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Physics LibreTexts

14.5: Shifting Theorem

( \newcommand{\kernel}{\mathrm{null}\,}\)

This is a very useful theorem, and one that is almost trivial to prove. (Try it!) It is

L(eaty(t))=ˉy(s+a).

For example, from the table, we have L(t)=1/s2. The shifting theorem tells us that L(teat)=1/(s+a)2. I'm sure you will now want to expand your table even more. Or you may want to go the other way, and cut down the table a bit! After all, you know that L(1)=1/s. The shifting theorem, then, tells you that L(eat)=1/(sa), so that entry in the table is superfluous! Note that you can use the theorem to deduce either direct or inverse transforms.


This page titled 14.5: Shifting Theorem is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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