Since the question states it is an ideal diode, I don't think this would ever be in a lab! It probably assumes that the battery - terminal is the reference point. Paper exercise only.The voltage source sucks. it's not [latex]12sin(\omega t)[/latex]). We might think of it as 12 V RMS which changes the problem. That's the only 12 that makes sense/ But, in the lab you probably font have a meter that would read 12 for that source -- Not enough frequency response.
Where is the reference? Vo relative to what?
No, it is not correct.