Answer
$- \dfrac{s \cdot e^{-\pi s}}{s^2+1}$
Work Step by Step
We are given that $f(t)=\cos (t) u_{\pi} (t)=-\cos (t-\pi) u_{\pi} (t)$
Now,$F(s)=L[-\cos (t-\pi) u_{\pi} (t)] \\= -e^{-\pi s} L [\cos t]=- \dfrac{s \cdot e^{-\pi s}}{s^2+1}$
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.7 The Second Shifting Theorem - Problems - Page 704: 5
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