Obtain the Laplace Transform of Lleft{t^3-t^2+4tright} Lleft{3e^{4t}-e^{-2t}right}

e1s2kat26 2021-02-02 Answered
Obtain the Laplace Transform of
L{t3t2+4t}
L{3e4te2t}
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Expert Answer

irwchh
Answered 2021-02-03 Author has 102 answers
Step 1
Question (1) −
Let the given function be y −
y=L{t3t2+4t}
Using laplace transformation formula −
L[tn]=(n!)sn+1
then,
y=F(s)=L{t3t2+4t}
F(s)=3!s3+12!s2+1+41!s1+1
F(s)=321s421s3+41s2
F(s)=6s42s3+4s2
Step 2
Question (2) −
Given function −
F(s)=L{3e4te2t}
Using Laplace transformation formula −
L[eat]=1sa
F(s)=3[1(s4)][1s(2)]
F(s)=3(s4)1(s+2)
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