Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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(c) Translate the pulse, i.e. move the nonzero value of the func-
tion to a different location while maintaining the width [for
example, let f(t) = 1 for 1 ≤ t ≤ 2 and zero elsewhere; then
try for f(t) = 1 for 2 ≤ t ≤ 3 and zero elsewhere; and so
on.] Show that it obeys the translation property of Laplace
Transforms, L{f(ta)} = e-as F(s).
(d) Widen the pulse, i.e. keep the other eage at zero and in-
crease the width of the nonzero value [for example, extend
to f(t) = 1 for 0 ≤ t ≤ 2 and zero elsewhere; the do for
f(t) = 1 for 0 ≤ t ≤ 3 and zero elsewhere]. Show that
<
you can get the scaling property of the Laplace Transform,
L {f(at)} = F (₁).
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Transcribed Image Text:(c) Translate the pulse, i.e. move the nonzero value of the func- tion to a different location while maintaining the width [for example, let f(t) = 1 for 1 ≤ t ≤ 2 and zero elsewhere; then try for f(t) = 1 for 2 ≤ t ≤ 3 and zero elsewhere; and so on.] Show that it obeys the translation property of Laplace Transforms, L{f(ta)} = e-as F(s). (d) Widen the pulse, i.e. keep the other eage at zero and in- crease the width of the nonzero value [for example, extend to f(t) = 1 for 0 ≤ t ≤ 2 and zero elsewhere; the do for f(t) = 1 for 0 ≤ t ≤ 3 and zero elsewhere]. Show that < you can get the scaling property of the Laplace Transform, L {f(at)} = F (₁).
3. Laplace Transform. Consider a rectangular pulse given by the
following equation:
f(t)
( 1, 0 ≤ t ≤ 1
0, elsewhere
(5)
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Transcribed Image Text:3. Laplace Transform. Consider a rectangular pulse given by the following equation: f(t) ( 1, 0 ≤ t ≤ 1 0, elsewhere (5)
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