mechanical "strange oscillator" problem

Hi all

I have a mechanical problem, but i don't a have a mathematical skill to solve it, I hope that someone could help me👃

in first, see simplified drawing:

1. 

    in yellow box , is a winch

2.  wire betwen winch and pulley (steel cable,the length is low, the elongation can be a constant, maybe )
3. pulley connected to ground with spring
4. wire betwen mechanical elbow and pulley (steel cable,the length is high, i need to use Hooke's law for evaluate elongation, and correct this to calculate good Lw parameter)
   
5. mechanical elbow
6. mechanical load mg ( for simplify what happens in mechanicel elbow, we consider un traction forces on wire node at elbow)

At t0 system at rest  : it is as if the spring is a bar

At t1, the winch pulls to make an ordered value for alpha

Find Lw according to alpha angle, the object of the game is that the winch gives a Lw length which allows to maintain alpha angle according to the instructions (angle ordered)

What i feel : variable is a function f(x)=k(x) , here is a differential equation

I do not know, neither to pose this problem nor to solve it😓

this is above my skills, but it's very interesting

Anyone can help me ? I would like to learn how to solve this