I would have used an alternative explanation so here goes!
saturated 6 membered rings are basically unstrained, so the carbonyl in structure 1 should stretch like a normal ester (1735cm^-1).
The carbonyl of an ester is strengthened by the inductive withdrawal of the alcoholic O, but weakened by donation of the lone pair on the same O into the carbonyl pi* (you can draw resonance structures for both).
In structure 2 the lone pair is less able to donate into the carbonyl because it is delocalised into the neighbouring c=c pi* this would give compound 2 the highest stretching frequency 1769cm^-1.
For structure 3, the c=c bond is now in such a position that, rather than interacting with the lone pair on oxygen, it too can donate into the carbonyl pi* so structure 3 has 2 weakening effects and hence the lowest stretching frequency of 1720cm^-1.