Laplace transform of cos(4t-1)u(t-1) and cos⁴(t-1)u(t-1)

[gsan]

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!

 

[Gokul43201]

gsan, you've been told before that we can not help you until you first show us your effort.

 

[gsan]

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. ?

 

[lightgreen]

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!

 

[Tareth]

For part ii you need to use the idenity for cos(A-B)

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