. a, b and c. Final answers are given.
Transcribed Image Text:Final Answers:
a) 3u(t-4) - u(t - 6)
b) 8-9u(t-1) + u(t - 2)
c) t+ (1 - t)u(t - 4)
d) sin(t) + sin(t)u(t - 2π)
e) 2u(t-1) + (-2t+4)u(t-2) + (2t - 6)u(t - 3)
f) Σu(t-n), t > 0
∞
n=1
∞
g) 1+u(t-n), t ≥ 0
n=1
h) Σ 2u(t - n),t 20
n=1
220
Transcribed Image Text:1. Come up with a combination of Heaviside functions whose graph:
a) has a constant height of 0 until t = 4, jumps up to 3 until t = 6, and then falls to 2
thereafter.
b) has a constant height of 8 until t = 1, falls to -1 from t = 1 to t = 2, and has a height
of 0 thereafter.
c) follows the line y = t until t = 4, and then has a height of 1 thereafter.
d) follows the curve y = sin(t) until t = 27, and then follows y =
e) looks like this:
2
O
1
2 3
2 sin(t) thereafter.
t
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