Question

Compute the Laplace transform. Your answer should be a function of the variable s: L { 6 + u_1(t)e^{2t} sin(?t) } = (6/s)+pi/((s-2)^2+pi^2) You may find the following formulas useful: cos(bt + ?) = - cos(bt) sin(bt + ?) = - sin(bt) cos(bt + ?/2) = - sin(bt) sin(bt + ?/2) = cos(bt) If you don't get this in 2 tries, you can get a hint. Hint:

          Compute the Laplace transform. Your answer should be a function of the variable s:
L { 6 + u_1(t)e^{2t} sin(?t) } = (6/s)+pi/((s-2)^2+pi^2)
You may find the following formulas useful:
cos(bt + ?) = - cos(bt)
sin(bt + ?) = - sin(bt)
cos(bt + ?/2) = - sin(bt)
sin(bt + ?/2) = cos(bt)
If you don't get this in 2 tries, you can get a hint.
Hint:

Compute the Laplace transform. Your answer should be a function of the variable s:
L 6 + u1(t)e^2t sin(?t) = (6/s)+pi/((s-2)^2+pi^2)
You may find the following formulas useful:
cos(bt + ?) = - cos(bt)
sin(bt + ?) = - sin(bt)
cos(bt + ?/2) = - sin(bt)
sin(bt + ?/2) = cos(bt)
If you don't get this in 2 tries, you can get a hint.
Hint:

Added by Steven S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/13/2023

Step 1

The Laplace transform of a constant c is simply c/s. The Laplace transform of a function multiplied by a unit step function U1(t) is the Laplace transform of the function shifted by 1 in the s-domain. So, the Laplace transform of U1(t)e^2t sin(rt) is e^(-s) * Show more…

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Compute the Laplace transform. Your answer should be a function of the variable s: L {6 + u1(t)e^2t sin(pi t)} = (6/s)+pi/((s-2)^2+pi^2) You may find the following formulas useful: cos(bt + pi) = - cos(bt) sin(bt + pi) = - sin(bt) cos(bt + pi/2) = - sin(bt) sin(bt + pi/2) = cos(bt) If you don't get this in 2 tries, you can get a hint.