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 Homework Statement:
 A mass is attached to an unstretched spring, vertically, what displacement does it make finding displacement using forces (F_g=F_s) gives half the answer from energy method (U_g=U_s), what mistake am I making?
 Relevant Equations:

mg=kx
mgx=0.5kx^2
The spring is first relaxed at its lower end h_1, thats when we attached mass m to itand let it fall freely and come to rest. Now by Force analysis we can show that in final position of mass the forces of gravity and restoring force from spring are balanced. i.e. F_g=F_s which yields
x=mg/k.
Solving the same problem with energy argument; initial potential energy in mass in mgh_1 and final would be mgh_2, meanwhile the initial potential energy in spring is zero and finally it would be0.5kx^2.
Solving by enrgy, K_i + U_g_i + U_s_i = K_f + U_g_f + U_s_f
=> 0 + mgh_1 + 0 = 0 + mgh_2 + 0.5k(h_1h_2)^2
=> mg(h_1h_2) = 0.5k(h_1h_2)^2
=> mgx = 0.5kx^2
=> x = 2mg/k
which is double the displacement we found from force method... what is going wrong here
x=mg/k.
Solving the same problem with energy argument; initial potential energy in mass in mgh_1 and final would be mgh_2, meanwhile the initial potential energy in spring is zero and finally it would be0.5kx^2.
Solving by enrgy, K_i + U_g_i + U_s_i = K_f + U_g_f + U_s_f
=> 0 + mgh_1 + 0 = 0 + mgh_2 + 0.5k(h_1h_2)^2
=> mg(h_1h_2) = 0.5k(h_1h_2)^2
=> mgx = 0.5kx^2
=> x = 2mg/k
which is double the displacement we found from force method... what is going wrong here