Laplace Transform: Answers for cos(4t-1)u(t-1) & cos4(t-1)u(t-1)

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Discussion Overview

The discussion revolves around the Laplace transform of two expressions involving cosine functions and the unit step function, specifically cos(4t-1)u(t-1) and cos4(t-1)u(t-1). Participants are interested in comparing the results of the Laplace transforms for these two cases.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant asks for the Laplace transform of cos(4t-1)u(t-1) and cos4(t-1)u(t-1) to compare the results.
  • Another participant emphasizes the need for the original poster to show their effort before receiving help.
  • A participant suggests that e^-s/(s^2 + 4^2) is the answer for the first question but is uncertain if it applies to the second question as well.
  • One participant explains that the first question's answer relates to the second shift theorem, noting that the value of 'd' must be the same, which is 1 in this case, but expresses uncertainty regarding the second question.
  • Another participant proposes using the identity for cos(A-B) to approach the second question.

Areas of Agreement / Disagreement

There is no consensus on the correct answers for the Laplace transforms of the two expressions. Participants express differing levels of certainty and propose various methods for solving the problems.

Contextual Notes

Participants have not provided complete solutions or shown their work, leading to uncertainty in the discussion. The application of the second shift theorem and the cosine identity has been mentioned but not fully explored.

gsan
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what's the answer for laplace transform of the questions below?

1. cos(4t-1)u(t-1)
2. cos4(t-1)u(t-1)

I want to compare the difference between these two answer. Thanks!
 
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gsan, you've been told before that we can not help you until you first show us your effort.
 
Gokul43201 said:
gsan, you've been told before that we can not help you until you first show us your effort.

e^-s/(s^2 + 4^2) is the answer for i. or ii. ?
 
Your answer is the answer for question i. This is because when we refer to the second shift theorem in laplace transform, we can see that the value of 'd' must be the same. In this question, d = 1. Then from there, we can do the laplace transform. For the question ii, I myself not very sure.
Please correct me if I'm wrong. Thank you!
 
For part ii you need to use the idenity for cos(A-B)

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
 

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