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Chapter 7: Q9RP (page 415)

In Problems 3-10, determine the Laplace transform of the given function.t2u(t-4)

Short Answer

Expert verified

Therefore, the solution is.L{t2u(t-4)}=e-4s(2s3+8s2+16s)

Step by step solution

01

Given Information

The given function value ist2u(t-4)

02

Determining the Laplace transform

Using the following Laplace transform property, to find the Laplace of given integral:

L{f(t)u(t-a)}=eatL{f(t+a)}

Let. f(t)=t2On applying linearity of Laplace and we get:

L{t2u(t-4)}=e-4sL{f(t+4)}=e-4sL{(t+4)2}=e-4sL{t2+8t+16}=e4s(L{t2}+8L{t}+16L{1})

Simplify further as follows:

L{t2u(t-4)}=e-4s2!s3+81!s2+161s=e-4s2s3+8s2+16s

ThereforeL{t2u(t-4)}=e-4s2s3+8s2+16s

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