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In each problem sketch the graph of the given function and express f(t) in terms of the unit step function uc(t). 11. t, 0 ≤ t < 1, t-1, 1≤t<2, t-2, 2≤t <3, 0, t≥ 3, Solution: f(t)=t-u₁(t) - u₂(t) + (2-t)uz(t) 0.8 0,6 0,4 0.2 0

In each problem sketch the graph of the given function and express f(t) in terms of the unit step function uc(t). 11. t, 0 ≤ t < 1, t-1, 1≤t<2, t-2, 2≤t <3, 0, t≥ 3, Solution: f(t)=t-u₁(t) - u₂(t) + (2-t)uz(t) 0.8 0,6 0,4 0.2 0

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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In each problem sketch the graph of the given function and express f(t) in terms of the unit step function uc(t). 11. t₂ 0 < t < 1, t-1, 1≤ t < 2, t-2, 2≤t <3, 0, t≥ 3, Solution: f(t) = t - u₁(t) − u₂(t) + (2 t)uz(t) - 13. Find the Laplace transform of the given function. t< 2, :- 2)², t≥ 2, Solution: Using the unit step function, we can write W 0.4 Thus, the Laplace transform is f(t) = (t - 2)² u₂(t). 2e-2s 83
Transcribed Image Text:In each problem sketch the graph of the given function and express f(t) in terms of the unit step function uc(t). 11. t₂ 0 < t < 1, t-1, 1≤ t < 2, t-2, 2≤t <3, 0, t≥ 3, Solution: f(t) = t - u₁(t) − u₂(t) + (2 t)uz(t) - 13. Find the Laplace transform of the given function. t< 2, :- 2)², t≥ 2, Solution: Using the unit step function, we can write W 0.4 Thus, the Laplace transform is f(t) = (t - 2)² u₂(t). 2e-2s 83
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