Find inverse laplace transform. F(s)=\frac{1}{s(s^2+s+1)}

geduiwelh

geduiwelh

Answered question

2021-09-18

Find inverse laplace transform.
F(s)=1s(s2+s+1)

Answer & Explanation

komunidadO

komunidadO

Skilled2021-09-19Added 86 answers

Given:
F(s)=1s(s2+s+1)
Now, 1s(s2+s+1)=As+Bs+Cs2+s+1=A(s2+s+1)+(Bs+C)ss(s2+s+1)
Compairing with both sicly we get
1=As2+As+A+Bs2+Cs
=(A+B)s2+(A+C)s+A
Therefore. A=1
A+B=0
A+C=0
1+B=0
1+C=0
B=1
C=1
Therefore
1s(s2+s+1)=1ss+1s2+s+1
F(s)=1ss+1s2+212s+14+114
=1ss+1(s+12)2+34
=1ss+12+12(s+12)2+(32)2
=1ss+12(s+12)2+(32)2121(s+12)2+(32)2

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