# physics problem solving with differential equations

Hi, I'm new in this community.

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: http://img805.imageshack.us/img805/70...

I have two masses (1/3*m the first, 2/3*m 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) -2/3*m*g+T=2/3*m*d2/dt2_y
2) -1/3m*g+Sy=1/3*m*d2/dt2_j
3) Sx=1/3*m*d2/dt2_x
4) abs(T)=sqrt(Sx^2+Sy^2)
5) 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) T force sustaining the second mass 2) Sx x-component of force sustaining the first mass 3) Sy y-component of force sustaining the first mass 4) y(t) position of the second mass 5) x(t) x-position of the first mass 6) 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!!