A chain of length 3 feet has linear mass density of  0.2  pounds per foot.
The coefficient of friction between the chain and my desk is  0.5.  I hold
the chain on my desk with  2  feet hanging over the edge and let go.

(a)   Write down a differential equation, with initial conditions, that describes
the motion of the chain after I release it.  Let  y(t) be the length of the chain
(in feet) hanging over the edge of the desk at time  t  seconds after it is released.

(b)   Solve the differential equation you wrote down in (a) by converting it
to a system of two first order equations (reduction of order).  The answer to
this part of the problem should be a general solution to the differential equation.

(c)   Now solve the initial value problem you wrote down in part (a).

(d)   Find a solution to the differential equation you wrote down in part (a)
with the initial conditions  y(0) = 0  and  y'(0) = 0.

(e)   Does the solution you found in (d) describe the motion of the chain if
it placed on the table with no part hanging off the edge?  Why or why not?