# Inverse Laplace Transformation

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1. Apr 27, 2015

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1. The problem statement, all variables and given/known data

Solve the following:

$$\mathscr{L}_s^{-1} \left\{ \frac{s}{s^2-s+\frac{17}{4}} \right\}$$

2. Relevant equations

Table of Laplace Transforms.

3. The attempt at a solution

The solution is
$$f(t) = (1/4 )e^{t/2} (\sin(2 t)+4 \cos(2 t))$$

I know I need to break up $F(s)$ into more common Laplace transforms, but I'm not quite sure how to begin.

2. Apr 27, 2015

### LCKurtz

Hint: Begin by completing the square in the denominator.

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