Hello, I am having trouble transforming this circuit to s-domain using Laplace Transformation and then transforming back. It would be great if I could get some help in a step by step manner. I have attached my workings as well but didn't get the answer correct. Question is in attachment. My workings are as follows:

 

voltage divider ...
\({V_o=V_i*Z_2/(Z_1+Z_2)}\)

 

Ah, thanks for spotting the mistake. I finally solved it. Thank you!

 

Even leaving that error aside, you got a wrong answer. Look at the units on your final result -- they don't work out.

If you are taking the ratio of the two impedances, each of which has a resistance in the numerator, how is it that the ratio has BOTH resistances in the numerator?

Always, always, ALWAYS track your units.