Motion of the core

Assumptions:
I_P= V_in/R
Where R= 10KΩ
Inner Radius Of the Coil =R_i
Outer Radius Of the Coil = R_o
Ratio of Outer radius to the inner radius:
R_o /R_i= 2
Length of the primary winding(b) = 20mm
Length of Secondary Winding (m) = 10mm

V_Out = fI_p(N_pN_s μ₀bx/3mlog(R_o/R_i))(1-x²/2b²)

Graph