Find the Laplace transform L{u_3(t)(t^2-5t+6)} a) F(s)=e^(-3s)(2/s^4-5/s^3+6/s^2)

generals336 2020-11-02 Answered

Find the Laplace transform L{u3(t)(t25t+6)}
a)F(s)=e3s(2s45s3+6s2)
b)F(s)=e3s(2s35s2+6s)
c)F(s)=e3s2+ss4
d)F(s)=e3s2+ss3
e)F(s)=e3s211s+30s2s3

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Expert Answer

Mitchel Aguirre
Answered 2020-11-03 Author has 94 answers
Step 1
According to the given information, it is required to determine the laplace transform of the given function.
L{u3(t)(t25t+6)}
Step 2
Use the below formula to find the laplace transform.
L(uc(t)g(t))=ecsL(g(t+c))
L(uc(t))=ecss
Step 3
Solving further to get:
L(u3(t)(t25t+6))=L(u3(t)t2)5L(u3(t)t)+6L(u3(t))
=e3sL((t+3)2)5e3sL(t+3)+6e3ss
=e3s[2s3+6s2+9s]5e3s[1s2+3s]+6e3ss
=e3s[2s3+6s2+9s5s215s+6s]
=e3s[2s3+1s2]
L(u3(t)(t25t+6))=e3s[2+ss3]
Step 4
Therefore, the correct option is (D).
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