Question

(e) (2 points) If the Laplace transform of a function x(t) is X(s) = \frac{e^{-s}}{s+1}, then the transform of f(t) = t^2x(t) is: A. F(s) = -e^{-s}\frac{s-1}{(s+1)^2} B. F(s) = e^{-s}\frac{s+2}{(s+1)^2} C. F(s) = -e^{-s}\frac{s-1}{(s+1)^3} D. F(s) = e^{-s}\frac{s^2+4s+5}{(s+1)^3} E. F(s) = e^{-s}\frac{s^2-2s-3}{(s+1)^3}

          (e) (2 points) If the Laplace transform of a function x(t) is X(s) = \frac{e^{-s}}{s+1}, then the transform of f(t) = t^2x(t) is:
A. F(s) = -e^{-s}\frac{s-1}{(s+1)^2}
B. F(s) = e^{-s}\frac{s+2}{(s+1)^2}
C. F(s) = -e^{-s}\frac{s-1}{(s+1)^3}
D. F(s) = e^{-s}\frac{s^2+4s+5}{(s+1)^3}
E. F(s) = e^{-s}\frac{s^2-2s-3}{(s+1)^3}

(e) (2 points) If the Laplace transform of a function x(t) is X(s) = (e^-s)/(s+1), then the transform of f(t) = t^2x(t) is:
A. F(s) = -e^-s(s-1)/((s+1)^2)
B. F(s) = e^-s(s+2)/((s+1)^2)
C. F(s) = -e^-s(s-1)/((s+1)^3)
D. F(s) = e^-s(s^2+4s+5)/((s+1)^3)
E. F(s) = e^-s(s^2-2s-3)/((s+1)^3)

Added by Margarita T.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

07/20/2023

Step 1

Step 1: The Laplace transform of a function t is given as X(s) = 1/s^2. Show more…

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Please solve the problem it details. 2 points If the Laplace transform of a function t is X(s) = then the transform s+1 of f(t) = tX(t) is 3+12 s+12 s+13 -s+4s+5 D.F(s) = e s+13 -82-25-3 E.F(s) = e s+13