Find inverse laplace transform for x(s) = (2)/(s(s+1)^2)
1 answer:
Answer:
x(t)=
Step-by-step explanation:
The function x(s) = (2)/(s(s+1)^2) can be expressed as partial fractions:
X(s)=
2=A·(s+1)²+B·s·(s+1)+C·s
2=A·(s²+2s+1)+B·(s²+s)+C·s
2=A·s²+2sA+A+B·s²+Bs+C·s
2=s²(A+B)+s(2A+B+C)+A
So we can find the values of A, B and C by solving these equations:
A+B=0 ⇒ 2+B=0 ⇒ B= -2
2A+B+C=0 ⇒ 2·2+(-2)+C=0 ⇒ C= -2
A=2
So X(s) is expressed as:
X(s)=
Using the inverse laplace transform tables we obtain x(t):
ℒ⁻¹{X(s)}=ℒ⁻¹{}
ℒ⁻¹{X(s)}=ℒ⁻¹{}+ℒ⁻¹{}+ℒ⁻¹{}
x(t)=
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