determine a function f(t) that has the given Laplace transform F(s). F(s) = frac{3}{(s^2)}

Tyra 2020-12-28 Answered
determine a function f(t) that has the given Laplace transform F(s).
F(s)=3(s2)
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Expert Answer

Jaylen Fountain
Answered 2020-12-29 Author has 170 answers
Step 1
Given,
F(s)=3(s2)
Step 2
Formula:
(1)tn=L1{(n!)sn+1}
Constant Multiplication property:
(2)L1{aF(s)}=aL1{F(s)}
Step 3
Consider, F(s)=3(s2)
Apply Laplace inverse transform on both sides
L1{F(s)}=L1{3(s2)}
f(t)=L1{31(s2)}
f(t)=3L1{1(s2)}( Constant multiplication property )
f(t)=3L1{1!s1+1}
f(t)=3t1( Formula 1 )
f(t)=3t
Therefore, f(t)=3t that gives a Laplace transform F(s)=3(s2)
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