This is a difficult question. There isn't a simple equation  that will provide the answer.  You neglected friction.
You need to know the spring constant so you know how the opposing force increases as a function of distance.  Knowing the force at the end of stroke is not enough.  Now you need to know the the pushing forces.  You need to know how pressure increases as a function of time or flow.  This is very non linear because the flow will decrease as pressure increases.  On top of that the bulk modulus of air changes as a function of pressure.  This makes the the calculation even harder.  See the thread on the simulation software.  Your problem is not a simple one as it requires solving a system of non linear differential equations.  So how good is your math?  It is easier just to try it.