# Find the inverse Laplace transform?

1. Aug 8, 2013

### Success

1. The problem statement, all variables and given/known data
Find the inverse Laplace transform of F(s)=(8s^2-4s+12)/(s(s^2+4)).

2. Relevant equations
A/s+(Bs+C)/(s^2+4)
8s^2-4s+12=A(s^2+4)+(Bs+C)(s)=As^2+4A+Bs^2+Cs=s^2(A+B)+Cs+4A
8=A+B
C=-4
A=3
B=5
L^-1 (3/s)+L^-1 ((5s-4)/(s^2+4))
=3+ (Now I'm stucked.)

3. The attempt at a solution
The answer is f(t)=3-2 sin 2t+5 cos 2t.

2. Aug 8, 2013

### pasmith

$$\frac{5s - 4}{s^2 + 4} = 5\frac{s}{s^2 + 4} - 2\frac{2}{s^2 + 4}$$

Hopefully you should recognise the two terms on the right hand side as being Laplace transforms.

3. Aug 9, 2013

### Success

Yes, I did. Thank you.