How to Determine Equations of Motion for a String with a Mass at the Boundary?

[wingnut290]

Two strings with identical mass densities and tensions are attached in the middle by a mass m, an incident pulse is traveling from the left, I need to find the equations of motion for the string on the right.

The pulse is y=Aexp[i(kx-wt)]

work so far:
the mass will act as a moving boundary condition because of the vertical component of the string. So i have m(d^2y/dt^2)=-T dy/dt, i am having trouble in where to go next, can anyone help?

 

[Meir Achuz]

Draw an old fashioned FBD of the forces on the mass.
This will give you a BC relating dy/dx for each string.