Laplace Transform Question`

Response of an dampened system to a single square wave.

y'' + 4y = r(t); y(0) = 0; y0(0) = 0 :

where r(t) = 1 if 0 < a < t < b and 0 otherwise.

Find the condition on a and b such that the system is at rest when

t > b

I found the equation for this system, and it goes something like this

I change r(t)=H(t)=1/s

Then I let L(y(t))=F(s) Laplace Transformation

Then F(s)=1/s*(s^2+4) I manipulated this to get

1/4s -1/4 (s/(s^2+4)) then changing it back to in terms of t yields

1/4 -1/4 cos(2t)

So I don't know how to go about in finding out the conditions for a,b !!

Thanks in advance!