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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?
Since the question states it is an ideal diode
Huh. Clever clogs...Check out the "Ideal diode controllers" from Linear Technology.
No, it is not correct.