Invert the following system to the time domain using partial fraction. f(s)=frac(6)(s^2(s+2)(s+4))

Jason Farmer 2021-09-15 Answered

Invert the following system to the time domain using partial fraction
f(s)=6s2(s+2)(s+4)

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Expert Answer

Faiza Fuller
Answered 2021-09-16 Author has 108 answers

Step 1
By using partial fraction method and the table of Laplace transform we solve the given problem as follows:
Step 2
f(s)=6s2(s+2)(s+4) By using partial fraction
6s2(s+2)(s+4)=As+Bs2+Cs+2+Ds+4
6=A(s3+6s2+8s)+B(s2+6s+8)+C(s3+4s2)+D(s2+2s2)
6=(A+C+D)s3+(6A+B+4C+2D)s2+(8A+6B)s+8B
A+C+D=0,6A+B+4C+2D=0
8A+6B=0,8B=6B=34
on solving thus we get
A=916,B=34,C=34,D=316
6s2(s+2)(s+4)=916s+34s2+34s+2+316s+4
Now apply inverse laplace we get
L1{6s2(s+2)(s+4)}=916L1{1s}+34L1{1s2}+34L1{1s+2}316L1{1s+4}
f(t)=916+34t+34e2t316e4t

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