Question

a) Evaluate the Laplace transform of the following functions: i. f(t) = sin 2t + cos t ii. f(t) = t^3 + e^-2t iii. f(t) = te^-2t + t b) Express (2s+2)/(s^2+5s+6) in partial fraction form and then find the inverse Laplace transform of (2s+2)/(s^2+5s+6) using the partial fraction obtained.

          a) Evaluate the Laplace transform of the following functions:
i. f(t) = sin 2t + cos t
ii. f(t) = t^3 + e^-2t
iii. f(t) = te^-2t + t
b) Express (2s+2)/(s^2+5s+6) in partial fraction form and then find the inverse Laplace transform of (2s+2)/(s^2+5s+6) using the partial fraction obtained.

$a) Evaluate the Laplace transform of the following functions: i. f(t) = sin 2t + cos t ii. f(t) = t^3 + e^-2t iii. f(t) = te^-2t + t b) Express (2s+2)/(s^2+5s+6) in partial fraction form and then find the inverse Laplace transform of (2s+2)/(s^2+5s+6) using the partial fraction obtained.$

Added by Natasha M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

06/14/2023

Step 1

i. $f(t) = \sin(2t) + \cos(t)$ Using the Laplace transform formulas, we have: $\mathcal{L}\{\sin(2t)\} = \frac{2}{s^2 + 4}$ and $\mathcal{L}\{\cos(t)\} = \frac{s}{s^2 + 1}$ So, the Laplace transform of the given function is: \(\mathcal{L}\{f(t)\} = Show more…

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a) Evaluate the Laplace transform of the following functions: i. f(t) = sin 2t + cos t ii. f(t) = t^3 + e^-2t iii. f(t) = te^-2t + t b) Express (2s+2)/(s^2+5s+6) in partial fraction form and then find the inverse Laplace transform of (2s+2)/(s^2+5s+6) using the partial fraction obtained.