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 (1/3m 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) -2/3mg+T=2/3md2/dt2_y 2) -1/3mg+Sy=1/3md2/dt2_j 3) Sx=1/3m*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!!