Hi,
Writing a little hard to read, if it was typed out it would be much easier to read.
However, a quick look, i have to wonder where you came up with the 2.8 from. If it is because the amplitude is 8, then shouldnt it be 2*2.8, or more exactly, 2*sqrt(8) ?
Also, another approach which might be a little interesting is to solve this circuit backwards. If Vo was the input and Vi was the output, you could easily solve it, right? By 'backwards' though i mean to solve the circuit 'forward' the way you normally would, then simply solve for the input rather than the output. Writing it forward you'll come out with the same equation as if you were solving for Vout, but then solve for Vin instead of Vout as the following will illustrate:
General form for the forward equation:
Vout=Vin*H(s)
So we just solve this for Vin:
Vin=Vout/H(s)
It's always good to have a second way to calculate something so that you can check your results.