Laplace transformation problem

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jamshaid
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Homework Statement



L{4u(t-ர)cos2t}

Homework Equations



I have used UNIT STEP FUNCTION but could not get the result

The Attempt at a Solution

 
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L{4u(t-ர)cos2t
f(t) = cos2t
F(s) = s/ s^2+4
therefore

4s e^-ர(cosர + sinர)/s^2 +4 Ans
________________________________
that is my work
 
jamshaid said:
L{4u(t-ர)cos2t
f(t) = cos2t
F(s) = s/ s^2+4
therefore

4s e^-ர(cosர + sinர)/s^2 +4 Ans
________________________________
that is my work

Where is the factor the of [itex]4e^{-\tau}(\sin\tau+\cos\tau)[/itex] coming from? What rule are you trying to apply here?
 
here is my solve, if I have done correctly.
laplace.gif
 
Please expert help me.
 
jamshaid said:
here is my solve, if I have done correctly.
View attachment 28107

It looks good to me (although you have a very strange way of writing [itex]\pi[/itex]). On a side note, since trig functions are [itex]2\pi[/itex] periodic, you should have immediately recognized that [itex]\cos(2t+2\pi)=\cos(2t)[/itex] without appealing to a trig identity.
 
here is my final Answer
4e^(-as) s/(s^(2) + 4)

what do you think...
 
vela said:
The variable a shouldn't be in the final answer.

can you giving me some hints?