A function f (t) that has the given Laplace transform F (s).

Rui Baldwin 2020-10-21 Answered
A function f (t) that has the given Laplace transform F (s).
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Expert Answer

Cullen
Answered 2020-10-22 Author has 89 answers
Given:
Laplace transform F (s) of a function f (t) defined on an interval [0,)F(s)=2s(s2+16)
Calculation:
Given,
F(s)=2s(s2+16)
Partial fraction decomposition,
F(s)=2s(s2+16)
Approach:
The
=As+Bs+Cs2+16
2=A(s2+16)+s(Bs+C)
=s2(A+B)+Cs+16A
Compare the Left hand side and Right hand side,
A=18
B=18
C=0
Substitute -
F(s)=18ss8(s2+16)
Laplace transform,
L[f]=0estf(t)dt
=F(s)
=2s(s2+16)
=18ss8(s2+16)
Inverse Laplace transform-
L1[F](t)=L1[2s(s2+16)]
=L1[18ss8(s2+16)]
=18L1[1s]18L1[ss2+42]
=1818cos(4t)
L1[F](t)=18(1cos(4t))
=f(t)
Conclusion:
Hence, a function f (t) that has the given Laplace transform
F(s)=2s(s2+16)is18(1cos(4t)).
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