Whoops!
It's apparent from your Force_estimation sheet that you're using a "less than full functioned" Mathcad; it won't accept programming, and it probably won't do differential equation solving either.
The "old" mathcad would allow an iterative solution to be done, but Prime won't accept the structure when I type it in, which is why you can find ITR as a program which (I assume) didn't run for you either.
Going to have to think about this a bit.
You changed the table to reflect stroke; does the spring force increase or decrease as stroke goes from 0 mm to 2 mm?
PS: The lines where I put a fixed time into a function (AC_Factor and Fn) were temporary diagnostics (Making sure the function would evaluate to a reasonable answer.) Further along you can then use the function with a variable time to get the AC factor or the force at that time. (The goal is to solve this problem with time as a variable; two approaches--very small time steps (iteration) or solving the differential equation of motion (A = F/m)