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Verify the time-shifting property (3.16); that is, sło X(s) R' = R (1 – 1)x

Verify the time-shifting property (3.16); that is, sło X(s) R' = R (1 – 1)x

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Verify the time-shifting property (3.16); that is, \[ x(t - t_0) \longleftrightarrow e^{-st_0} X(s) \] \[ R' = R \] **Explanation:** - The equation \( x(t - t_0) \longleftrightarrow e^{-st_0} X(s) \) represents the time-shifting property in the context of Laplace transforms. It states that if you shift a function in time by \( t_0 \), the Laplace transform is multiplied by an exponential factor \( e^{-st_0} \). - The expression \( R' = R \) implies that the region of convergence of the Laplace transform does not change with the time shift.
Transcribed Image Text:Verify the time-shifting property (3.16); that is, \[ x(t - t_0) \longleftrightarrow e^{-st_0} X(s) \] \[ R' = R \] **Explanation:** - The equation \( x(t - t_0) \longleftrightarrow e^{-st_0} X(s) \) represents the time-shifting property in the context of Laplace transforms. It states that if you shift a function in time by \( t_0 \), the Laplace transform is multiplied by an exponential factor \( e^{-st_0} \). - The expression \( R' = R \) implies that the region of convergence of the Laplace transform does not change with the time shift.
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