Find the inverse laplace transform of the function Y(s)=e−ss(2s−1)

boitshupoO

boitshupoO

Answered

2020-11-05

Find the inverse laplace transform of the function
Y(s)=ess(2s1)

Answer & Explanation

unett

unett

Expert

2020-11-06Added 119 answers

Step 1
The Laplace transform is given Y(s)=ess(2s1)
Convert the laplace transform into partial derivative ,
1s(2s1)=As+B2s1
1=A(2s1)+B(s)
1=2AsA+Bs
1=s(2A+B)A
Compare the coefficient of terms,
A=1
2A+B=02
Step 2 Substitute value of A in equation 2,
2(1)+B=0
B=2
The value of A is -1 and B is 2.
The expression is written as,
1s(2s1)=1s+22s1
=1s+1(s12
For finding the inverse Laplace transform , use theorem below.
L1[esTF(s)]=f(tT)u(tT)
Step 3
Applying the theorem , the given Laplace transform is written as,
L1[es(1s+1(s12]=(e(t212)1)u(t1)
The inverse Laplace transform of the function Y(s)=ess(2s1) is , (e(t212)1)u(t1)

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