Engineering Board Exam Reviewer · Inverse Laplace Transforms · medium

Find the inverse Laplace transform of F(s)=2s+5/s2+4s+8.

1. e- 2 t 2 t + 2 e- 2 t 2 t
2. e2 t 2 t2 + 2 e2 t 2 t
3. e- 2 t 2 t2 + 2 e- 2 t 2 t
4. 5 e- 2 t 2 t2 + 2 e- 2 t 2 t

Answer

C. e- 2 t 2 t2 + 2 e- 2 t 2 t

Solution

s2+4s+8=(s+2)2+4 and 2s+5=2(s+2)+1. So F=2·s+2/(s+2)2+4+ 12·2/(s+2)2+4, giving f(t)=2e-2t 2t+ 12e-2t 2t.

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