use properties of the Laplace transform and the table of Laplace transforms to determine L[f] f(t)=int_0^t (t-w)cos(2w)dw

Kyran Hudson 2021-03-02 Answered
use properties of the Laplace transform and the table of Laplace transforms to determine L[f] f(t)=0t(tw)cos(2w)dw
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Expert Answer

Bertha Stark
Answered 2021-03-03 Author has 96 answers
Step 1
We have given,
f(t)=0t(tw)cos(2w)dw
This can be written as,
f(t)=0ttcos(2w)dw0twcos(2w)dw
We have to find,
L{f(t)}=L{0ttcos(2w)dw}L{0twcos(2w)dw}
Step 2
We know that,
L{f(t)}=F(s)
L{0tf(u)du}=1sF(s)
So L{0ttcos(2w)dw}=ts(ss2+4)
L{0ttcos(2w)dw}=ts2+4
And
L{0twcos(2w)dw}=1s(s2+4(s2+4)2)
On plugging these values in our equation , we get,
L{f(t)}=L{0ttcos(2w)dw}L{0twcos(2w)dw}
L{f(t)}=(ts2+4)+1s(s2+4(s2+4)2)

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