As shown in the figure, a small ball with gravity g is placed vertically on a smooth big ring with radius r, and the stiffness coefficient is k, which is self-adjusting As shown in the figure, a small ring B with weight of G is set on a smooth large ring with radius of R placed vertically, a stiffness coefficient of K and a natural length of L (L)

As shown in the figure, a small ball with gravity g is placed vertically on a smooth big ring with radius r, and the stiffness coefficient is k, which is self-adjusting As shown in the figure, a small ring B with weight of G is set on a smooth large ring with radius of R placed vertically, a stiffness coefficient of K and a natural length of L (L)

As shown in the figure, for the force analysis of the ball, there are g, F, N, and let the angle between the spring and the vertical direction be θ
Because △ BAC ∽ CDE
So CD = Ge
That is g = n
And because of the balance of the three forces
So the sum of the component forces of G and N in the CE direction is equal to F
That is G &; Cos θ n &; Cos θ = F
2G &; Cos θ = f
Count the f-bomb again
Because delta ABC is an isosceles triangle
Easy to get BC = 2R &; Cos θ
So the spring variation △ L = 2R &; Cos θ - L
F bullet = K &; (2R &; Cos θ - L)
So 2G &; Cos θ = K &; (2R &; Cos θ - L)
2G•cosθ=2Rk•cosθ-kL
cosθ=kL/（2Rk-2G）