Here is what I am thinking so far:
At V2 the system is at equilibrium, so p2 equals p_atm since the spring exerts no force.
So p2 is known.
I now need p1. I am not sure where to go from here. I have V1, V2 and p2.
I think that spring-force/area is part of p1...
Can someone give me a hint? Just a hint....