In Exercise 21, use Theorem 8.4.2 to express the inverse transforms in terms of step functions, andthen find distinct formulas the for inverse transforms on the appropriate intervals, as in Example 8.4.7.Where indicated by C/G , graph the inverse transform. 2s21.C/G| H(s) =%3D52 Theorem 8.4.2 [Second Shifting Theorem] If t 2 0 and L(g) exists fors > Sg then L(u(t -t)g(t-t))exists for s > So andL(ud- rig(t - r)) = e"L(g().or, equivalently.if gtr)- G(s). then u(t- tlg((8.4.12)REMARK: Recall that the First Shifting Theorem (Theorem 8.1.3 states that multiplying a function bye corresponds to shifting the argument of its transform bya units. Theorem 8.4.2 states that multiplyinga Laplace transform by the exponential eby z units.corresponds to shifting the argument of the inverse transform

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Answered: 2s 1. C/G| H(s)=

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 Exercise 21, use Theorem 8.4.2 to express the inverse transforms in terms of step functions, and then find distinct formulas the for inverse transforms on the appropriate intervals, as in Example 8.4.7. Where indicated by C/G , graph the inverse transform.

Theorem 8.4.2 [Second Shifting Theorem] If t 2 0 and L(g) exists fors > Sg then L(u(t -t)g(t-t))
exists for s > So and
L(ud- rig(t - r)) = e"L(g().
or, equivalently.
if gtr)
- G(s). then u(t- tlg(
(8.4.12)
REMARK: Recall that the First Shifting Theorem (Theorem 8.1.3 states that multiplying a function by
e corresponds to shifting the argument of its transform bya units. Theorem 8.4.2 states that multiplying
a Laplace transform by the exponential e
by z units.
corresponds to shifting the argument of the inverse transform

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