I need a little help with figuring out this problem. I understand most of it but the main part I don't understand is:
The signal $h''(t)+2*h'(t)+2*h(t)$ is of finite duration.
In the problem we are supposed to be find $H(s)$, we know it is a rational, causal, stable LTI system. With hints from the teacher I've gotten $H(s)=A*s/p(s)$. Now he said that figuring out this part will allow us to find $p(s)$, but I'm not sure on how. I guess the real part I'm confused about is what it means to be of finite duration.
Thank you in advance,
EDIT1: The other hints to finding $H(s)$
$H(1)=0.2$ (Will allow me to find A)
When input is unit step $U(t)$ the output is absolutely integrable ($H(s)=(s^n)*q(s)/p(s):n>0$)
When input is ramp $t*U(t)$ the output is not absolutely integrable($n=1$)
$H(s)$ has exactly one zero at infinity.($q(s)=1$)