Question

1. (a) (5%) Find the Laplace transform R(s) of a signal r (t), if r(t) = 0, t < 0 ; r(t) = e^-0.4t cos14t , t ? 0. (b) (5%) Find the inverse Laplace transform of F(s), where F(s) = 8 / (s(s^2 + 4s + 8)). (c) (5%) By applying the final value theorem, find the final value of f(t). The Laplace transform of f(t) is F(s) = 8 / (s(s^2 + 4s + 8)). Verify this result by taking the inverse Laplace transform of F(s) and letting t ? ?.

          1. (a) (5%) Find the Laplace transform R(s) of a signal r (t), if
r(t) = 0, t < 0 ; r(t) = e^-0.4t cos14t , t ? 0.
(b) (5%) Find the inverse Laplace transform of F(s), where F(s) = 8 / (s(s^2 + 4s + 8)).
(c) (5%) By applying the final value theorem, find the final value of f(t). The Laplace transform of f(t) is F(s) = 8 / (s(s^2 + 4s + 8)). Verify this result by taking the inverse Laplace transform of F(s) and letting t ? ?.

1. (a) (5%) Find the Laplace transform R(s) of a signal r (t), if
r(t) = 0, t < 0 ; r(t) = e^-0.4t cos14t , t ? 0.
(b) (5%) Find the inverse Laplace transform of F(s), where F(s) = 8 / (s(s^2 + 4s + 8)).
(c) (5%) By applying the final value theorem, find the final value of f(t). The Laplace transform of f(t) is F(s) = 8 / (s(s^2 + 4s + 8)). Verify this result by taking the inverse Laplace transform of F(s) and letting t ? ?.

Added by Victoria V.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Adi S

06/23/2023

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(a) (5%) Find the Laplace transform R(s) of the signal r(t), if r(t) = 0, t < 0 and r(t) = cos(t - 120). (b) (5%) Find the inverse Laplace transform of F(s), where F(s) = (s + 45) / (s^2 + 45s + 8). (c) (5%) By applying the final value theorem, find the final value of f(t). The Laplace transform of f(t) is F(s). Verify this result by taking the inverse Laplace transform of F(s) and letting s approach infinity.