# Laplace Transform, transfer function

1. Feb 15, 2012

### sandy.bridge

1. The problem statement, all variables and given/known data
Given transfer function $H(s)=s^2+4$ and input $x(t)=sin(2t)$, find the ouput y(t) in time domain, and show whether bounded or unbounded.

Okay, so I know $L^{-1}[sin(2t)]=2/(s^2+4)=2/[(s+j2)(s-j2)]$

and that $Y(s)=H(s)X(s)=2$

Therefore, $y(t)=2\delta{(t)}$

However, I am a little bit confused as to how I should show if it is bounded or unbounded.

2. Feb 16, 2012

### vela

Staff Emeritus
Is the delta function bounded?

3. Feb 16, 2012

### sandy.bridge

I believe it is. However, this question seems rather simple considering the professor stated it was "tricky".

4. Feb 16, 2012

### vela

Staff Emeritus