Find the inverse laplace trans. displaystyle{F}{left({s}right)}=frac{10}{{{s}{left({s}^{2}+{9}right)}}}

tricotasu 2021-02-19 Answered
Find the inverse laplace trans.
F(s)=10s(s2+9)
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Expert Answer

avortarF
Answered 2021-02-20 Author has 113 answers
Step 1
Given,
F(s)=10s(s2+9)
Find the inverse Laplace transform of this function.
Step 2
F(s)=10s(s2+9)
=109s10s9(s2+9)
Taking inverse Laplace transform of both sides,
L1[F(s)]=L1[109s10s9(s2+9)]
Then, f(t)=L1[109s]L1[10s9(s2+9)]
=109L1[1s]109L1[ss2+9]
=109L1[1s]109L1[ss2+32]
Step 3
Use the formula such that
L1[1s]=t
L1[ss2+a2]=cos(at)
f(t)=109t109cos(3t)
=109[tcos(3t)]
Step 4
Hence,
f(t)=109[tcos(3t)]
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