Laplace Transform, transfer function

[sandy.bridge]

Homework Statement

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.

 

[vela]

Is the delta function bounded?

 

[sandy.bridge]

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

 

[vela]

What's your definition of bounded?