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by 29. Engineers frequently use the Heaviside function, defined if t < 0, 1. ift ≥ 0. to emulate turning on a switch at a certain instant in time. Sketch the graph of H(t) = y(t) = H(t – 3)e21 Calculate its Laplace transform.

by 29. Engineers frequently use the Heaviside function, defined if t < 0, 1. ift ≥ 0. to emulate turning on a switch at a certain instant in time. Sketch the graph of H(t) = y(t) = H(t – 3)e21 Calculate its 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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Question 29 please!

29. Engineers frequently use the Heaviside function, defined by H(t): 0, if t < 0, 1, ift 20 0, to emulate turning on a switch at a certain instant in time. Sketch the graph of y(t) = H(t - 3)e 0.21. Calculate its Laplace transform. 30. This exercise discusses some ideas that make Theo- rem 1.16 plausible. Suppose that the function f is contin- uous on the interval [0, ∞) and of exponential order; that is, there exists constants C and a such that f(t)| ≤ Ceat for all t > 0. (a) Show that |f(t)es | ≤ Ce-(-a)t for all t > 0. (b) Since it is true that √ dr| ≤ f \ƒ(1)e="| dr five f(t)e-st dt ≤ S = f.° Ce-(s-a)t dt, VI 31. 32 5.2 Basic Properties This section will discuss th of the Laplace We will state each property Transform The Laplace transform The most important property transform and the derivativ when using the Laplace tran PROPOSITION 2.1 Suppose y is a piecewise d tial orc
Transcribed Image Text:29. Engineers frequently use the Heaviside function, defined by H(t): 0, if t < 0, 1, ift 20 0, to emulate turning on a switch at a certain instant in time. Sketch the graph of y(t) = H(t - 3)e 0.21. Calculate its Laplace transform. 30. This exercise discusses some ideas that make Theo- rem 1.16 plausible. Suppose that the function f is contin- uous on the interval [0, ∞) and of exponential order; that is, there exists constants C and a such that f(t)| ≤ Ceat for all t > 0. (a) Show that |f(t)es | ≤ Ce-(-a)t for all t > 0. (b) Since it is true that √ dr| ≤ f \ƒ(1)e="| dr five f(t)e-st dt ≤ S = f.° Ce-(s-a)t dt, VI 31. 32 5.2 Basic Properties This section will discuss th of the Laplace We will state each property Transform The Laplace transform The most important property transform and the derivativ when using the Laplace tran PROPOSITION 2.1 Suppose y is a piecewise d tial orc
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