Engineering Board Exam Reviewer · Laplace Transforms · hard

Find the Laplace transform of f(t)=t t.

1. 2 s≤ft(s2 + 1 )2
2. s≤ft(s2 + 1 )2
3. s2 - 1≤ft(s2 + 1 )2
4. 2 ss2 + 1

Answer

A. 2 s≤ft(s2 + 1 )2

Solution

Multiplication by t corresponds to -d/ds. With F(s)=1/s2+1: Lt t=-F'(s)=2s/(s2+1)2.

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