Having trouble with this impedance problem

[mcah5]

The problem follows:
Suppose you have a massless dashpot having two moving parts 1 and 2 that can move relative to one another along the x direction, which is transverse to the string direction z. Friction is provided by a fluid that retards the relative motion of the two moving parts. The friction is such that the force needed to maintain relative velocity x_1 - x_2 between the two moving parts is Z_d*(x_1 - x_2), where Z_d is the impedance of the dashpot. The input (part 1) is connected to the end of a string of impedance Z_1 stretching from -infinity to 0. The output (part 2) is connected to a string of impedance Z_2 that extends to z = infinity. Show that a wave incident from the left experiences an impedance at z = 0 which is as if the impedances Z_d and Z_2 where connected in parallel.
I'm thinking:
The wave incident from -infinity will hit the dashpot and experience a force in the opposite direction of x_1 * Z_L, where Z_L is the "load" impedance we are trying to show is equal to Z_d*Z_2 / (Z_d + Z_2). This means that a force x_1 * Z_L is exerted on "part 1" of the dashpot. The second part of the dashpot experiences a force Z_2 * {x_2} on it. Therefore, the dashpot has a "tension" of x_1 * Z_L + Z_2 * x_2 and the two parts of the dashpot will be moving with relative velocity x_1 - x_2. So I have the equation x_1 * Z_L + Z_2 * x_2 = Z_d (x_1 - x_2)
Problem is that this doesn't get me to my desired answer of Z_L = Z_d*Z_2/(Z_d+Z_2). I was wondering what other information I need to solve the problem.
edit: I can't seem to get \\dot{x} to work. Please pretend all the x's have dots over them

 

[thermodynamicaldude]

I'm not sure, but if you say that the tension of the dashpot is Z_d*(x_1 - x_2), then this is the magnitude of the force the dashpot exerts on the strings. Using Newtons third law, the strings will exert an opposite and equal force on the dashpot. Thus, we would have Z_d*(x_1 - x_2) = Z_L*(x_1) and Z_d*(x_1 - x_2) = Z_2*(x_2). Using the 2nd eq., we can then express x2 in terms of x1 for the first equation, then divide by x1, and acquire the intended result. Somebody please correct me if I'm wrong. (Note, there should be dots on all the x's)