A rope and a frictionless table

[davesface]

Homework Statement

A rope of mass M and length L lies on a frictionless table, with a short portion L₀ hanging through a hole. Initially the rope is at rest. Evaluate A and B so that the initial conditions are satisfied.

The Attempt at a Solution

Ok, so I understand the problem and have gotten the final 2 equations (according to my book):
yAe^yt-yBe^-yt=0
L₀=Ae^yt+Be^-yt

It looks like, according to the first equation, Be^-yt=Ae^yt. Plugging this into the second equation, L₀=2Ae^yt and L₀=2Be^-yt. This seems intuitively wrong, but I'm not sure exactly why. Any thoughts?

 

[davesface]

Bump. All I need is some confirmation, or a way to confirm, that I have the correct equations.