I am deriving the transfer function of the circuit below:

I have determined it to be 1/[(s^2*L*C2)+(C2/C1)+1]. I have values for the elements as follows: C1 = 0.1 F, C2 = 0.01F, L = 0.5H. When I substitute these values in the transfer function, I have the expression

T = 200/(s^2 + 220). I do not know how to simplify it so that I would be able to take the inverse Laplace and convert it to time domain; been trying all day long now. Here is what I have:

Please share any suggestions. Thank you.