Find the inverse laplace transforms for the following functions F(s)=frac{e^{-3s}}{s^2} F(s)=frac{2e^{-5s}}{s^2+4}

facas9 2021-02-13 Answered
Find the inverse laplace transforms for the following functions
F(s)=e3ss2
F(s)=2e5ss2+4
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Expert Answer

Ezra Herbert
Answered 2021-02-14 Author has 99 answers
Step 1
Given
the given functions are
F(s)=e3ss2
F(s)=2e5ss2+4
Apply formula L1{G(s)eas}=g(ta)u(ta)
Step 2
F(s)=e3ss2
L1(1s2)=t
Apply formula.
L1{(1s2)e3s}=(t3)u(t3)
Hence inverse Laplace transform of the function is F(t)=(t3)u(t3)
F(s)=2e5s(s2+4)
L1(2(s2+4))=2L1(1(s2+4))=2sin(2t)2=sin(2t)
Apply formula.
L1{(2s2+4)e5s}=sin[2(t5)]u(t5)=sin[2t10]u(t5)
Hence inverse Laplace transform of the function is F(t)=sin[2t10]u(t5)
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