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I want to solve a physic problem which requires differential equation system solutions.

I don't know if my equations are correctly set. Any suggestion is good. My problem is described by this image:

I have two masses (1/3m the first, 2/3m the second) linked with a rope. The rope is free to slide around a nail (the big black point in the image). The image shows the starting condition: a man keeps the first mass stopped and so the rope is kept stretched by the second mass.

I search three functions describing the kinematics of two masses after the man will leave the fist mass: vertical movement of mass A y(t), vertical movement of mass B j(t), and horizontal movement of mass B x(t).

My Cartesian reference system is x-y system in the image.

I have to solve the following equations: 1)

  1. List item -2/3mg+T=2/3md2/dt2_y
  2. List item -1/3mg+Sy=1/3md2/dt2_j
  3. List item Sx=1/3m*d2/dt2_x
  4. List item abs(T)=sqrt(Sx^2+Sy^2)
  5. List item abs(y(t))=sqrt(x(t)^2+j(t)^2)

From the forth and the fifth equations I obtain two equations, so I have 5 equations in 5 unknowns. They are: 1. List item T force sustaining the second mass 2. List item Sx x-component of force sustaining the first mass 3. List item Sy y-component of force sustaining the first mass 4. List item y(t) position of the second mass 5. List item x(t) x-position of the first mass 6. List item j(t) y-position of the first mass

I hope my explanation is clear.

How can I obtain my solutions using Sage?

Thank you very much!!