Find the laplace transform of the following: Change of Scale text{If } Lleft{f(t)right}=frac{s^2-s+1}{(2s+1)^2(s-2)} text{ , find } Lleft{f(2t)right}

Harlen Pritchard 2020-12-29 Answered
Find the laplace transform of the following:
Change of Scale
If L{f(t)}=s2s+1(2s+1)2(s2) , find L{f(2t)}
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Expert Answer

brawnyN
Answered 2020-12-30 Author has 91 answers
Step 1
According to change of scale property in Laplace transform
If L{f(t)}=F(s) then
L{f(at)}=1aF(sa)
Given that
L{f(t)}=s2s+1(2s+1)2(s2)
Step 2
Using the change scale property, here a=2 , we get
L{f(2t)}=12(s2)2s2+1(2s2+1)2(s21)
=12×s24s2+1(s+1)2(s22)
=12×s22s+44(s+1)2(s2)2
=14s22s+4(s+1)2(s2)
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