\( \mathcal{L} \left\{ 5 + u_1(t)e^{-t} \sin(\pi t) \right\} = \)
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Step 1: The Laplace transform of a sum is the sum of the Laplace transforms. Show more…
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Compute the Laplace transform. Your answer should be a function of the variable s: L { 6 + u3(t)e^-2t sin(pi t) } = 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.
Adi S.
Compute the Laplace transform. Your answer should be a function of the variable s: 2 + u3(t)e^(-5t) sin(̀πt) You may find the following formulas useful: cos(bt + π) = - cos(bt) sin(bt + π) = - sin(bt) cos(bt + π/2) = - sin(bt) sin(bt + π/2) = cos(bt) If you don't get this in 2 tries, you can get a hint. Hint: Remember that L{k} = k/s For the u3(t)e^(-5t) sin(πt) term, it is probably easiest to first pull e^(-5t) out of L. When u3(t) comes out of L, it changes sin(πt) to be sin(π(t + 3)) = sin(πt + 3π) which simplifies to - (sin(πt)).
Compute the Laplace transform. Your answer should be a function of the variable s: L { 4 + u_1(t)e^{3t} sin(pi*t) } = (4/s)-e^((3s/2)(pi/(((s-3)^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.
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