Solve for the Inverse Laplace Transformations. Show the solution. F(s)=frac{6}{(s^2+4s+20)^2}

Carol Gates 2020-11-26 Answered
Solve for the Inverse Laplace Transformations. Show the solution.
F(s)=6(s2+4s+20)2
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Expert Answer

saiyansruleA
Answered 2020-11-27 Author has 110 answers
Step 1
Given,
F(s)=6(s2+4s+20)2
Find the inverse Laplace Transform of the given function.
Step 2
Now
F(s)=6(s2+4s+20)2
=6((s2+4s+4)+16)2
=6((s+2)2+42)2
Taking inverse Laplace Transform of both sides,
L1[F(s)]=L1[6((s+2)2+42)2]
f(t)=L1[6((s+2)2+42)2]
Step 3 Use the formula such that
L1[F(s)]=f(t)
L1[F(sa)]=eatf(t)
Then,
f(t)=L1[6((s+2)2+42)2]
=e2tL1[6(s2+42)2]
Again the formula,
L1[2a3(s2+a2)2]=sin(at)atcos(at)
Step 4
So,
f(t)=e2tL1[6(s2+42)2]
=343e2tL1[243(s2+42)2]
=364e2t[sin(4t)4tcos(4t)]
Hence, =364e2t[sin(4t)4tcos(4t)]
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