Find the inverse Laplace transforms of the functions given. Accurately sketch the time functions. a) F(s)=frac{3e^{-2s}}{s(s+3)} b) F(s)=frac{e^{-2s}}{s(s+1)} c) F(s)=frac{e^{-2s}-e^{-3s}}{2}

FizeauV 2021-02-04 Answered
Find the inverse Laplace transforms of the functions given. Accurately sketch the time functions.
a) F(s)=3e2ss(s+3)
b) F(s)=e2ss(s+1)
c) F(s)=e2se3s2
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Expert Answer

odgovoreh
Answered 2021-02-05 Author has 107 answers
Step 1
given that a) F(s)=3e2ss(s+3)
b) F(s)=e2ss(s+1)
find the inverse laplace transform of the above functions
Step 2
a)first lets find the inverse laplace transform of 3s(s+3) let it write interms of partial fractions
3s(s+3)=As+B(s+3)
3=A(s+3)+Bs
put s=0 then 3=3A,A=1
put s=3 then 3=3B,B=1
lets substitute A and B values
3s(s+3)=1s1(s+3)
L1[3s(s+3)]=L1[1s1(s+3)]
=1e3t
L1[3e2ss(s+3)]=(1e3(t2))u(t2)
Step 3
b) F(s)=e2ss(s+1)
First lets find the inverse laplace transform of 1s(s+1) for this lets write interms of partial fractions
1s(s+1)=As+B(s+1)
1=A(s+1)+Bs
put s=0 then 1=A,A=1
put s=1 then 1=B,B=1
1s(s+1)=1s+1(s+1)
L1[1s(s+1)]=L1[1s+1(s+1)]
=L1[1s]L1[1(s+1)]
=1et
next inverse laplace transform of e2ss(s+1) is (1e(t2))u(t2)
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