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Laplace Transforms 
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#1
Jul2311, 06:35 AM

P: 25

Ok, so I have uploaded/attached the question and the solution. I just need help understanding the solution please. I understand how to calculate the initial inverse transform, but I included it as the reference to the second part of the question regarding the y'' + 4y' = H(t3)
Can someone please explain the full steps to invert the laplace transform Y to f, like the solution shows in the last step? I have got to the following point, but I think I may be forgetting some Laplace Transform identities needed to make my life easier? I can split the equation into parts where I recognise a few Laplace Transforms but not sure about the rest, cheers... Y(s) = (1/s).e^{3s}.[1/(s^{2}+2^{2})] + [s/(s^{2}+2^{2})]  [2/s^{2}+2^{2}] I recognise a few inverse laplace transforms there but without adding my confusion to the mess can someone please clarify how they got the answer? many thanks in advance. hopefully I didnt make this post toooo convoluted with my thoughts! 


#2
Jul2311, 11:48 AM

P: 436

U are confused because they have skipped a step.
I bet u must have recognised this part: [s/(s2+22)]  [2/s2+22] For this part: (1/s).e3s.[1/(s2+22)] : (1/(s(s²+2²))) =(1/4)((1/s)(s/(s²+2²))) =(1/4)(H(t3)cos(2(t3))) 


#3
Jul2311, 12:27 PM

P: 25

How did you get rid of the e^(3s) ? thanks for helping. 


#4
Jul2311, 11:01 PM

P: 436

Laplace Transforms
You are most welcome adam :)
[tex]L^{1}(e^{cs}F(s))=f(tc)[/tex] Given : [tex] L^{1}(F(s))=f(t) [/tex] 


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