Question

Q1 (a) Find the Laplace Transform of: e^{-t} sin 2t u(t - ?). [Hint: sin 2t = sin 2(t - ?)] (b) A signal is given by: x(t) = { 2, 0 ? t < 1; t, 1 ? t < 2; e^{2t}, t ? 2 } i. Rewrite x(t) in terms of unit step function ii. Find the Laplace transform of x(t). (c) Determine the inverse Laplace transform of the following functions i. Y(s) = (2 - 3s^2 + s^3) / s ii. Y(s) = (s - 6) / (s^2 + 2s + 4) (d) By using the convolution theorem, find the inverse Laplace transform of: 2 / (s^2 + 4)^2

          Q1 (a) Find the Laplace Transform of:
e^{-t} sin 2t u(t - ?).
[Hint: sin 2t = sin 2(t - ?)]

(b) A signal is given by:
x(t) = { 2, 0 ? t < 1; t, 1 ? t < 2; e^{2t}, t ? 2 }

i. Rewrite x(t) in terms of unit step function
ii. Find the Laplace transform of x(t).

(c) Determine the inverse Laplace transform of the following functions
i. Y(s) = (2 - 3s^2 + s^3) / s
ii. Y(s) = (s - 6) / (s^2 + 2s + 4)

(d) By using the convolution theorem, find the inverse Laplace transform of:
2 / (s^2 + 4)^2

Q1 (a) Find the Laplace Transform of:
e^-t sin 2t u(t - ?).
[Hint: sin 2t = sin 2(t - ?)]

(b) A signal is given by:
x(t) = 2, 0 ? t < 1; t, 1 ? t < 2; e^2t, t ? 2

i. Rewrite x(t) in terms of unit step function
ii. Find the Laplace transform of x(t).

(c) Determine the inverse Laplace transform of the following functions
i. Y(s) = (2 - 3s^2 + s^3) / s
ii. Y(s) = (s - 6) / (s^2 + 2s + 4)

(d) By using the convolution theorem, find the inverse Laplace transform of:
2 / (s^2 + 4)^2

Added by Ronald M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

08/23/2023

Step 1

Using the time-shift property of Laplace Transform, we have: L{sin 2(t - π)u(t - π)} = e^{-πs}L{sin 2t} Now, we know that the Laplace Transform of sin 2t is: L{sin 2t} = \frac{2}{s^2 + 4} So, the Laplace Transform of sin 2(t - π)u(t - π) is: L{sin 2(t - Show more…

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Find the Laplace Transform of: e^{-t} sin 2t u(t - π). [Hint: sin 2t = sin 2(t - π)] A signal is given by: x(t) = { 2, 0 ≤ t < 1; t, 1 ≤ t < 2; e^{2t}, t ≥ 2 } i. Rewrite x(t) in terms of unit step function ii. Find the Laplace transform of x(t). Determine the inverse Laplace transform of the following functions i. Y(s) = (2 - 3s^2 + s^3) / s ii. Y(s) = (s - 6) / (s^2 + 2s + 4) By using the convolution theorem, find the inverse Laplace transform of: 2 / (s^2 + 4)^2