text{Find the Laplace transform } F(s)=Lleft{f(t)right} text{of the function } f(t)=6+sin(3t) text{defined on the interval } tgeq0

remolatg 2021-02-16 Answered
Find the Laplace transform  F(s)=L{f(t)} of the function  f(t)=6+sin(3t) defined on the interval  t0
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Expert Answer

Laaibah Pitt
Answered 2021-02-17 Author has 98 answers
Step 1
From the given statement, the function is  f(t)=6+sin(3t)
Step 2
To find the Laplace transform of the function as follows.
L(f(t))=L(6+sin(3t))
=L(6)+L(sin(3t))
Known fact: 
L(1)=1s
L(sin(ωt))=ωs2+ω2
Therefore, 
L(6)+L(sin(3t))=6L(1)+L(sin(3t))
=6(1s)+3s2+32
=6s+3s2+9
=6s2+3s+54s3+9s
Thus, the Laplace transform of the function is 6s2+3s+54s3+9s
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(ii) The team wants to transport this artifact to a museum. They know that vibrations from the truck that moves it result in vibrations of the system. They hope to avoid circular frequencies to which the system response has the greatest amplitude. What frequency should they avoid?

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