Equations of motion for a dual mass-spring-damper

[invariant99]

Homework Statement

We have been given the following mass-spring-damper diagram, and are asked to derive the equations of motion. The positions of the two masses are given as q1 and q2.

The Attempt at a Solution

I began by drawing free-body diagrams for each mass.

Then I set up the equations using F_net = mq'' = sum of the forces acting on the mass.

How does that look? I'm not very experienced at these, and I'm concerned that I've written some of the expressions incorrectly, and that I have some of the signs wrong as well. Thank you.

 

[haruspex]

Think again about the extension of the rightmost spring, and the direction of the force from the rightmost damper.