I am jist trying to understand the thresholds involved in pogo oscillation. I'm not sure where to start. But I will give a guess.
As rocket size increases the tension exterted on rocket walls increases due to pressure diameter relation. If we assume 1000 tons of fuel pressing against a 1m2 tank control valve that's 1000 ton per sq m. If the rocket doubles in size, then its fuel doubles and tank surface area increases as the 2/3rds power due to the pi d relation between pi and diameter. So we get an increase to the 1/3 power in area per force. Furthermore the rocket is accelerating at roughly g so the pressure is doubled.
So we have 20 mpa of force on this valve. Assume that there is a 1% error in the fuel flow and the resulting shockwave moves at 25 meters per second up the 25m tank. This causes a 1% amplification every second. This is a double exponential function due to the flow error affecting thrust.
After 100 seconds the total pressure has increased 4x growing at 2% per second. After 200 seconds the pressure has increased 32x growing at 4% for seconds. This is now a 640 mpa force on steel with a 200mpa strength.
So it looks like something the size of apollo is barely tractable in engineering terms.