Prove {F}{left({s}right)}=frac{1}{{{s}-{2}}} text{ then } f{{left({t}right)}} is a) {e}^{{{2}{t}}}{u}{left({t}right)} b) u(t+2) c) u(t-2) d) {e}^{{-{2}{t}}}{u}{left({t}right)}

Aneeka Hunt 2021-01-27 Answered
Prove F(s)=1s2  then  f(t) is
a) e2tu(t)
b) u(t+2)
c) u(t2)
d) e2tu(t)
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Expert Answer

Derrick
Answered 2021-01-28 Author has 94 answers
Step 1
Given F(s)=1s2
We have to find the f(t)
Use definition of inverse Laplace transform, which is given below
f(t)=L1{F(s)}(1)
Step 2
Take inverse Laplace transform of F(s)=1s2
Hence, L1{F}(s)=L1{1s2}(2)
From equation (1) and equation (2)
f(t)=L1{1s2}
=e2tu(t)
Therefore, f(t)=e2tu(t)
Hence, option (a) is correct.
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