# Error in asnwer? Finding the transfer function of a system

1. Dec 8, 2011

### toofle

1. The problem statement, all variables and given/known data
Find the transfer function and the impulse response for the system:

y'(t) + y(t) = x(t)

x = {1 if 0<=t<1,0 1<=t}

2. Relevant equations

d/dt y(t) ~ sY(s) -y(0)

3. The attempt at a solution

I transform into the laplace-domain:
sY(s) - y(0) + Y(s) = X(s)
Y(s)(s+1) - 1 = X(s)

Here I can't get H(s)=Y(s)/X(s) beacuse of y(0)=1 and not 0.

The answer is H(s) = 1/(s+1) . then it is easy to get the impulse response by backtransforming to the timedomain so thats no problem.
But there must be an error in the answer or problem statement right?

2. Dec 8, 2011

### Staff: Mentor

You have a mistake on the right side, in that you have not put in the function given as x(t).

x(t) = H(t) - H(t - 1), where H is the Heaviside function.

So $X(s) = \mathcal{L}(x(t)) = e^{-0} - e^{-s} = 1 - e^{-s}$
Now, substitute for X(s) above, and see how it come out.