(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

We are to use the convolution theorem to compute the inverse Laplace transform of the function

[tex]L=\frac{1}{s^2 + 16}e^{-2s}[/tex]

2. Relevant equations

Using a table, I find that [tex]L^{-1}[\frac{1}{s^2 + 16}] = \frac{1}{4}sin(4t)[/tex]

and

[tex]L^{-1}[e^{-2s}] = \delta(t-2)[/tex]

3. The attempt at a solution

Using the convolution theorem,

[tex]L^{-1}[\frac{1}{s^2 + 16}e^{-2s}] = \int_{0}^{t} \frac{1}{4}sin(4\tau)\delta(\tau-2)d\tau[/tex]

My question is, how do I evaluate that integral? I know that when you have the delta function, e.g. [tex]\delta(t-2)[/tex] times a function f(x), and the limits are negative infinity to infinity, it is just f(2). But what if the limits are 0 to t?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Calculating Inverse Laplace Using Convolutions

**Physics Forums | Science Articles, Homework Help, Discussion**