# Thread: [SOLVED] inverse Laplace transforms

1. ## [SOLVED] inverse Laplace transforms

Hi all.

I am doing some study for exams and have become completely stuck on Laplace transforms, mainly inverse Laplace transforms.

These are the three that I am having trouble with:

a) 1/(s^2 -2s-15)

b) e^-2s / (s+4)

c) 1/(s^2 +9)

any help would be great

thanks

2. Originally Posted by hellhound
Hi all.

I am doing some study for exams and have become completely stuck on Laplace transforms, mainly inverse Laplace transforms.

These are the three that I am having trouble with:

a) 1/(s^2 -2s-15)

b) e^-2s / (s+4)

c) 1/(s^2 +9)

any help would be great

thanks
a) Factorise the denominator, perform a partial fraction decomposition and use tables to recognise standard forms.

b) You're expected to know the 'second shift theorem': $LT[f(t)] = F(s)$ then $LT[u(t - a) f(t - a)] = e^{-as} F(s)$. In your case $F(s)$ is a standard form.

c) You have $\frac{1}{3} \, \frac{3}{s^2 + 3^2}$. Use tables to recognise a standard form.

3. wow thank you. I dont know why I didn't see those before, I've done heaps of these. Anyway thank you again.