What is the equation for the length of a falling chain through a hole?

[kraigandrews]

Homework Statement

A flexible chain of mass M and length L lies on a frictionless table, with a very short portion of its length L0 hanging through a hole. Initially the chain is at rest. Find a general equation for y(t), the length of chain through the hole, as a function of time.
(Hint: Use conservation of energy. The answer has the form y(t) = A eγt+ B e−γt where γ is a constant.)
Calculate the time when 1/2 of the chain has gone through the hole.
Data: M = 0.7 kg; L = 3.0 m; L0 = 0.5 m.

Homework Equations

E=U(y)+.5m(dy/dt)^2
dm=M/L

The Attempt at a Solution

U(y)=integral of(-gydm)
dm=M/L
then integral of(-g(M/L)ydm)=(-Mg/(2L))(y^2)=U(y)

then i plug into E(which is constant by conversation of energy)=U(y)+.5M(dy/dt)^2

don't know where to go from there.
thanks.

 

[RTW69]

Google "sliding chain brown university"

 

[kraigandrews]

Thank you