# Solving DE using laplace

1. Nov 21, 2011

### abrandt

so im working on a problem and i have a question about the step function. lets say that a decaying force is f(t). with u (t-11)= {0 if t< 11, 1 if t>=11}. the function of the force is then
g(t)=[1-u(t-11)]* f(t)

or g(t)=f(t)-[u(t-11)*f(t)]

as i understand it. in order to do the laplace transform f(t) has to be in the form f(t-11) so:

g(t)= f(t) - u(t-11)*f(t-11+11)

from here how would i proceed. i assume that i can take the laplace of f(t) + the transform of [u(t-11)*f(t-11+11)] how would i find this second transform.

2. Nov 22, 2011

### I like Serena

The Laplace transform of g(t) is:
$$\mathcal{L}_t[g(t)](s) = \int_0^\infty g(t) e^{-st}dt=\int_0^{11} f(t) e^{-st}dt$$