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
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!
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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