Question

Question 2. Use the table of Laplace transforms and properties of the transform to determine the following:

Please provided a clear and legible, step-by-step answer to this problem for A) , B) and C). Show your complete work to include the complete transformation. DO NOT BYPASS ANY STEPS PLEASE. A well organized and sequential answer will rate thumbs up right away.

Answer 1

Required formula's 1) t[k] = k/s 2) L [t^n] = n!/s^n + 1 3) L [sin a t] = a/s^2 + a^2 4) L[e^at] = 1/s - a 5) L [e^-at] = 1/s + a 6) L [t^n . e^at] = n!/(s - a)^n + 1 7) L [e^at . cos (bt)] = s - a/(s - a)^2 + b^2 Q1) L [6e^-3t - t^2 + 2t - 8] = L [6e^-3t] - L[t^2] + 2 L[t] - 8L[1] = 6/s + 3 - 2/s^3 + 2/s^2 - 8/5 Q2) L[t^3 - te^t + e^4t cos (t)] = L[t^3] - L[te^t] + L[e^4t (0)(t)] = 6/s^4 - 1/(s - 1)^2 + s - 4/(s - 4)^2 + 1 Q3) L[t^4 - t^2 - t + sin (squareroot 2t)] = L[t^4] - L[t^2] - L[t] + L [sin (squareroot 2t)] = 24/s^5 - 2/s^3 - 1/s^2 + squareroot 2/s^2 + 2